total mechanical energy problem solving

StickMan Physics

Animated Physics Lessons

Mechanical Energy Problem Solutions

Mechanical energy problems and solutions.

See examples of mechanical energy problems involving kinetic energy, potential energy, and the conservation of energy. Check your work with ours.

1. How much gravitational potential energy do you have when you lift a 15 N object 10 meters off the ground?

2. How much gravitational potential energy is in a 20 kg mass when 0.6 meters above the ground?

3. How much gravitational potential energy does a 35 kg boulder have when 30 meters off the ground?

4. How many times greater is an objects potential energy when three times higher?

If you need help on ratio problems click the link below:

Rule of Ones: analyzing equations to determine how other variables change

5. How much kinetic energy does a 0.15 kg ball thrown at 24 m/s have?

6. How many times greater is the kinetic energy of a ball that is going five times faster?

7. How much kinetic energy does a 1.2 kg ball have the moment it hits the ground 3.5 meters below when it starts from rest?

I cancelled out the initial kinetic energy because:

KE i = ½ mv f 2
KE i = (½)(3.5)(0 2 ) = 0 J

I cancelled out the final potential energy because:

PE f = mgh f
PE f = (3.5)(9.8)(0) = 0 J

8. How fast is a 1.2 kg ball traveling the moment it hits the ground 3.5 meters below when it starts from rest?

(Note: In many of these problems I could cancel out mass but did not since it was provided)

Since I did not cancel out mass I could answer the following questions if asked:

How much mechanical energy did you have at the beginning? (41.6 J)
How much kinetic energy did you have at the beginning? (0 J)
How much potential energy did you have at the beginning? (41.6 J)
How much potential energy do you have at the end? (0 J)

If I cancelled out mass in my work it would not show the actual initial potential energy since PE i = mgh and not just gh.

9. A 3.5 kg ball fell from a height of 12 meters. How fast is it traveling when its still 5 meters off the ground?

10. An 85kg roller coaster cart is traveling 4 m/s at the top of a hill 50 meters off the ground. How fast is it traveling at top of a second hill 20 meters off the ground?

Back to the Mechanical Energy Page
Back to the Main Work, Power, Mechanical Energy, and Simple Machines Page
Back to the Stickman Physics Home Page
For video tutorials and other physics resources check out HoldensClass.com
Find many of your animation resources in one place at the StickMan Physics Gallery
Equation Sheet

Terms and Conditions - Privacy Policy

Total mechanical energy is just the kinetic plus potential energy.
As long as there are no outside forces unaccounted for, we know that the totals before and after will be equal.

E k + E p = E k ’ + E p ’

Note: the little ’ just means “after”.

We usually call this the Law of Conservation of Energy . It grows out of the Laws of Thermodynamics .

First Law of Thermodynamics

“Energy can not be created or destroyed, only changed from one form to another.”

This just basically means that if one thing loses energy, something else must be gaining energy. The opposite is also true.
In an ideal situation this transfer of energy would be perfect and complete, but when was the last time you remember our universe being perfect…? This leads us to the second law …

Second Law of Thermodynamics

“In any energy conversion, there will always be some waste energy released as heat into the surrounding environment.”

In the second law we recognize that the total energy is constant, it’s just that some of the energy is released as unusable heat.

This energy naturally flows from a hotter source to the cooler environment.

In most of the work we do, we assume that we are living in a “perfect” universe.

This means that for the most part we will obey the first law, but ignore the second.
There will be some situations when we give you enough information to use the second law, but we will be pretty specific about telling you.
Most of the time we will say something about the friction involved, since this is the most common source for heat loss in your problems

Example 1 : A person is sitting on a toboggan at the top of a 23.7m tall hill. If the person and toboggan have a total mass of 37.3 kg determine how fast they will be going when they reach the bottom of the hill. Assume there is no friction.

At the top of the hill the person isn’t moving, so E k will be zero. At the bottom of the hill the E p will be zero. E k + E p = E k ’ + E p ’ ½ mv 2 + mgh = ½ mv’ 2 + mgh’ 0 + (37.3kg) (9.81m/s 2 ) (23.7m) = ½ (37.3kg) v’ 2 + 0 8.67e3 J = 18.7 v’ 2 v’ = 21.6 m/s

Notice how in this example all of the potential energy the object had at the top of the hill has been turned completely into kinetic energy at the bottom.

It’s also possible to analyze how the potential energy steadily changes into kinetic energy during a fall…

Example 2 : Wile E. Coyote is trying to drop a boulder off a cliff to hit the Roadrunner eating a bowl of birdseed. He wants to know the speed of the boulder at various points. He supplies you with the following blueprint…

The Coyote wants you to determine the velocity of the boulder at several different heights above the ground, assuming no air resistance…

a) 45 m b) 30 m c) 10 m d) 0 m a) Well, this one ain’t so tough! Since it’s sitting at the top of the cliff, its velocity is 0 m/s. It might be handy at this point to calculate how much E p the boulder has. E p = mgh = 200kg (9.81m/s 2 ) (45m) = 88290 J = 8.8e4 J TOTAL ENERGY = 8.8e4 J

b) First, ask yourself how much E p the boulder still has at 30m above the ground.

E p = mgh = 200kg (9.81m/s 2 ) (30m) = 58860 J = 5.9e4 J

That means that 8.8e4 J - 5.9e4 J = 2.9e4 J is missing, right?

Wrong! According to the conservation of energy, that energy must now be kinetic !

TOTAL ENERGY = 8.8e4 J

c) Again, calculate how much E p you have at this new height of 10 m…

E p = mgh = 200kg (9.81m/s2) (10m) = 19620 J = 2.0e4 J

That means that I have changed 6.9e4 J of energy into other forms… we’ll assume it all changed into kinetic energy.

d) By the time the boulder has reached the ground, all of its potential energy is gone (it’s zero metres above the ground!). We all know that when it actually hits the ground it will come to rest, but we are concerned with how fast it’s going when it is right at ground level but hasn’t actually touched the ground yet. We can assume that all of the potential energy the boulder had at the top is now kinetic energy at the bottom…

You could be finding the same answers based on kinematics formulas from Physics 20.

In fact, you’ll find that conservation of energy gives you new ways to do many problems that you did with kinematics formulas…

JEE-IIT-NCERT Physics & Math

Widget atas posting, conservation of mechanical energy problems and solutions.

Fig.1

Fig.2

Fig.3

Fig.4

Fig.5

Fig.6

Fig.7

Fig.8

Fig.9

Conservation of Energy

Already have an account? Log in here.

Shabarish Ch
Kishore S. Shenoy
Aakash Khandelwal
Shubhang Sharma
Josh Silverman

Some of the great tools in physics are so-called "conservation laws" that buttress the laws of motion with certain quantities that remain the same throughout time. Among these great laws is the conservation of energy which states that while energy can change forms, it cannot be created or destroyed.

Here we'll explore the partition between kinetic energy and potential energy, and how energy can in some sense replace forces in our calculations. We conclude with the introduction of formal methods of physics that analyze the dynamic behavior of systems solely in terms of energy, thus replacing the necessity of having to analyze forces at all. Such methods play a dominant role in systems of condensed matter, quantum field theory, and other problems far beyond elementary classical mechanics.

The Conservation of Kinetic Energy

Work-energy theorem, work with potential energy, conservation of kinetic and potential energies, conservation of energy in general, hamiltonians, lagrangians, and noether's theorem, additional conservation of energy problems solving.

For a person riding a bicycle, their kinetic energy \(E\) is equal to the amount of heat that would be dissipated from the moment they pull the brake to the moment they come to rest. If they don't skid, most of this heat will go into heating the brake pad and the metal rim of the wheel. If they do skid, most of the heat will go to the rubber in the tire and to the road. Before they pull the break, this energy can be observed as the ongoing motion of the parts of the bicycle, i.e. the net forward movement of the bicycle and the spinning of the wheels.

There are other forms of energy that a particle can have such as gravitational potential energy, chemical potential energy, electrical potential energy, spring potential energy, et cetera, but the kinetic energy is the portion of an object's energy that is due explicitly to its ongoing motion. For a point particle of mass \(\delta m\), moving at speed \(v\), the kinetic energy is given by the formula \(\frac12 \delta mv^2\), and the kinetic energy of any extended object can be built up from this. If a moving object collides with another object, and there is no dissipation, (no heat is given off, no chemical bonds are rearranged, etc.) then the total kinetic energy of the objects after the collision must equal the kinetic energy of the moving object before the collision.

In Isaac Newton's Principia Mathematica , momentum is defined and is said to be conserved, but there is no mention of energy anywhere in his treatise. Newton was able to work out the elliptical orbits of planets without any reference to energy at all. However, if we start with the assumption that momentum is conserved, we can derive the conservation of kinetic energy, and thus obtain the structure that lay hidden from Newton in his own theory.

Colliding balls on a table Consider a ball of mass \( m_{1} \) moving with velocity \( v_{0} \) in the direction of a stationary ball of mass \( m_{2} \). Let the velocities of the balls after the collision be \( v_{a} \) and \( v_{b} ,\) respectively. Moreover, suppose the collision is elastic, i.e. the relative velocity of approach is equal and opposite to the relative velocity of separation, i.e. \(\dfrac{\Delta v_i}{\Delta v_f} = -1\). Therefore, along with the conservation of momentum, we have \[\begin{align} v_{0} &= v_{b} - v_{a} \\ \\ m_{1}v_{0} &= m_{1}v_{a} + m_{2}v_{b}. \end{align}\] Solving these two equations for \( v_a \) and \( v_b ,\) we find \[\begin{align} v_a &= \dfrac{m_1 - m_2}{m_1 + m_2}v_0 \\\\ v_b &= \dfrac{2m_1}{m_1 + m_2}v_0. \end{align}\] Let us now calculate the initial and final kinetic energies \(\big(\frac12 mv^2\) for each ball\(\big):\) \[\begin{align} \textrm{KE} _{i} &= \dfrac{1}{2}m_{1}v_{0}^2 \\\\ \textrm{KE} _{f} &= \dfrac{1}{2}m_{1}v_{a}^2 + \dfrac{1}{2}m_{2}v_{b}^2. \end{align}\] Using the values of \( v_a \) and \( v_b \) from above we find (after some tedious algebra) \[\textrm{KE} _{initial} = \textrm{KE} _{final} .\] Hence, the total kinetic energy is conserved in elastic collisions. What about during the collision? Imagine we have two identical balls speeding with equal but opposite velocities to a collision. For an instant, neither ball is moving. So where did the kinetic energy of the balls go during this instant? The collision of the balls is not instantaneous. For a short interval, the kinetic energy of the balls is stored as elastic potential energy, after which it is reallocated to restore the original kinetic energy of the balls. Elastic energy is the potential energy stored in a deformed body, as for example with the compression of an elastic spring. At all times, the combined kinetic and elastic potential energy of the balls is constant. For more information on elastic collisions, see Analyzing Elastic Collisions .

In the previous example, we saw that the conservation of energy falls out in elastic collisions. What about when an object is accelerated by a gravitational field? Without a detailed understanding of potential energy, can we identify quantities that exchange with kinetic energy? Below, we analyze an especially profitable example of a skier on a frictionless slope.

The inclined plane Under constant acceleration, an object travels a distance \(d\) in the time \(t = \sqrt{\frac{2d}{a}}\). For a skier on an inclined plane, this time is given by \(\sqrt{\frac{2d}{g\sin\theta}}\). Also, starting from rest at the top of the incline, the skier has speed \(v = at = g\sin\theta \sqrt{\frac{2d}{g\sin\theta}} = \sqrt{2g\sin\theta d}\) at the bottom of the incline. Consider the change in kinetic energy \(\frac12 mv^2\). At the top of the incline, this quantity is equal to zero, and at the bottom of the incline it's equal to \(mgd\sin\theta\). We notice that \(mgd\sin\theta\) is simply the strength of the gravitational force times the vertical distance through which the skier has descended. Further, we notice that the quantity \(\frac12 mv^2 + mg(h_0-h)\) is a constant throughout the course of the skier's motion, i.e. kinetic energy exchanges with the quantity \(mg\Delta h\). Evidently, by falling through the distance \(\Delta h\), the skier has picked up kinetic energy \(\text{KE} = mg\Delta h\). This suggests that \(mg\Delta h\) is equal to the gravitational potential energy of the skier, which can reallocate to the kinetic energy, based on the skier's vertical position.

Thus, we have stumbled upon a conservation relation between kinetic energy and the gravitational potential energy. As you might imagine, in this example, the conservation is imposed by the fact that the system follows Newton's second law \(F = \frac{dp}{dt}\).

In general, we'll see that energy conservation holds in countless other scenarios. Further, in all the centuries of careful experimentation, a violation has never been identified (in macroscopic systems). For this reason, the conservation of energy has been elevated to the status of a law, i.e. a principle that is expected to hold for all processes in the universe.

In plain English, work means to do something productive. In physics, work is said to be done if force acts to displace an object. For example, when you push a sled across the snow, or lift a bucket of water onto a ledge, or pump up the tire on your bicycle, you've done work. This idea is captured in the definition of work which is the applied force along the direction of displacement times the displacement. Mathematically, we can write

\[W=\int \vec F\cdot d\vec s = Fs\cos\theta, \]

where \(\theta\) is the angle between the force and displacement vectors.

As you might imagine, performing work on an object cannot only change its displacement but its kinetic energy as well. We return once more to the example of the skier on the slope to see how these ideas are related.

Work on the skier Recall our results from above regarding the skier on the slope. Now, consider the work \(F\cdot s\), where \(F\) is the force of gravity along the incline, and \(s\) is the distance traveled along the incline. With \(F = mg\sin\theta\) and \(s=d\), we find \(F\cdot s = mg\sin\theta d\). This is curious. In descending the slope, we showed that the skier gained an amount of kinetic energy \(mgd\sin\theta\) which is also equal to the product of the force that acted on the particle, and the distance over which the particle traveled. Moreover, if we were to pull the skier up the slope at constant velocity, he'd have gained potential energy in the amount \(mgd\sin\theta\). One might be tempted to hypothesize that work delivers energy to objects. Indeed, during his descent the gravitational field does work upon the skier to speed him toward Earth, and in pulling him up the hill, we do work against the gravitational field. Work against a field can always be recouped later and thus we say it is stored kinetic energy or, in other words, potential energy.

Mathematically, we've shown \(\vec{F}\cdot\vec{d} = \Delta \textrm{KE} +\Delta \textrm{PE}= \frac12mv_f^2-\frac12mv_i^2 + mg\left(h_f-h_i\right)\).

This suggests that the cumulative pull of the skier by gravity has given rise to the kinetic energy of the particle at the expense of his initial potential energy. Thus, we can either look at the exchange as work done on the skier by the gravitational field, or as a reallocation of potential energy to kinetic energy.

This relationship would be quite useful if it holds in general, but as yet, it is just a nice coincidence we've noticed in our calculation. Next we look to Newton's laws for a way to put it on firm ground.

Newton's laws: a basis for work According to the second law, we have the following relationship between changes in velocity and a net applied force (for simplicity we work in one dimension, though the result easily generalizes): \[\begin{align}F_\textrm{net}&=ma\\ &=m\frac{\Delta v}{\Delta t}.\end{align}\] Rearranging, we have \[\begin{align} F_\textrm{net} \Delta t &= m \Delta v \\ &= \Delta p.\end{align}\] Because \(\displaystyle\Delta x = v \Delta t\), we can write \(\displaystyle F_\textrm{net} \Delta x / v = m \Delta v\), or \[ F_\textrm{net} \Delta x = m v\Delta v. \] This relation shows that if the object is traveling with velocity \(v\) and it is pushed through some small distance \(\Delta x\) parallel to the force \(\displaystyle F_\textrm{net}\), it will pick up the additional velocity \(\displaystyle \Delta v = \frac{F_\textrm{net}\Delta x}{mv}\). In three dimensions, our result is \(\displaystyle \vec{F}_\textrm{net}\cdot\Delta\vec{x} = m\vec{v}\cdot\Delta\vec{v}\). This relation provides the basis for what we suspected above, that forces can do work to endow particles with kinetic energy. We can now exploit the relation to prove the work-kinetic energy theorem.

Relation between work and kinetic energy

Work-Kinetic Energy Theorem The net work (i.e. work minus work performed against any external fields) done by the force on an object is equal to its change in kinetic energy: \[\Delta \text{KE} = \int \vec F \cdot d\vec s.\]

Now think about the ways in which you can prove this theorem before you reveal the proof, try proving it yourself, and don't worry if you weren't able to crack it because most of the people can't do it in a single go.

Proof for Work-Energy Theorem

Proof 1 : If we add up all of the incremental pushes \(F_\textrm{net}\Delta s\) that the particle receives over the distance \(d\), we get \(F_\textrm{net}\sum \Delta s = F_\textrm{net}d\). However, we showed that \(F_\textrm{net}\Delta s = mv\Delta v\), so we have \(F_\textrm{net}d = m\sum v\Delta v\), a sum over the incremental increases in velocity. Let us now perform the sum of the \(mv\Delta v\). To start, when \(v\) is zero, \(mv\) is zero; at the end, it is equal to \(mv_f \). If we divide the increases up into \(n\) equal pieces, the velocity increases \(\Delta v\) are each given by \(\frac{1}{n}v_f\), which we can pull out of the sum so that the sum becomes \(\dfrac{v_f}{n}\sum v\). Suppose we divide the velocity increase over many moments so that \(n\) is large and the changes are small. Now, the sum of \(v\) from \(0\) to \(v_f\) in \(n\) equally sized chunks is simply \(v\) times the average value of \(v\) over the range: \[\sum\limits_{v=0}^{v_f} v= n\frac{v_f}{2}.\] Therefore, \(\sum mv\Delta v\) is equal to \[\dfrac{mv_f}{n}\sum\limits_{v=0}^{v_f}\Delta v = \frac{mv_f}{n}n\dfrac{v_f}{2} = \dfrac12 mv_f^2,\] which implies \(F_\textrm{net}d=\frac12 mv_f^2.\) This proves that if we act on an object of mass \(m\) with a force \(F_\textrm{net}\) over a distance \(d,\) it ends up with a kinetic energy \(\frac12 mv_f^2\), where the velocity \(v_f\) is given by \(\sqrt{2F_\textrm{net}d/m}\). \(_\square\) \[\] Proof 2 : We know \[W = \int \vec F \cdot d\vec s.\] Since \(\vec F =m \vec a=m\dfrac{d\vec v}{dt},\) it follows that \[\begin{align} W &= \int \vec F \cdot d\vec s \\ &=\int m\dfrac{d\vec v}{dt}\cdot d\vec s =\int\limits_{\vec {v_0}}^{\vec{v_f}}m\dfrac{d\vec s}{dt} d\vec v \\ &=m\int\limits_{\vec {v_0}}^{\vec{v_f}} \vec v \cdot d\vec v =\Delta \textrm{KE}, \end{align}\] which proves \(\Delta \textrm{KE} = W. \ _\square\)

Thus, a force acting on an object through a distance transfers energy to the object, and we call this quantity, \(W_\textrm{net} = \displaystyle\int \vec{F}\cdot d\vec{s}\), the work. In a frictionless system, the work is equal to the change in energy caused by the force:

\[W_\textrm{net} = \Delta \textrm{KE} + \Delta \textrm{PE}.\]

More generally, the work is equal to the change in energy plus whatever heat is dissipated to the environment.

Potential energy is a form of energy due to the configuration or position of an object in a field. It can be seen as a stored form on kinetic energy in that it can be converted to kinetic energy by allowing an object to relax its position or configuration in a field. For example, if we release an electric dipole previously restrained at an angle in an electric field, or drop a massive object in a gravitational field, potential energy is converted to movement through relaxation.

Dams contain massive amount of water stored at a considerable height. When this water is released, the gravitational potential energy is converted to kinetic energy and the water flows, which in turn spins the turbines to generate electricity which can be stored as electric potential energy in batteries. Thus the water which was stored at a height is used to generate electricity in a time of scarcity. Thus kinetic energy can be captured and stored in various forms of potential energy to be extracted later.

Gottfried Wilhelm Leibniz in 1676-1689 was the first to attempt a definition of kinetic energy, and noticed that for some mechanical systems it seemed to be conserved. But remarkably, it was a French mathematician, Emilie du Chatelet, who was the first to propose and derive the conservation of total kinetic and potential energy. She was aware of Isaac Newton's Principia Mathematica and undertook its translation into French, which she completed in 1749. During those years of translation, she included her derivation of the conservation law as a supplement to Newton's treatise. Soon afterwards, mathematicians Leonhard Euler and Joseph-Louis Lagrange went on to develop a mathematical formalism of classical mechanics, based on her works.

The Ball In this example, we see the interplay of kinetic and potential energies of a falling ball such that their sum is constant, when air resistance is ignored. Consider a ball of mass \( m \) falling from rest from a height \( H \) above the ground. Initially, since the ball is at rest its kinetic energy and potential energy, respectively, are \[\begin{array} &\textrm{KE}_i = 0, &\textrm{PE}_i = mgH. \end{array} \] Let \(v\) be the speed of the ball when it is at height \( h \) above the ground. From the second kinematic equation we have \( v^2 = 2g(H-h) \). Hence, the kinetic energy of the ball at height \( h \) is \[\textrm{KE}_h = \dfrac{1}{2}mv^2 = mg(H-h). \] From the expression of potential energy, the potential energy at height \( h \) is \[\textrm{PE}_h = mgh. \] Thus, the sum of energies is \(\textrm{KE}_h + \textrm{PE}_h = mgH \), which is the same as the initial sum of energies.

Spring With Oscillating Mass When an ideal spring is either compressed or stretched a distance \(x\) from the origin where the spring force \(=0\), the potential energy stored in the spring with a spring constant \(k\) \((\)which comes from using force to compress the spring against the spring force \(F=kx)\) is \[PE = \dfrac{1}{2}kx^2,\] while kinetic energy of the oscillating mass \(m\) moving at velocity \(v\) is \[KE = \dfrac{1}{2}mv^2,\] the sum of which is the total energy \(E\). \(\;\) Since total energy is conserved , \(E\) is a constant over time, so differentiating both sides by time \(t\), we have \[\dfrac { d }{ dt } E=0 =\dfrac {dx}{dt} \dfrac { d }{ dx } \left( \dfrac { 1 }{ 2 } k{ x }^{ 2 } \right) +\dfrac {dv}{dt} \dfrac { d }{ dv } \left( \dfrac { 1 }{ 2 } m{ v }^{ 2 } \right) \implies vkx+amv=0.\] Simplifying, we have \[ -kx = ma = F,\] which is Hooke's Law stating that the spring force exerted on mass \(m\) at any point is equal to \(-kx\), a linear function of the distance from the origin where the force \(= 0,\) in the direction towards the origin. This can be restated in terms of time \(t\) \[\dfrac { m }{ k } \dfrac { { d }^{ 2 }x }{ d{ t }^{ 2 } } +x =0,\] a \(2^{\text{nd}}\) order differential equation which has the solution, where \(b\) is a constant: \[x \left( t \right) =b\sin\left( \sqrt { \dfrac { k }{m } }\, t \right). \] Thus, the spring with oscillating mass has a period \(T,\) which is \[T=2\pi \sqrt { \dfrac { m }{ k } }. \]

The pendulum When a pendulum of massless arm length \(L\) with mass \(m\) at the end of it is at angle \(\theta\) from vertical, the gravitational potential energy is \[PE=mgh=mgL(1-\cos\theta), \] while the rotational kinetic energy of the mass \(m\) is \[KE=\dfrac { 1 }{ 2 } I{ { \omega }^{ 2 } }=\dfrac { 1 }{ 2 } m{ L }^{ 2 }{ \omega }^{ 2 },\] the sum of which is the total energy \(E\). \(\;\) Since total energy is conserved , \(E\) is a constant over time, so differentiating both sides with respect to time \(t\), we have \[\begin{align} \dfrac { d }{ dt } E&=0\\ \dfrac { d\theta }{ dt } \dfrac { d }{ d\theta } [mgL( 1-\cos\theta)] +\dfrac { d\omega }{ dt } \dfrac { d }{ d\omega } \left( \dfrac { 1 }{ 2 } m{ L }^{ 2 }{ \omega }^{ 2 } \right)&=0 \\ \dfrac { d\theta }{ dt } mgL\sin\theta +\dfrac { d\omega }{ dt } m{ L }^{ 2 }\omega &=0\\ \frac { d\theta }{ dt } mgL\sin\theta +\frac { { d }^{ 2 }\theta }{ d{ t }^{ 2 } } m{ L }^{ 2 }\frac { d\theta }{ dt }&=0 \\ \dfrac { L }{ g } \dfrac { { d }^{ 2 }\theta }{ d{ t }^{ 2 } } +\sin\theta &=0. \end{align}\] As an approximation for small \(\theta\), we have \[\dfrac { L }{ g } \dfrac { { d }^{ 2 }\theta }{ d{ t }^{ 2 } } +\theta =0,\] a \(2^{\text{nd}}\) order differential equation which has the solution, where \(b\) is a constant: \[\theta \left( t \right) =b\sin\left( \sqrt { \dfrac { g }{ L } }\, t \right). \] Thus, the simple pendulum, for small \(\theta\), has a period \(T\) which is dependent only on \(L\) and \(g:\) \[T=2\pi \sqrt { \dfrac { L }{ g } }. \] Or more generally, for small \(\theta\) but with a rotational inertia of \(I\) \[T=2\pi \sqrt { \dfrac { I }{ mgL } } ,\] where \(L\) is the distance from the pivot to the center of mass of the pendulum. Compare the equations of both spring oscillation and simple pendulum, and see how there's an analogy of Hooke's Law in the latter.

Throughout the first half of the \(19^\text{th}\) century, engineers realized that thermal heat was another form of energy, capable of mechanical work. By 1850, the law of conservation of energy was formally stated for the first time, as the first law of thermodynamics . In the last decades of the \(19^\text{th}\) century, Ludwig Boltzmann developed the statistical mechanics theory of heat and entropy, showing the equivalence of kinetic and thermal heat energies, based on the theory that matter was made of atoms. Over time, other forms of energy were recognized such as elastic, electromagnetic, chemical, and nuclear energies, and the law of conservation of energy was generalized to include all such forms of energies.

Firing an Inelastic Shell A tank fires a special hollow shell that has \(N\) neon atoms inside it, so cold (somewhere near absolute zero Kelvin) that relative to the shell the atoms are not moving. The shell has a velocity of \(680\) meters per second, and it slams into a dirt wall and suffers a 100% inelastic collision, where the shell comes to a dead stop. But the neon atoms continue to bounce around inside the shell at the same velocity. What is the temperature of the neon gas inside the shell, after the shell has come to a dead stop? Treat neon as an ideal gas, i.e. point-like particles with mass, and disregard the mass or size of the hollow shell. Neon atoms are \(20.1797\text{ amu},\) or \(\frac { 20.1797 }{ \text{mole} } \) grams, where \(1\text{ mole} = 6.022\times { 10 }^{ 23 }\). The kinetic energy of \(N\) neon atoms travelling at \(680\) meters per second is \[N\frac { 1 }{ 2 } m{ v }^{ 2 }=N\frac { 1 }{ 2 } \left( \frac { 20.1797 }{ 6.022\times { 10 }^{ 23 } } \frac { 1 }{ { 10 }^{ 3 } } \right) { \left( 680 \right) }^{ 2 }\text{ Joules}=N\left( 7.747\times { 10 }^{ -21 } \right)\text{ Joules}.\] Since total energy is conserved , the kinetic energy of the neon atoms has been converted into thermal heat energy. From statistical mechanics of ideal gases, we then have \[N\left( 7.747\times { 10 }^{ -23 } \right)\text{ Joules}=N\frac { 3 }{ 2 } kT \text{ Joules},\] where \(k=1.381\times { 10 }^{ -23 }\text{ Joules/Kelvin}\) is the Boltzmann Constant, and \(T\) is temperature in \(\text{Kelvin}\). From this, we have \[\left( 7.757\times { 10 }^{ -21 } \right) \frac { 2 }{ 3k } =374.088\text{ Kelvin},\] which is just above the boiling point of water. Note that this result does not depend on the number \(N\) of neon atoms so that there could be a gram of neon in the shell, or a single atom of neon. The temperature of an ideal gas depends solely on the mass of the atom and the average velocity of the atoms, is not a form of energy, and does not have the physical dimensions of energy, which thermal heat energy does.

The Rocket Rocket physics describes one kind of rocket that uses fuel as a stored form of chemical energy, which is released in the combustion chamber of the rocket to generate the thrust to propel it. As the fuel is used up, the mass of the rocket drops, while its velocity increases. Using the law of conservation of momentum , velocity of a rocket as a function of mass describes how the following rocket equation can be derived: \[\begin{align} v_f &= v_0 + u\log \frac{M_0}{M_f} , \end{align}\] where \(v_f\) and \(M_f\) are the final velocity and mass, respectively, \(v_0\) and \(M_0\) are the initial velocity and mass, respectively, and \(u\) is the velocity of the rocket exhaust relative to the rocket. \[\text{Indian Polar Satellite Launch Vehicle XL which uses HTPB propellant}\] We can use the law of conservation of energy to derive the same result as follows: Let \(M_0-m\) be the rocket’s mass, where \(m\) is the consumed mass of fuel. Also, let \(v(m)\) be the velocity of the rocket as a function of \(m\), and \(u\) the velocity of the exhaust relative to the rocket. Then we have the following as the total energy of the rocket/exhaust gas system: \[E=\displaystyle \int _{ 0 }^{ m }{ \dfrac { 1 }{ 2 } } \big[ u-v\left( m \right) \big]^2\, dm+\dfrac { 1 }{ 2 } \left( { M }_{ 0 }-m \right) \big[v(m)\big]^2+{ PE }_{ \text{Fuel} }\left( { M }_{ 0 }-m \right), \] where the first term is the kinetic energy of the rocket exhaust gas, the second term is the kinetic energy of the rocket, and the last term \({ PE }_{\text{Fuel} }\left( { M }_{ 0 }-m \right) \) is the potential energy contained in the unburned fuel. The kinetic potential energy of this fuel when it is converted into exhaust gas is simply the kinetic energy it has at velocity \(u\), so we can rewrite this equation as \[E=\displaystyle \int _{ 0 }^{ m }{ \dfrac { 1 }{ 2 } } \big[u-v(m)\big]^2 \, dm+\dfrac { 1 }{ 2 } \left( { M }_{ 0 }-m \right) \big[v(m)\big]^2+\dfrac { 1 }{ 2 } \left( { M }_{ 0 }-m \right) { u }^{ 2 }.\] Since total energy is conserved , we can differentiate both sides by \(m\) with the result \[\begin{align} \dfrac { dE }{ dm } &=0\\\\ \dfrac { 1 }{ 2 }\big[u-v(m)\big]^2-\dfrac { 1 }{ 2 }\big[v(m)\big]^2-\left( {M}_ {0}-m \right) v\left( m \right) \dfrac { dv }{ dm } -\dfrac { 1 }{ 2 } { u }^{ 2 }&=0\\\\ -u-\left( {M}_ {0}-m \right) { \dfrac { dv }{ dm } }&=0\\\\ -\int _{ 0 }^{ m }{ \frac { u }{ {M}_ {0}-m } } \, dm&=\int dv \\\\ u\log\left( \dfrac { {M}_ {0 }}{ {M}_ {0}-m } \right) &={v}_{m}-{v}_{0}, \end{align}\] which agrees with the rocket equation given above. This equation is the most simplified form of rocket physics, which assumes that all the thrust is provided by the exhaust velocity of the combustion gases alone. A real rocket involves other considerations such as combustion gas pressure inside the nozzle.

Mass Energy in Nuclear Reactions A Deuterium atom, \(_1 ^2\ce{H}\), is an isotope of hydrogen that has a nucleus containing one proton and one neutron. Two of them, if collided together at a sufficiently high speed to overcome the Coulomb barrier, can fuse and produce a helium-3 atom \(\left(_2 ^3\ce{He}\right)\) and a free neutron \(\left(_0 ^1\ce{n}\right)\). \(_2 ^3\ce{He}\) is an isotope of helium that has two protons but only one neutron. Excess energy is produced from this fusion, which is carried away as kinetic energy in the products. In atomic mass units \((\text{amu})\), the masses of the nuclei are \[\begin{array}{llll} _1 ^2\ce{H}&=&2.01410179 &\text{ (amu)}\\ _2 ^3\ce{He}&=&3.0160293 &\text{ (amu)}\\ _0 ^1\ce{n}&=&1.008664916 &\text{ (amu)}. \end{array}\] Per Einstein’s \(E=m{ c }^{ 2 }\), mass-to-energy conversion from \(\text{amu}\) to million electron Volts is \[1\text{ amu} = 941.494\text{ MeV}.\] Now, calculate the energy \(E\) in \(\text{MeV}\), produced as the result of the following Deuterium+Deuterium fusion reaction: \[_{ 1 } ^{ 2 }\ce{H} + \ _{ 1 } ^{ 2 }\ce{H} \to \ _{ 2 }^{ 3 }\ce{He}+ \ _0^1\ce{n}+{ E }_{ \text{MeV} }.\] Two deuterium nuclei have a total mass of \(4.02820358\text{ amu},\) but the total mass of \(_2 ^3\ce{He}\) and \(_0 ^1\ce{n}\) is \(4.024694216\text{ amu},\) which is less. The theory of relativity says mass is another form of energy, so since total energy is conserved that missing \(0.00350936\text{ amu}\) mass was converted into energy. Using the mass-to-\(\text{MeV}\) conversion, this works out to about \(E=3.26895\text{ MeV}.\) Note: \(\text{eV}\), or electron volt, is not to be confused with \(\text{V}\), or volt. \(\text{eV}\) has dimensions of energy, or joules, while \(\text{V}\) is joules divided by charge.

If the energy produced is carried away by the products, and if both kinetic energy and momentum are conserved, what is the kinetic energy of the neutron after this fusion reaction? (Disregard the initial kinetic energies of the reactant Deuterium nuclei.) The conservation equations are \[\begin{align} \dfrac { 1 }{ 2 } m_{(^3\ce{He})} v_{(^3\ce{He})}^2+\dfrac { 1 }{ 2 } m_n v_n^2&=E\\ { m }_{ (^3\ce{He}) }{ { v }_{ (^3\ce{He}) } }+{ m }_{ n }{ { v }_{ n } }&=0. \end{align}\] Letting \({ E }_{(^3\ce{He} ) } \) and \({ E }_{ n }\) be the kinetic energies of the products resulting from the fusion, we can restate the two equations from both conservation laws as follows: \[\begin{align} { E }_{ (^3\ce{He}) }+{ E }_{ n }&=E\\ { E }_{(^3\ce{He})}{ m }_{ (^3\ce{He}) }&={ E }_{ n }{ m }_{ n }. \end{align}\] From these, we can work out the kinetic energy of the neutron \[{ E }_{ n }=\dfrac { { m }_{ (^3\ce{He}) } }{ { m }_{ (^3\ce{He}) }+{ m }_{ n } } E,\] which works out to approximately \(2.44969\text{ MeV}\) or \(2.450\text{ MeV}\), which is the usual published value.

ATP synthase, a molecular motor

Spring Pendulum: A Preview of Lagrangian Mechanics Examples given above included a pendulum in a gravitational field, and an oscillating spring-mass system. What if we were to combine them? A massless pendulum arm of relaxed length \(L\) is capable of stretching or compressing lengthwise, and a mass \(m\) is attached to the end of it. Then the position of the mass can be described by two functions to be determined: \[\begin{align} \text{Distance from pivot point } &=L+x(t) \\ \text{Angle from vertical } &=\theta(t). \end{align}\] The total kinetic energy is then the sum of radial and tangential components \[T=\dfrac { 1 }{ 2 } m { \left( \dfrac { dx }{ dt } \right) }^{ 2 }+\dfrac { 1 }{ 2 } m { \left( (L+x)\dfrac { d\theta }{ dt } \right) }^{ 2 } \] and the total potential energy is the sum of gravitational and spring potentials \[V=V\left(x,\theta\right)=-mg(L+x)\cos \theta +\dfrac { 1 }{ 2 } k{ x }^{ 2 },\] where \(g\) is the gravitational acceleration and \(k\) is the spring constant. There are two approaches to classical mechanics (see Lagrangian formulation of mechanics ), which can be briefly summarized as follows: \[\begin{array}{rl} \text{Hamiltonian:} &\mathcal{H} = T+V\\ \text{Lagrangian:} &\mathcal{L}=T-V, \end{array}\] which can be shown to be equivalent through the Legendre transform. In this exercise, we express this spring pendulum by its Lagrangian as follows: \[\mathcal{L}=T-V= \dfrac { 1 }{ 2 } m{ { \dot { x } }^{ 2 }+ \dfrac { 1 }{ 2 } m { \left( (L+x) \dot {\theta } \right) }^{ 2 } }+mg(L+x)\cos \theta -\dfrac { 1 }{ 2 } k{ x }^{ 2 }.\] The two Euler-Lagrange equations for these are then \[\begin{align} \dfrac { d }{ dt } \left( \dfrac { \partial \mathcal {L} }{ \partial \dot { x } } \right) &=\dfrac { \partial \mathcal {L} }{ \partial x } \implies m\ddot { x } =m(L+x){ \dot { \theta } }^{ 2 }+mg\cos \theta –kx\\ \dfrac { d }{ dt } \left( \dfrac { \partial \mathcal {L} }{ \partial \dot { \theta } } \right) &=\dfrac { \partial \mathcal {L} }{ \partial \theta } \implies m(L+x)\ddot { \theta } +2m\dot { x } \dot { \theta } =-mg\sin\theta. \end{align}\] The first is the radial force along the length of the pendulum arm while the second is the tangential force. The complete solution to this pair of differential equations is beyond the scope here, but this example is given to illustrate the generalized utility of treating problems of classical mechanics through the use of kinetic and potential energies, rather than the use of forces and momenta.

The LC Circuit: Via the Lagrangian Approach The classic LC circuit, in the simplest form, consists of an inductor and a capacitor, both of which are capable of storing energy: one electromagnetic and the other electrostatic. This circuit can be analyzed using Kirchhoff’s laws, which is the conventional approach. However, to demonstrate the power of the Lagrangian method, which treats energy as a generalized abstract quantity, the following is a way how the LC circuit can be analyzed in terms of energies alone: Let \(q\left(t\right)\) be the charge as a function of time \(t\). Also, let \(L\) be the inductance of the inductor, and \(C\) the capacitance of the capacitor. Then we can make the analogy of kinetic and potential energies as follows: \[\begin{align} T&=\dfrac { 1 }{ 2 } L{ \left( \dfrac { dq }{ dt } \right) }^{ 2 }\\ V&=\dfrac { 1 }{ 2C } { q }^{ 2 }. \end{align}\] The Lagrangian is then \[\mathcal{L}=\mathcal{L}\left( \dot { q } ,q \right) =T-V=\dfrac { 1 }{ 2 } L{ \dot { q } }^{ 2 }-\dfrac { 1 }{ 2C } { q }^{ 2 }.\] The Euler-Lagrange equation is then \[\dfrac { d }{ dt } \left( \dfrac { \mathcal{L} }{ \partial \dot { q } } \right) -\dfrac { \mathcal{L} }{ \partial q } =0\implies \ddot { q } +\dfrac { q }{ LC } =0,\] which yields the same solution as can be found by using Kirchhoff’s laws \[q\left( t \right) ={ q }_{ 0 }\cos\left( \omega t \right) \] given that \(q\left(0\right)=0, \dot{q}\left(0\right)=0\) and \(\omega =\frac { 1 }{ \sqrt { LC } } .\)

The total mechanical (kinetic + potential) energy of a free falling object are always equal to the potential energy at the height from which it was dropped from rest. Is this statement true or false?

Neglect air resistance.

An object is dropped from rest from a height of \(h\). What is the velocity of the object in the middle of its journey, i.e. when the object is at half its original distance to its destination?

Two bodies \(A\) and \(B\) have an equal momentum. But the mass of \(A\) is less than the mass of \(B\).

Which of the two will have more kinetic energy?

This problem is posted in connection to the upcoming collaboration party hosted by me! Interested people may come forward (just ping me on slack).

Problem Loading...

Note Loading...

Set Loading...

8.3 Conservation of Energy

Learning objectives.

By the end of this section, you will be able to:

Formulate the principle of conservation of mechanical energy, with or without the presence of non-conservative forces
Use the conservation of mechanical energy to calculate various properties of simple systems

In this section, we elaborate and extend the result we derived in Potential Energy of a System , where we re-wrote the work-energy theorem in terms of the change in the kinetic and potential energies of a particle. This will lead us to a discussion of the important principle of the conservation of mechanical energy. As you continue to examine other topics in physics, in later chapters of this book, you will see how this conservation law is generalized to encompass other types of energy and energy transfers. The last section of this chapter provides a preview.

The terms ‘conserved quantity’ and ‘conservation law’ have specific, scientific meanings in physics, which are different from the everyday meanings associated with the use of these words. (The same comment is also true about the scientific and everyday uses of the word ‘work.’) In everyday usage, you could conserve water by not using it, or by using less of it, or by re-using it. Water is composed of molecules consisting of two atoms of hydrogen and one of oxygen. Bring these atoms together to form a molecule and you create water; dissociate the atoms in such a molecule and you destroy water. However, in scientific usage, a conserved quantity for a system stays constant, changes by a definite amount that is transferred to other systems, and/or is converted into other forms of that quantity. A conserved quantity, in the scientific sense, can be transformed, but not strictly created or destroyed. Thus, there is no physical law of conservation of water.

Systems with a Single Particle or Object

We first consider a system with a single particle or object. Returning to our development of Equation 8.2 , recall that we first separated all the forces acting on a particle into conservative and non-conservative types, and wrote the work done by each type of force as a separate term in the work-energy theorem. We then replaced the work done by the conservative forces by the change in the potential energy of the particle, combining it with the change in the particle’s kinetic energy to get Equation 8.2 . Now, we write this equation without the middle step and define the sum of the kinetic and potential energies, K + U = E ; K + U = E ; to be the mechanical energy of the particle.

Conservation of Energy

The mechanical energy E of a particle stays constant unless forces outside the system or non-conservative forces do work on it, in which case, the change in the mechanical energy is equal to the work done by the non-conservative forces:

This statement expresses the concept of energy conservation for a classical particle as long as there is no non-conservative work. Recall that a classical particle is just a point mass, is nonrelativistic, and obeys Newton’s laws of motion. In Relativity , we will see that conservation of energy still applies to a non-classical particle, but for that to happen, we have to make a slight adjustment to the definition of energy.

It is sometimes convenient to separate the case where the work done by non-conservative forces is zero, either because no such forces are assumed present, or, like the normal force, they do zero work when the motion is parallel to the surface. Then

In this case, the conservation of mechanical energy can be expressed as follows: The mechanical energy of a particle does not change if all the non-conservative forces that may act on it do no work. Understanding the concept of energy conservation is the important thing, not the particular equation you use to express it.

Problem-Solving Strategy

Identify the body or bodies to be studied (the system). Often, in applications of the principle of mechanical energy conservation, we study more than one body at the same time.
Identify all forces acting on the body or bodies.
Determine whether each force that does work is conservative. If a non-conservative force (e.g., friction) is doing work, then mechanical energy is not conserved. The system must then be analyzed with non-conservative work, Equation 8.12 .
For every conservative force that does work, choose a reference point and determine the potential energy function for the force. The reference points for the various potential energies do not have to be at the same location.
If no non-conservative work is done, apply the principle of mechanical energy conservation by setting the sum of the kinetic energies and potential energies equal at every point of interest.

Example 8.7

Simple pendulum.

Since the particle is released from rest, the initial kinetic energy is zero. At the lowest point, we define the gravitational potential energy to be zero. Therefore our conservation of energy formula reduces to

The vertical height of the particle is not given directly in the problem. This can be solved for by using trigonometry and two givens: the length of the pendulum and the angle through which the particle is vertically pulled up. Looking at the diagram, the vertical dashed line is the length of the pendulum string. The vertical height is labeled h . The other partial length of the vertical string can be calculated with trigonometry. That piece is solved for by

Therefore, by looking at the two parts of the string, we can solve for the height h ,

We substitute this height into the previous expression solved for speed to calculate our result:

Significance

Check your understanding 8.7.

How high above the bottom of its arc is the particle in the simple pendulum above, when its speed is 0.81 m / s ? 0.81 m / s ?

Example 8.8

Air resistance on a falling object.

Step 2: Gravitational force is acting on the panel, as well as air resistance, which is stated in the problem.

Step 3: Gravitational force is conservative; however, the non-conservative force of air resistance does negative work on the falling panel, so we can use the conservation of mechanical energy, in the form expressed by Equation 8.12 , to find the energy dissipated. This energy is the magnitude of the work:

Step 4: The initial kinetic energy, at y i = 1 km , y i = 1 km , is zero. We set the gravitational potential energy to zero at ground level out of convenience.

Step 5: The non-conservative work is set equal to the energies to solve for the work dissipated by air resistance.

Check Your Understanding 8.8

You probably recall that, neglecting air resistance, if you throw a projectile straight up, the time it takes to reach its maximum height equals the time it takes to fall from the maximum height back to the starting height. Suppose you cannot neglect air resistance, as in Example 8.8 . Is the time the projectile takes to go up (a) greater than, (b) less than, or (c) equal to the time it takes to come back down? Explain.

In these examples, we were able to use conservation of energy to calculate the speed of a particle just at particular points in its motion. But the method of analyzing particle motion, starting from energy conservation, is more powerful than that. More advanced treatments of the theory of mechanics allow you to calculate the full time dependence of a particle’s motion, for a given potential energy. In fact, it is often the case that a better model for particle motion is provided by the form of its kinetic and potential energies, rather than an equation for force acting on it. (This is especially true for the quantum mechanical description of particles like electrons or atoms.)

We can illustrate some of the simplest features of this energy-based approach by considering a particle in one-dimensional motion, with potential energy U ( x ) and no non-conservative interactions present. Equation 8.12 and the definition of velocity require

Separate the variables x and t and integrate, from an initial time t = 0 t = 0 to an arbitrary time, to get

If you can do the integral in Equation 8.14 , then you can solve for x as a function of t .

Example 8.9

Constant acceleration.

Solving for the position, we obtain x ( t ) = x 0 − 1 2 ( E / m x 0 ) t 2 x ( t ) = x 0 − 1 2 ( E / m x 0 ) t 2 .

Check Your Understanding 8.9

What potential energy U ( x ) U ( x ) can you substitute in Equation 8.13 that will result in motion with constant velocity of 2 m/s for a particle of mass 1 kg and mechanical energy 1 J?

We will look at another more physically appropriate example of the use of Equation 8.13 after we have explored some further implications that can be drawn from the functional form of a particle’s potential energy.

Systems with Several Particles or Objects

Systems generally consist of more than one particle or object. However, the conservation of mechanical energy, in one of the forms in Equation 8.12 or Equation 8.13 , is a fundamental law of physics and applies to any system. You just have to include the kinetic and potential energies of all the particles, and the work done by all the non-conservative forces acting on them. Until you learn more about the dynamics of systems composed of many particles, in Linear Momentum and Collisions , Fixed-Axis Rotation , and Angular Momentum , it is better to postpone discussing the application of energy conservation to then.

This book may not be used in the training of large language models or otherwise be ingested into large language models or generative AI offerings without OpenStax's permission.

Want to cite, share, or modify this book? This book uses the Creative Commons Attribution License and you must attribute OpenStax.

Access for free at https://openstax.org/books/university-physics-volume-1/pages/1-introduction

Authors: William Moebs, Samuel J. Ling, Jeff Sanny
Publisher/website: OpenStax
Book title: University Physics Volume 1
Publication date: Sep 19, 2016
Location: Houston, Texas
Book URL: https://openstax.org/books/university-physics-volume-1/pages/1-introduction
Section URL: https://openstax.org/books/university-physics-volume-1/pages/8-3-conservation-of-energy

© Jul 23, 2024 OpenStax. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution License . The OpenStax name, OpenStax logo, OpenStax book covers, OpenStax CNX name, and OpenStax CNX logo are not subject to the Creative Commons license and may not be reproduced without the prior and express written consent of Rice University.

Intro Physics Homework Help
Advanced Physics Homework Help
Precalculus Homework Help
Calculus Homework Help
Bio/Chem Homework Help
Engineering Homework Help

Follow along with the video below to see how to install our site as a web app on your home screen.

Note: This feature may not be available in some browsers.

Homework Help
Introductory Physics Homework Help

Total Mechanical Energy Problem

Thread starter Snape1830
Start date Jan 15, 2012
Tags Energy Mechanical Mechanical energy
Jan 15, 2012
Research team uses tunable laser to develop straightforward broadband spectroscopy method with Hz-level precision
Scientists observe first neutrinos with prototype detector
Chip that entangles four photons opens up possibility of inviolable quantum encryption

Without friction, total mechanical energy is a conserved quantity. What's the total mechanical energy at location A?

gneill said: Without friction, total mechanical energy is a conserved quantity. What's the total mechanical energy at location A?

Snape1830 said: PE= mgh. So PE= 17640 J Ohh I get it! So 17640=TME since kientic energy is 0 J. I completely forgot about that. Thanks!

Jan 22, 2012

Hello, To calculate the total mechanical energy (TME) of the roller coaster at points B, C, and D, we first need to find the velocity at these points. We can use the principle of conservation of energy, which states that energy cannot be created or destroyed, only transferred from one form to another. At point A, the roller coaster has only potential energy (PE) as it is at rest. As it moves down the hill, this potential energy is converted into kinetic energy (KE). At point B, the roller coaster has lost some potential energy but gained some kinetic energy. We can use the equation PE = mgh (mass x gravity x height) to calculate the potential energy at point A. Since the velocity at the top of the hill is 0 m/s, the kinetic energy at point A is also 0. At point B, the roller coaster has lost 15 m of height, so the potential energy is now mgh = (120 kg)(9.8 m/s^2)(15 m) = 17,640 J. To find the velocity at point B, we can use the equation KE = 1/2mv^2 (1/2 x mass x velocity squared). We know the mass (120 kg) and the kinetic energy (17,640 J), so we can solve for the velocity: v = √(2KE/m) = √(2 x 17,640 J / 120 kg) = 14.7 m/s. We can use the same process to find the velocity at points C and D. At point C, the height has decreased by 12 m, so the potential energy is now mgh = (120 kg)(9.8 m/s^2)(12 m) = 11,520 J. The velocity can be found using the same equation as before: v = √(2KE/m) = √(2 x 11,520 J / 120 kg) = 12.3 m/s. At point D, the height has decreased by 8 m, so the potential energy is now mgh = (120 kg)(9.8 m/s^2)(8 m) = 9,600 J. Again, we can use the same equation to find the velocity: v = √(2KE/m) = √(2 x 9,600 J / 120 kg) = 10 m

2. How is total mechanical energy calculated?

The total mechanical energy of a system is calculated by adding the kinetic energy, which is equal to 1/2mv^2, and the potential energy, which is equal to mgh, where m is the mass of the object, v is its velocity, g is the acceleration due to gravity, and h is the height of the object.

3. Is total mechanical energy conserved?

According to the law of conservation of energy, total mechanical energy is conserved in a closed system. This means that the total amount of energy in the system remains constant, even if it is transferred between different forms of energy such as kinetic and potential energy.

4. What happens to total mechanical energy when work is done on a system?

When work is done on a system, the total mechanical energy of the system will change. If work is done by a conservative force, such as gravity, the change in total mechanical energy will be equal to the work done. However, if work is done by a non-conservative force, such as friction, some of the mechanical energy will be converted into other forms of energy, such as heat.

5. How is total mechanical energy useful in solving problems?

Total mechanical energy is useful in solving problems because it allows us to analyze the motion of an object by considering its energy instead of individual forces. By using the conservation of energy principle, we can solve for unknown variables, such as velocity or height, without needing to know the specific forces acting on the object.

Similar threads

Mar 13, 2021
Jul 14, 2022
May 10, 2024
Nov 20, 2019
Jun 30, 2024
Jun 27, 2024
Oct 30, 2022
Apr 27, 2020
May 7, 2023
Sep 6, 2020

Hot Threads

Current through a circuit when the key is open
Small oscillations of a simple pendulum placed on a moving block
How to Calculate Water Leakage in an Inverted Bottle Experiment?
Vertical displacement with time of a projectile
Acceleration in uniform circular motion is uniform or non-uniform?

Recent Insights

Insights PBS Video Comment: “What If Physics IS NOT Describing Reality”
Insights Aspects Behind the Concept of Dimension in Various Fields
Insights Views On Complex Numbers
Insights Addition of Velocities (Velocity Composition) in Special Relativity
Insights Schrödinger’s Cat and the Qbit
Insights The Slinky Drop Experiment Analysed

New Hampshire
North Carolina
Pennsylvania
West Virginia
Online hoaxes
Coronavirus
Health Care
Immigration
Environment
Foreign Policy
Kamala Harris
Donald Trump
Mitch McConnell
Hakeem Jeffries
Ron DeSantis
Tucker Carlson
Sean Hannity
Rachel Maddow
PolitiFact Videos
2024 Elections
Mostly True
Mostly False
Pants on Fire
Biden Promise Tracker
Trump-O-Meter
Latest Promises
Our Process
Who pays for PolitiFact?
Advertise with Us
Suggest a Fact-check
Corrections and Updates
Newsletters

Stand up for the facts!

Our only agenda is to publish the truth so you can be an informed participant in democracy. We need your help.

I would like to contribute

Fact-checking donald trump’s rally in bozeman, montana.

2024 Senate Elections

Republican presidential nominee former President Donald Trump pauses to talk to onlookers after speaking at an Aug. 9, 2024, campaign rally in Bozeman, Montana. (AP)

In his first campaign rally since Vice President Kamala Harris selected Minnesota Gov. Tim Walz as her running mate for the 2024 presidential election, former President Donald Trump attacked Walz and rallied support for a crucial Senate seat in Montana.

"If Comrade Walz and Comrade Harris win this November, the people cheering will be the pink-haired Marxists, the looters, the perverts, the flag burners," Trump said, invoking a common but misleading line of attack that seeks to paint Democrats’ policies as socialist.

Trump took the stage later than expected at his Friday night rally in Bozeman, Montana, after a mechanical problem forced his plane to divert 140 miles east to Billings. The plane landed without incident. Trump’s vice presidential running mate, Ohio Sen. J.D. Vance, did not attend.

In his speech, Trump zeroed in on the state’s Democratic senator, Jon Tester, criticizing the votes Tester took to support major legislation passed under President Joe Biden’s administration, such as the Inflation Reduction Act. Tim Sheehy, the Republican running to unseat Tester, spoke alongside Trump.

Trump also criticized Harris and Biden on issues such as immigration and the economy. We fact-checked five of his claims.

Trump: I handed Biden "a surging economy with no inflation."

This is inaccurate . Trump has made this claim before.

Although inflation was lower during Trump’s presidency than it has been under Biden’s, the Consumer Price Index 12-month change was never at zero percent.

It fell close to zero in April and May 2020, shortly after the COVID-19 pandemic’s onset. The lowest inflation rate was 0.1% in May 2020.

That’s because the American economy took a major hit as the demand for goods and services plunged during the pandemic’s initial lockdowns. Trump claiming credit for the low inflation at that time ignores that the rate dropped because of economic crisis, not success.

For much of Trump’s presidency until the pandemic, inflation ranged from 1.5% to 3%. When Biden entered office in January 2021, inflation was at 1.4%.

Trump: "By the millions and millions, (immigrants are) coming from prisons, they’re coming from jails."

Pants on Fire!

Trump’s claim that immigrants are flowing across the border from prisons and mental institutions lacks evidence, and data and expert analysis reveal his description of them coming by the "millions and millions" to be so implausible as to be ridiculous.

U.S. Customs and Border Protection data shows that officials have arrested just more than 110,000 noncitizens with criminal convictions, whether in the U.S. or abroad. Not all were let into the country. The data reflects numbers the federal government knows about, but it isn’t exhaustive.

There have been about 8 million encounters at the border since Biden took office. But encounters data represents events, not people. For example, if one person tries to cross the border three times and is stopped each time, that would count as three encounters.

Trump: Harris "wants to get rid of ICE."

Harris was critical of the U.S. Immigrations and Customs Enforcement — the agency in charge of detaining and deporting immigrants who are in the U.S. illegally — during Trump’s presidency. She criticized many of his border policies, including one that led to family separations at the border, but she hasn’t called to abolish the agency.

She said in a 2018 MSNBC interview that Immigration and Customs Enforcement should exist, but she called for reexamining its role and scope. During a separate interview in 2018 , she said that the U.S. should "reexamine ICE and its role" and mission, and "even think about starting from scratch." Harris has not stumped in 2024 to end the agency; her campaign has not released a written policy platform for her 2024 run. But her 2019 presidential primary immigration platform called for restructuring the agency, not abolishing it.

Trump: "They're destroying Social Security and Medicare by allowing all of these people to come in on the plan."

Most immigrants in the country illegally are not eligible for Social Security. Some who have been granted humanitarian parole for more than one year may be eligible for Social Security for up to seven years, according to the Congressional Research Service.

Immigrants in the U.S. illegally are typically ineligible to enroll in federally funded health care programs such as Medicare and Medicaid. Some states offer Medicaid coverage under state-funded programs regardless of immigration status, and immigrants are eligible for emergency Medicaid regardless of status.

Immigration also does not threaten Social Security’s sustainability. The program has shortfalls because the ranks of retirees outpace the numbers of workers feeding their tax dollars into the system. Immigrants who meet the legal requirements to receive retirement benefits can access Social Security only after working and contributing to Social Security taxes for a minimum of 10 years.

Trump: Harris "wants to have all of your guns taken away."

Mostly False .

As presidential candidate in 2019, Harris said she supported a "mandatory gun buyback program" for assault weapons.

The proposed program did not apply to all guns. Handguns, which would not have been affected, make up the majority of guns sold in the U.S.

Since Harris has become the Democratic presidential nominee, her campaign has said she does not support a mandatory buyback program. The campaign said she supports banning assault weapons but not requiring people to sell them to the federal government.

Our Sources

Sources linked in article

Browse the Truth-O-Meter

More by caleb mccullough.

Memberships

MoSCoW Method of Prioritization explained

MoSCoW Method: This article explains MoSCoW Method in a practical way. Next to what it is (meaning, acronym and origin), and which advantages are connected to using this model, this article also highlights the MoSCoW Method requirements, including a practical example. You will also learn how applying this method will enable you and the team to reach deadlines in time. Enjoy reading!

What is the MoSCoW Method of Prioritization?

Prioritising is often challenging. Particularly when it comes the implementation of new ideas and / or technologies. Everyone in an organisation always wants everything to be done right away and that is practically impossible. There are several tools available to make prioritisation easier. The MoSCoW Method of Prioritization is one them.

The MoSCoW Method is a prioritization technique, which can be used in a variety of situations.

Origin and advantages of the MoSCoW Method

The method was developed by Dai Clegg, a developer working for the software company Oracle .

Originally, it was used to categorize product features, derived from user stories. It was later used in the Dynamic System Development Method (DSDM) . The method contains multiple prioritization categories, with labels for each requirement, making it easier to prioritise.

Even though the origin of this prioritize method is in software development, it is also highly applicable for agile project management, market launches, product releases, starting a new business or change processes.

With the MoSCoW Method, requirements are determined for the result of the project or product. It is about setting requirements by order of priority. The most important requirements need to be met first for a greater chance of success.

Meaning and acronym of the MoSCoW Method

Moscow is an acronym made up of the first letters. The two Os have been added to make the word ‘moscow’ readable, they don’t have any meaning themselves. The M stands for ‘Must haves’ , S for ‘Should haves’ , C for ‘Could haves’ and W for ‘Won’t haves’ or ‘Would haves’ .

Figure 1 – the MoSCoW Method acronym

The requirements when you start with the MoSCoW Method

It’s a good idea to first specify the requirements together with all team members before starting the MoSCoW Method. When determining the requirements, you should take into account what is important to all the stakeholders. Brainstorming with everyone involved will lead to good, qualitative requirements.

The requirements are prioritised to prevent them from becoming to expensive or unrealistic. The main goal is to come up with requirements that add the most value for the company. The project requirements are divided into one of the following categories:

M – Must haves

These are about the minimal requirements that are determined in advance that the end-result has to meet.

Without meeting these requirements, the project fails and the product won’t be use-able. They are a necessity for a workable product and there is no alternative. The ‘Must haves’ are essential. MUST is also explained as an acronym that stands for Minimum Use-able SubseTs.

As an extra exam assignment, University of Applied Sciences Automotive students have been asked to design a car that can at least drive (minimal requirements).

It’s okay if the car only has a chassis, without any bodywork. It’s about the construction of the individual parts and drive train to the combustion engine. In this case, the Must have is that they have a drivable car by the end of the academic year.

S – Should haves

These are additional and much desired requirements that have a high priority, but are not essential for a usable end product. The product will be usable even if these requirements aren’t met. When they are met, they will only add to the value of the product. Depending on the available time, you can always return to these requirements at a later time.

The University of Applied Sciences Automotive student might like to add a tow bar to the car (should have), but as long as the car can drive without the tow bar, their project will be successful. They can always add the tow bar at a later stage.

C – Could haves

These requirements can be considered if there’s time left. If not, it’s no problem and will not have a negative effect on the final result. The ‘Could haves’ have a lower priority than the ‘Should haves’ .

This option will only be included if there really is more than enough time to make it work. This category is also referred to as ‘nice to have’; they’re more a wish than an absolute requirement.

The University of Applied Sciences Automotive students would perhaps like to install a tachometer in the car. It’s not an important (exam) requirement, but it’d be great if they manage to do it.

W – Won’t haves (and would haves)

These are about wishes for the future that are often impossible to realise or cost a lot of time. If it’s simply not possible, it’s best not to waste any energy on it.

If it is achievable, then a lot of time (and money) will have to be invested and it’s labelled a ‘Would have’. ‘Would haves’ are often followed upon at a later stage after the initial project is finished.

The University of Applied Sciences Automotive students don’t have to make a car that will actually drive on public roads.

It’s meant for study. If they do want to take it on public roads, it will need bodywork and comply with safety standards. It also involves getting approval from the Vehicle Standards Agency in elaborate process.

How to reach deadlines using the MoSCoW Method of Prioritization?

Correctly applying and sticking to the MoSCoW Method will lead to a clear way to lead a project. Everyone involved with the project will know what needs to be done first, when it has to be finished and why it’s important. By assigning priorities to requirements, a project becomes more manageable and it’ll be easier to meet the deadline.

It’s Your Turn

What do you think? How do you apply the MoSCoW analysis in your project or organisation? Do you recognize the practical explanation or do you have more additions? What are your success factors for applying the MoSCoW Method?

Share your experience and knowledge in the comments box below.

More information

Baxter, R. (2004). Software engineering is software engineering . In 26th International Conference on Software Engineering, W36 Workshop Software Engineering for High Performance System (HPCS) Applications (pp. 4-18).
Stephens, R. (2015). Beginning Software Engineering . Wrox Publishing .
Hatton, S. (2008). Choosing the right prioritisation method. In Software Engineering, 2008. ASWEC 2008 . 19th Australian Conference on (pp. 517-526). IEEE.
Robson, W.A., Simon, Shena. (2014). Moscow in the making . Taylor & Francis Ltd.

How to cite this article: Mulder, P. (2017). MoSCoW Method of Prioritization . Retrieved [insert date] from Toolshero: https://www.toolshero.com/project-management/moscow-method/

Original publication date: 05/12/2017 | Last update: 05/27/2024

Add a link to this page on your website: <a href=”https://www.toolshero.com/project-management/moscow-method/”> Toolshero: MoSCoW Method of Prioritization</a>

Did you find this article interesting?

Your rating is more than welcome or share this article via Social media!

Average rating 3.8 / 5. Vote count: 8

No votes so far! Be the first to rate this post.

We are sorry that this post was not useful for you!

Let us improve this post!

Tell us how we can improve this post?

Patty Mulder

Patty Mulder is an Dutch expert on Management Skills, Personal Effectiveness and Business Communication. She is also a Content writer, Business Coach and Company Trainer and lives in the Netherlands (Europe). Note: all her articles are written in Dutch and we translated her articles to English!

DevOps methodology explained

RASCI Chart explained including an example

Learning Management System (LMS)

Stage Gate Process by Robert Cooper - Toolshero

Stage Gate Process by Robert Cooper explained

Test Driven Development (TDD)

feature driven development fdd toolshero

Feature Driven Development Methodology (FDD)

Also interesting.

Gantt Chart explained plus template

prince2 prince ii project management toolshero

Prince2 Methodology: Phases and Principles

Responsibilty Assignment Matrix - Toolshero

Responsibility Assignment Matrix: the Basics and Template

One response to “moscow method of prioritization explained”.

Thanks for providing a concise and easily understandable explanation. The one thing that stood out to me however, is the example for the Should Have section. Tow bars are clearly “Could have” at best and in this situation would probably end up in the “Won’t have” bucket simply because there’s no justification for them at all on an experimental vehicle that will not be driven on a public road. To make this more believable I’d recommend changing the example for “Should Haves” to either: Seats – the vehicle should have a seat for the driver but as long as someone can drive it somehow it’s not critical. Or Steering Wheel – ideally the vehicle should have a steering wheel, but as long as it CAN be steered (perhaps by levers) then the project will pass. Otherwise, this is a really useful article. Thanks again.

BOOST YOUR SKILLS

Toolshero supports people worldwide ( 10+ million visitors from 100+ countries ) to empower themselves through an easily accessible and high-quality learning platform for personal and professional development.

By making access to scientific knowledge simple and affordable, self-development becomes attainable for everyone, including you! Join our learning platform and boost your skills with Toolshero.

ABOUT TOOLSHERO

Free Toolshero e-book
Memberships & Pricing

TPC and eLearning
What's NEW at TPC?
Read Watch Interact
Practice Review Test
Teacher-Tools
Request a Demo
Get A Quote
Subscription Selection
Seat Calculator
Ad Free Account
Edit Profile Settings
Metric Conversions Questions
Metric System Questions
Metric Estimation Questions
Significant Digits Questions
Proportional Reasoning
Acceleration
Distance-Displacement
Dots and Graphs
Graph That Motion
Match That Graph
Name That Motion
Motion Diagrams
Pos'n Time Graphs Numerical
Pos'n Time Graphs Conceptual
Up And Down - Questions
Balanced vs. Unbalanced Forces
Change of State
Force and Motion
Mass and Weight
Match That Free-Body Diagram
Net Force (and Acceleration) Ranking Tasks
Newton's Second Law
Normal Force Card Sort
Recognizing Forces
Air Resistance and Skydiving
Solve It! with Newton's Second Law
Which One Doesn't Belong?
Component Addition Questions
Head-to-Tail Vector Addition
Projectile Mathematics
Trajectory - Angle Launched Projectiles
Trajectory - Horizontally Launched Projectiles
Vector Addition
Vector Direction
Which One Doesn't Belong? Projectile Motion
Forces in 2-Dimensions
Being Impulsive About Momentum
Explosions - Law Breakers
Hit and Stick Collisions - Law Breakers
Case Studies: Impulse and Force
Impulse-Momentum Change Table
Keeping Track of Momentum - Hit and Stick
Keeping Track of Momentum - Hit and Bounce
What's Up (and Down) with KE and PE?
Energy Conservation Questions
Energy Dissipation Questions
Energy Ranking Tasks
LOL Charts (a.k.a., Energy Bar Charts)
Match That Bar Chart
Words and Charts Questions
Name That Energy
Stepping Up with PE and KE Questions
Case Studies - Circular Motion
Circular Logic
Forces and Free-Body Diagrams in Circular Motion
Gravitational Field Strength
Universal Gravitation
Angular Position and Displacement
Linear and Angular Velocity
Angular Acceleration
Rotational Inertia
Balanced vs. Unbalanced Torques
Getting a Handle on Torque
Torque-ing About Rotation
Properties of Matter
Fluid Pressure
Buoyant Force
Sinking, Floating, and Hanging
Pascal's Principle
Flow Velocity
Bernoulli's Principle
Balloon Interactions
Charge and Charging
Charge Interactions
Charging by Induction
Conductors and Insulators
Coulombs Law
Electric Field
Electric Field Intensity
Polarization
Case Studies: Electric Power
Know Your Potential
Light Bulb Anatomy
I = ∆V/R Equations as a Guide to Thinking
Parallel Circuits - ∆V = I•R Calculations
Resistance Ranking Tasks
Series Circuits - ∆V = I•R Calculations
Series vs. Parallel Circuits
Equivalent Resistance
Period and Frequency of a Pendulum
Pendulum Motion: Velocity and Force
Energy of a Pendulum
Period and Frequency of a Mass on a Spring
Horizontal Springs: Velocity and Force
Vertical Springs: Velocity and Force
Energy of a Mass on a Spring
Decibel Scale
Frequency and Period
Closed-End Air Columns
Name That Harmonic: Strings
Rocking the Boat
Wave Basics
Matching Pairs: Wave Characteristics
Wave Interference
Waves - Case Studies
Color Addition and Subtraction
Color Filters
If This, Then That: Color Subtraction
Light Intensity
Color Pigments
Converging Lenses
Curved Mirror Images
Law of Reflection
Refraction and Lenses
Total Internal Reflection
Who Can See Who?
Formulas and Atom Counting
Lab Equipment
Atomic Models
Bond Polarity
Entropy Questions
Cell Voltage Questions
Heat of Formation Questions
Reduction Potential Questions
Oxidation States Questions
Measuring the Quantity of Heat
Hess's Law
Oxidation-Reduction Questions
Galvanic Cells Questions
Thermal Stoichiometry
Molecular Polarity
Quantum Mechanics
Balancing Chemical Equations
Bronsted-Lowry Model of Acids and Bases
Classification of Matter
Collision Model of Reaction Rates
Density Ranking Tasks
Dissociation Reactions
Complete Electron Configurations
Elemental Measures
Enthalpy Change Questions
Equilibrium Concept
Equilibrium Constant Expression
Equilibrium Calculations - Questions
Equilibrium ICE Table
Intermolecular Forces Questions
Ionic Bonding
Lewis Electron Dot Structures
Limiting Reactants
Line Spectra Questions
Mass Stoichiometry
Measurement and Numbers
Metals, Nonmetals, and Metalloids
Metric Estimations
Metric System
Molarity Ranking Tasks
Mole Conversions
Name That Element
Names to Formulas
Names to Formulas 2
Nuclear Decay
Particles, Words, and Formulas
Periodic Trends
Precipitation Reactions and Net Ionic Equations
Pressure Concepts
Pressure-Temperature Gas Law
Pressure-Volume Gas Law
Chemical Reaction Types
Significant Digits and Measurement
States Of Matter Exercise
Stoichiometry Law Breakers
Stoichiometry - Math Relationships
Subatomic Particles
Spontaneity and Driving Forces
Gibbs Free Energy
Volume-Temperature Gas Law
Acid-Base Properties
Energy and Chemical Reactions
Chemical and Physical Properties
Valence Shell Electron Pair Repulsion Theory
Writing Balanced Chemical Equations
Mission CG1
Mission CG10
Mission CG2
Mission CG3
Mission CG4
Mission CG5
Mission CG6
Mission CG7
Mission CG8
Mission CG9
Mission EC1
Mission EC10
Mission EC11
Mission EC12
Mission EC2
Mission EC3
Mission EC4
Mission EC5
Mission EC6
Mission EC7
Mission EC8
Mission EC9
Mission RL1
Mission RL2
Mission RL3
Mission RL4
Mission RL5
Mission RL6
Mission KG7
Mission RL8
Mission KG9
Mission RL10
Mission RL11
Mission RM1
Mission RM2
Mission RM3
Mission RM4
Mission RM5
Mission RM6
Mission RM8
Mission RM10
Mission LC1
Mission RM11
Mission LC2
Mission LC3
Mission LC4
Mission LC5
Mission LC6
Mission LC8
Mission SM1
Mission SM2
Mission SM3
Mission SM4
Mission SM5
Mission SM6
Mission SM8
Mission SM10
Mission KG10
Mission SM11
Mission KG2
Mission KG3
Mission KG4
Mission KG5
Mission KG6
Mission KG8
Mission KG11
Mission F2D1
Mission F2D2
Mission F2D3
Mission F2D4
Mission F2D5
Mission F2D6
Mission KC1
Mission KC2
Mission KC3
Mission KC4
Mission KC5
Mission KC6
Mission KC7
Mission KC8
Mission AAA
Mission SM9
Mission LC7
Mission LC9
Mission NL1
Mission NL2
Mission NL3
Mission NL4
Mission NL5
Mission NL6
Mission NL7
Mission NL8
Mission NL9
Mission NL10
Mission NL11
Mission NL12
Mission MC1
Mission MC10
Mission MC2
Mission MC3
Mission MC4
Mission MC5
Mission MC6
Mission MC7
Mission MC8
Mission MC9
Mission RM7
Mission RM9
Mission RL7
Mission RL9
Mission SM7
Mission SE1
Mission SE10
Mission SE11
Mission SE12
Mission SE2
Mission SE3
Mission SE4
Mission SE5
Mission SE6
Mission SE7
Mission SE8
Mission SE9
Mission VP1
Mission VP10
Mission VP2
Mission VP3
Mission VP4
Mission VP5
Mission VP6
Mission VP7
Mission VP8
Mission VP9
Mission WM1
Mission WM2
Mission WM3
Mission WM4
Mission WM5
Mission WM6
Mission WM7
Mission WM8
Mission WE1
Mission WE10
Mission WE2
Mission WE3
Mission WE4
Mission WE5
Mission WE6
Mission WE7
Mission WE8
Mission WE9
Vector Walk Interactive
Name That Motion Interactive
Kinematic Graphing 1 Concept Checker
Kinematic Graphing 2 Concept Checker
Graph That Motion Interactive
Two Stage Rocket Interactive
Rocket Sled Concept Checker
Force Concept Checker
Free-Body Diagrams Concept Checker
Free-Body Diagrams The Sequel Concept Checker
Skydiving Concept Checker
Elevator Ride Concept Checker
Vector Addition Concept Checker
Vector Walk in Two Dimensions Interactive
Name That Vector Interactive
River Boat Simulator Concept Checker
Projectile Simulator 2 Concept Checker
Projectile Simulator 3 Concept Checker
Hit the Target Interactive
Turd the Target 1 Interactive
Turd the Target 2 Interactive
Balance It Interactive
Go For The Gold Interactive
Egg Drop Concept Checker
Fish Catch Concept Checker
Exploding Carts Concept Checker
Collision Carts - Inelastic Collisions Concept Checker
Its All Uphill Concept Checker
Stopping Distance Concept Checker
Chart That Motion Interactive
Roller Coaster Model Concept Checker
Uniform Circular Motion Concept Checker
Horizontal Circle Simulation Concept Checker
Vertical Circle Simulation Concept Checker
Race Track Concept Checker
Gravitational Fields Concept Checker
Orbital Motion Concept Checker
Angular Acceleration Concept Checker
Balance Beam Concept Checker
Torque Balancer Concept Checker
Aluminum Can Polarization Concept Checker
Charging Concept Checker
Name That Charge Simulation
Coulomb's Law Concept Checker
Electric Field Lines Concept Checker
Put the Charge in the Goal Concept Checker
Circuit Builder Concept Checker (Series Circuits)
Circuit Builder Concept Checker (Parallel Circuits)
Circuit Builder Concept Checker (∆V-I-R)
Circuit Builder Concept Checker (Voltage Drop)
Equivalent Resistance Interactive
Pendulum Motion Simulation Concept Checker
Mass on a Spring Simulation Concept Checker
Particle Wave Simulation Concept Checker
Boundary Behavior Simulation Concept Checker
Slinky Wave Simulator Concept Checker
Simple Wave Simulator Concept Checker
Wave Addition Simulation Concept Checker
Standing Wave Maker Simulation Concept Checker
Color Addition Concept Checker
Painting With CMY Concept Checker
Stage Lighting Concept Checker
Filtering Away Concept Checker
InterferencePatterns Concept Checker
Young's Experiment Interactive
Plane Mirror Images Interactive
Who Can See Who Concept Checker
Optics Bench (Mirrors) Concept Checker
Name That Image (Mirrors) Interactive
Refraction Concept Checker
Total Internal Reflection Concept Checker
Optics Bench (Lenses) Concept Checker
Kinematics Preview
Velocity Time Graphs Preview
Moving Cart on an Inclined Plane Preview
Stopping Distance Preview
Cart, Bricks, and Bands Preview
Fan Cart Study Preview
Friction Preview
Coffee Filter Lab Preview
Friction, Speed, and Stopping Distance Preview
Up and Down Preview
Projectile Range Preview
Ballistics Preview
Juggling Preview
Marshmallow Launcher Preview
Air Bag Safety Preview
Colliding Carts Preview
Collisions Preview
Engineering Safer Helmets Preview
Push the Plow Preview
Its All Uphill Preview
Energy on an Incline Preview
Modeling Roller Coasters Preview
Hot Wheels Stopping Distance Preview
Ball Bat Collision Preview
Energy in Fields Preview
Weightlessness Training Preview
Roller Coaster Loops Preview
Universal Gravitation Preview
Keplers Laws Preview
Kepler's Third Law Preview
Charge Interactions Preview
Sticky Tape Experiments Preview
Wire Gauge Preview
Voltage, Current, and Resistance Preview
Light Bulb Resistance Preview
Series and Parallel Circuits Preview
Thermal Equilibrium Preview
Linear Expansion Preview
Heating Curves Preview
Electricity and Magnetism - Part 1 Preview
Electricity and Magnetism - Part 2 Preview
Vibrating Mass on a Spring Preview
Period of a Pendulum Preview
Wave Speed Preview
Slinky-Experiments Preview
Standing Waves in a Rope Preview
Sound as a Pressure Wave Preview
DeciBel Scale Preview
DeciBels, Phons, and Sones Preview
Sound of Music Preview
Shedding Light on Light Bulbs Preview
Models of Light Preview
Electromagnetic Radiation Preview
Electromagnetic Spectrum Preview
EM Wave Communication Preview
Digitized Data Preview
Light Intensity Preview
Concave Mirrors Preview
Object Image Relations Preview
Snells Law Preview
Reflection vs. Transmission Preview
Magnification Lab Preview
Reactivity Preview
Ions and the Periodic Table Preview
Periodic Trends Preview
Chemical Reactions Preview
Intermolecular Forces Preview
Melting Points and Boiling Points Preview
Bond Energy and Reactions Preview
Reaction Rates Preview
Ammonia Factory Preview
Stoichiometry Preview
Nuclear Chemistry Preview
Gaining Teacher Access
Task Tracker Directions
Conceptual Physics Course
On-Level Physics Course
Honors Physics Course
Chemistry Concept Builders
All Chemistry Resources
Users Voice
Tasks and Classes
Webinars and Trainings
Subscription
Subscription Locator
1-D Kinematics
Newton's Laws
Vectors - Motion and Forces in Two Dimensions
Momentum and Its Conservation
Work and Energy
Circular Motion and Satellite Motion
Thermal Physics
Static Electricity
Electric Circuits
Vibrations and Waves
Sound Waves and Music
Light and Color
Reflection and Mirrors
About the Physics Interactives
Task Tracker
Usage Policy
Newtons Laws
Vectors and Projectiles
Forces in 2D
Momentum and Collisions
Circular and Satellite Motion
Balance and Rotation
Electromagnetism
Waves and Sound
Atomic Physics
Forces in Two Dimensions
Work, Energy, and Power
Circular Motion and Gravitation
Sound Waves
1-Dimensional Kinematics
Circular, Satellite, and Rotational Motion
Einstein's Theory of Special Relativity
Waves, Sound and Light
QuickTime Movies
About the Concept Builders
Pricing For Schools
Directions for Version 2
Measurement and Units
Relationships and Graphs
Rotation and Balance
Vibrational Motion
Reflection and Refraction
Teacher Accounts
Kinematic Concepts
Kinematic Graphing
Wave Motion
Sound and Music
About CalcPad
1D Kinematics
Vectors and Forces in 2D
Simple Harmonic Motion
Rotational Kinematics
Rotation and Torque
Rotational Dynamics
Electric Fields, Potential, and Capacitance
Transient RC Circuits
Light Waves
Units and Measurement
Stoichiometry
Molarity and Solutions
Thermal Chemistry
Acids and Bases
Kinetics and Equilibrium
Solution Equilibria
Oxidation-Reduction
Nuclear Chemistry
Newton's Laws of Motion
Work and Energy Packet
Static Electricity Review
NGSS Alignments
1D-Kinematics
Projectiles
Circular Motion
Magnetism and Electromagnetism
Graphing Practice
About the ACT
ACT Preparation
For Teachers
Other Resources
Solutions Guide
Solutions Guide Digital Download
Motion in One Dimension
Work, Energy and Power
Chemistry of Matter
Measurement and the Metric System
Algebra Based On-Level Physics
Honors Physics
Conceptual Physics
Other Tools
Frequently Asked Questions
Purchasing the Download
Purchasing the Digital Download
About the NGSS Corner
NGSS Search
Force and Motion DCIs - High School
Energy DCIs - High School
Wave Applications DCIs - High School
Force and Motion PEs - High School
Energy PEs - High School
Wave Applications PEs - High School
Crosscutting Concepts
The Practices
Physics Topics
NGSS Corner: Activity List
NGSS Corner: Infographics
About the Toolkits
Position-Velocity-Acceleration
Position-Time Graphs
Velocity-Time Graphs
Newton's First Law
Newton's Second Law
Newton's Third Law
Terminal Velocity
Projectile Motion
Forces in 2 Dimensions
Impulse and Momentum Change
Momentum Conservation
Work-Energy Fundamentals
Work-Energy Relationship
Roller Coaster Physics
Satellite Motion
Electric Fields
Circuit Concepts
Series Circuits
Parallel Circuits
Describing-Waves
Wave Behavior Toolkit
Standing Wave Patterns
Resonating Air Columns
Wave Model of Light
Plane Mirrors
Curved Mirrors
Teacher Guide
Using Lab Notebooks
Current Electricity
Light Waves and Color
Reflection and Ray Model of Light
Refraction and Ray Model of Light
Teacher Resources
Subscriptions

Newton's Laws
Einstein's Theory of Special Relativity
About Concept Checkers
School Pricing
Newton's Laws of Motion
Newton's First Law
Newton's Third Law

Mechanics: Work, Energy and Power

Work, energy and power: problem set overview.

There are 20 ready-to-use problem sets on the topic of Work, Energy, and Power. The problems target your ability to use equations related to work and power, to calculate the kinetic, potential and total mechanical energy, and to use the work-energy relationship in order to determine the final speed, stopping distance or final height of an object.

Work results when a force acts upon an object to cause a displacement (or a motion) or, in some instances, to hinder a motion of a moving object. Three variables are of importance in this definition - force, displacement, and the extent to which the force causes or hinders the displacement. Each of these three variables find their way into the equation for work. That equation is:

Work = Force • Displacement • Cosine(theta)

W = F • d • cos(Θ)

Since the standard metric unit of force is the Newton and the standard meteric unit of displacement is the meter, then the standard metric unit of work is a Newton•meter, defined as a Joule and abbreviated with a J.

The most complicated part of the work equation and work calculations is the meaning of the angle theta (Θ) in the above equation. The angle is not just any stated angle in the problem; it is the angle between the F and the d vectors. In solving work problems, one must always be aware of this definition - theta is the angle between the force and the displacement which it causes. If the force is in the same direction as the displacement, then the angle is 0 degrees. If the force is in the opposite direction as the displacement, then the angle is 180 degrees. If the force is up and the displacement is to the right, then the angle is 90 degrees. This is summarized in the graphic below.

Power is defined as the rate at which work is done upon an object. Like all rate quantities, power is a time-based quantity. Power is related to how fast a job is done. Two identical jobs or tasks can be done at different rates - one slowly or and one rapidly. The work is the same in each case (since they are identical jobs) but the power is different. The equation for power shows the importance of time:

Power = Work / time

The unit for standard metric work is the Joule and the standard metric unit for time is the second, so the standard metric unit for power is a Joule / second, defined as a Watt and abbreviated W . Special attention should be taken so as not to confuse the unit Watt, abbreviated W, with the quantity work, also abbreviated by the letter W.

Combining the equations for power and work can lead to a second equation for power. Power is W/t and work is F•d•cos(theta). Substituting the expression for work into the power equation yields P = F•d•cos(theta)/t. If this equation is re-written as

P = F • cos(Θ) • (d/t)

one notices a simplification which could be made. The d/t ratio is the speed value for a constant speed motion or the average speed for an accelerated motion. Thus, the equation can be re-written as

P = F • v • cos(Θ)

where v is the constant speed or the average speed value. A few of the problems in these problem sets will utilize this derived equation for power.

Mechanical, Kinetic and Potential Energies

There are two forms of mechanical energy - potential energy and kinetic energy.

Potential energy is the stored energy of position. In this set of problems, we will be most concerned with the stored energy due to the vertical position of an object within Earth's gravitational field. Such energy is known as the gravitational potential energy ( PE grav ) and is calculated using the equation

PE grav = m•g•h

where m is the mass of the object (with standard units of kilograms), g is the gravitational field constant (9.8 N/kg) and h is the height of the object (with standard units of meters) above some arbitraily defined zero level (such as the ground or the top of a lab table in a physics room). Potential energy can also be stored in a mass-spring system. This is known as elastic potential energy ( PE elastic ). As a spring is stretched some distance x from its equilibrium position, potential energy is stored in the spring-mass system. This type of potential energy is calculated using the equation

PE elastic = 1/2• k • x 2

where x is the amount of stretch from the equilibrium position and k is the spring constant of the spring.

Kinetic energy is defined as the energy possessed by an object due to its motion. An object must be moving to possess kinetic energy. The amount of kinetic energy ( KE ) possessed by a moving object is dependent upon mass and speed. The equation for kinetic energy is

KE = 0.5 • m • v 2

where m is the mass of the object (with standard units of kilograms) and v is the speed of the object (with standard units of m/s).

The total mechanical energy possessed by an object is the sum of its kinetic and potential energies.

Work-Energy Connection

There is a relationship between work and total mechanical energy. The relationship is best expressed by the equation

TME i + W nc = TME f

In words, this equation says that the initial amount of total mechanical energy ( TME i ) of a system is altered by the work which is done to it by non-conservative forces ( W nc ). The final amount of total mechanical energy ( TME f ) possessed by the system is equivalent to the initial amount of energy ( TME i ) plus the total work done by these non-conservative forces ( W nc ).

The mechanical energy possessed by a system is the sum of the kinetic energy and the potential energy. Thus the above equation can be re-arranged to the form of

KE i + PE i + W nc = KE f + PE f

0.5 • m • v i 2 + m • g • h i + F • d • cos(Θ) = 0.5 • m • v f 2 + m • g • h f

The work done to a system by non-conservative forces (W nc ) can be described as either positive work or negative work. Positive work is done on a system when the force doing the work acts in the direction of the motion of the object. Negative work is done when the force doing the work opposes the motion of the object. When a positive value for work is substituted into the work-energy equation above, the final amount of energy will be greater than the initial amount of energy; the system is said to have gained mechanical energy. When a negative value for work is substituted into the work-energy equation above, the final amount of energy will be less than the initial amount of energy; the system is said to have lost mechanical energy. There are occasions in which the only forces doing work are conservative forces (sometimes referred to as internal forces). Typically, such conservative forces include gravitational forces, elastic or spring forces, electrical forces and magnetic forces. When the only forces doing work are conservative forces, then the W nc term in the equation above is zero. In such instances, the system is said to have conserved its mechanical energy.

The proper approach to a work-energy problem involves carefully reading the problem description and substituting values from it into the work-energy equation listed above. Inferences about certain terms will have to be made based on a conceptual understanding of kinetic and potential energy. For instance, if the object is initially on the ground, then it can be inferred that the PE i is 0 and that term can be canceled from the work-energy equation. In other instances, the height of the object is the same in the initial state as in the final state, so the PE i and the PE f terms are the same. As such, they can be mathematically canceled from each side of the equation. In other instances, the speed is constant during the motion, so the KE i and KE f terms are the same and can thus be mathematically canceled from each side of the equation. Finally, there are instances in which the KE and or the PE terms are not stated; rather, the mass (m), speed (v), and height (h) is given. In such instances, the KE and PE terms can be determined using their respective equations. Make it your habit from the beginning to simply start with the work and energy equation, to cancel terms which are zero or unchanging, to substitute values of energy and work into the equation and to solve for the stated unknown.

Habits of an Effective Problem-Solver

An effective problem solver by habit approaches a physics problem in a manner that reflects a collection of disciplined habits. While not every effective problem solver employs the same approach, they all have habits which they share in common. These habits are described briefly here. An effective problem-solver...

...reads the problem carefully and develops a mental picture of the physical situation. If needed, they sketch a simple diagram of the physical situation to help visualize it.
...identifies the known and unknown quantities in an organized manner, often times recording them on the diagram itself. They equate given values to the symbols used to represent the corresponding quantity (e.g., m = 1.50 kg, v i = 2.68 m/s, F = 4.98 N, t = 0.133 s, v f = ???).
...plots a strategy for solving for the unknown quantity. The strategy will typically center saround the use of physics equations and is heavily dependent upon an understanding of physics principles.
...identifies the appropriate formula(s) to use, often times writing them down. Where needed, they perform the needed conversion of quantities into the proper unit.
...performs substitutions and algebraic manipulations in order to solve for the unknown quantity.

Additional Readings/Study Aids:

The following pages from The Physics Classroom tutorial may serve to be useful in assisting you in the understanding of the concepts and mathematics associated with these problems.

Sample Work Calculations
Resolving the Weight Vector on an Inclined Plane
Potential Energy
Kinetic Energy
Mechanical Energy
Situations Involving External Forces
Situations Involving Energy Conservation

Watch a Video

We have developed and continue to develop Video Tutorials on introductory physics topics. You can find these videos on our YouTube channel . We have an entire Playlist on the topic of Work and Energy .

Your Project
MoSCoW Method

What is the MoSCoW Method?

The MoSCoW Method is a prioritization tool that helps professionals in managing their time and effort .

To do so, it proposes to classify the importance of the different characteristics of a product (or a Project) according to their importance .

Its name is an acronym of the 4 Prioritization Categories proposed (adding two “o”):

M ust Have .
S hould Have .
C ould Have .
W on’t Have .

Four Prioritization Categories

Must Have : Essential Requirements that the product or project must have.

Critical Features without replacement.

Should Have : Important desired Requirements for the product or project.

They can be substituted if necessary.

Could Have : Improvements to the product or project.

There are different alternatives.

Won’t have : Characteristics agreed not to be adopted .

No one will waste time implementing them.

Let’s see the first example:

MoSCoW Method example

Imagine that you have been hired to create a Website for a Law firm.

They want a professional Site where people can Register and, once inside, track their court cases .

Since you want to deliver the best possible Site on time, you decide to follow the MoSCoW method .

How does it look like?

Must Have :

Solid programming without any bugs.
A Solid Register System.
A Safe and Reliable personal directory.

Should Have :

A Fast Site.
An outstanding Design.
Notifications sent by e-mail.

Could Have :

Custom menus.
Suggestions.
A Blog section with latest news.

Won’t Have :

Paid content.
A Public Members section.

As we usually say, this Method may seem obvious.

Then… Why is it important?

Why is the MoSCoW Method important?

Many of professionals end up wasting time , effort and resources on useless task s that are ultimately not essential at all.

Surely you have experienced this situation working in a Team:

Everyone spends hours modifying a minor feature and, ultimately, the important thing is missing .

That is why this Method is so important:

Because it concentrates your efforts and forces you to think about what is really important .

As you can imagine, this Tool can be employed in practically all kinds of situations.

But when do we especially recommend it?

When should you use the MoSCoW Method?

We highly recommend to use the MoSCoW Method:

To put order and prioritization.
To avoid wasting time with non-essential touch-ups.
In order to meet the Essential Requirements.
When the product can have very different characteristics.

Now, let’s see more examples:

MoSCoW Method examples

We have chosen different real examples where the MoSCoW Method can be of great help for the development of certain products.

Let’s begin:

A Wallet - MoSCoW Method example

Let’s imagine that you are developing a wallet .

As you know, wallets are very modular products.

They can have:

Several or few departments for cards.
Coin purse… or not.
1 or 2 bill slots.

There is not a canonical wallet (one that is the benchmark for all the others).

That is why you decided to use the MoSCoW Method to develop it.

After some thoughts, you decide that your wallet:

2 bill slots.
8 compartments for credit cards.
High resistance materials and sewing.
Leather as its main material.
A translucid Credit card compartment.
A transverse horizontal compartment.
A striking color on the inside of the bill slots.
Completely black exterior color.
One translucid compartment for small photos.
A Coin purse.
A Passport compartment.

Making a Cake - MoSCoW Method example

In this example, we’ll imagine that you are preparing a wedding Cake .

You have a very rigid deadline (the wedding day, of course).

In addition, as you also know, Cakes can have lots of variations.

We could say they are very modular .

That is why you decide to use the MoSCoW Method.

How does it look?

Well, your Cake:

White coating.
Two sugar figurines on top.
6 layers of sponge cake inside.
Belgian chocolate between the layers.
Decorations on the edges
Sugar flowers.
Chocolate balls.
Scattered sugar pearls.
Multicolor layers.
An excessive amount of decoration.
Fruit flavor.

Designing a Poster - MoSCoW Method example

You are now an artist hired to Design a poster for a Rock concert.

Obviously, this is a Design job with infinite variations possible.

Also, you have a close deadline to finish it.

No need to mention that you will use the MoSCoW Method.

Finally, the Poster:

The name of the Main rock band, very prominent.
Images and colors that best suit their style.
A typeface that best suits the musical style.
An illustration related to Rock in the middle.
The name of the rest of the bands that will play.
Where and when it will take place.
Where you can buy the tickets.
Nearby metro and bus stations.
The name of the city.
The maximum capacity of the stadium
At what time each band will play.

Summarizing

The MoSCoW Method is a prioritization tool that helps professionals in managing their time and effort.

It proposes to classify the importance of the different characteristics of a product in 4 Categories :

M ust Have.
S hould Have.
C ould Have.
W on’t Have.

Although this Method can be used in all kinds of situations, we highly recommend to use it:

When working in a team .
In Design tasks .
When there is a close deadline .
With modular products or projects .
Economies of Scale
Business Plan for Beginners
Business Plan Basics
How to write a Business Plan
Cash Flow Calculation
Raising Funds for a Business
4 C’s of Credit
Business Plan Templates
Customer Insight
Customer Experience
Customer Pain Points
4C Marketing Model
RATER Model
Augmented Product
Product Mix
Unique Selling Proposition
DAGMAR Model
Marketing Storytelling
Content Marketing
Psychographics
Barnum Effect
Market Segmentation
Market Research & Big Data
Marketing to Generation Z
4P Marketing Mix
7P Marketing Mix
Sales Funnel
Loyalty Ladder
RACE Planning
Push and Pull Marketing
Marketing Strategy
Marketing Templates
Starting your own business
From Startup to a Business
Entrepreneur FAQs
Start your Business Idea
Entrepreneur Golden Rules
Innovate or Imitate?
Design Thinking
SCAMPER Model
AAR Process
Work From Home
Growth strategies for Startups
VMOST Analysis
3P Framework
SOAR Analysis
TELOS Analysis
5 C’s of Entrepreneurship
Crowdfunding
BATNA & ZOPA Negotiation
Entrepreneur with no Money
Entrepreneurship Templates
Strategy vs Tactics
Mission and Vision
Business Values
Value Chain
Scenario Planning
Porter 6 Forces
Bowman’s Strategy Clock
GE-McKinsey Matrix
Delta Model
PEST Analysis
PESTEL Analysis
SWOT Analysis
VRIO Framework
Strategy Canvas
Competitive Advantages
Porter’s Four Corners
5 Ps of Strategy
Porter’s Generic Strategies
Porter’s Diamond Model
Wardley Map
Core Competencies
Resource Based View
Bridges Transition Model
CAGE Distance Framework
McKinsey’s 3 Horizons
Vertical Integration
Horizontal Integration
Blue Ocean Strategy
Red Ocean Strategy
Porter 5 Forces
Ansoff Matrix
McKinsey 7S Framework
CATWOE Analysis
Strategy Pyramid
Bain’s RAPID Framework
Balanced Scorecard
Resources and Capabilities
Strategy of Apple
Strategy of Amazon
Strategy of Starbucks
Strategy Templates
Communicate Effectively
COIN Conversation Model
SCARF Model
SBI Feedback Model
CEDAR Feedback Model
How to behave at a meeting
Gibbs’ Reflective Cycle
Bloom’s Taxonomy
5E Learning Model
9-Box Performance Grid
SEEDS Bias Model
Halo Effect
Pygmalion Rosenthal Effect
Dunning-Kruger Effect
How to be an Entrepreneur
How to be a Leader
Mintzberg Managerial Roles
Cog’s Ladder
The Peter Principle
How to Negotiate
Teamwork Skills and Profiles
Gantt Chart
RACI Matrix
Eisenhower Matrix
FMEA Process
Problem Solving
Ishikawa Fishbone diagram
5 Whys Method
8 Disciplines Method
ADDIE Model
ORAPAPA Method
Cynefin Framework
Just In Time
SMART Goals
KISS Principle
Birkinshaw’s 4 Dimensions
Parkinson’s Law
OGSM Framework
OKR Methodology
APQP Framework
Theory of Constraints
Success through Organization
ADKAR Model
Lewin’s Change Model
Kotter’s 8-Step Model
The Greiner Curve
GAP Analysis
Planning Templates
Mean, Median and Mode
Define your Data
Pareto Principle 80/20 Rule
Decision Matrix
Decision Tree
TARA Framework
Root Cause Analysis
Simplex Process
Forecasting Methods
Product Life Cycle
How to use Google Trends
Correlation vs Causation

We're not around right now. But you can send us an email and we'll get back to you, asap.

Log in with your credentials

Forgot your details.

Guide: MoSCoW Method

Author: Daniel Croft

Daniel Croft is an experienced continuous improvement manager with a Lean Six Sigma Black Belt and a Bachelor's degree in Business Management. With more than ten years of experience applying his skills across various industries, Daniel specializes in optimizing processes and improving efficiency. His approach combines practical experience with a deep understanding of business fundamentals to drive meaningful change.

The MoSCoW Method transcends being just a prioritization tool; it is a strategic approach for navigating the intricate decision-making in project management. This methodology excels by offering a structured framework, facilitating discussions among stakeholders to assess and align on the relative importance of various tasks and features in a project.

Central to MoSCoW is its acronym, denoting four priority categories – Must have, Should have, Could have, and Won’t have. This classification is crucial in managing stakeholder expectations, directing the project team’s focus towards critical elements, and charting a clear course for project advancement.

What is the MoSCoW Method?

The MoSCoW method is used as a prioritization tool, but it is more than just that; it is also a strategic approach to handling complex decision-making processes that you can encounter in project management. This method shines by offering a structured framework for stakeholders to discuss, debate, and ultimately agree on the relative importance of different tasks or features within a project.

The uniqueness of the MoSCoW method is within its acronym, which represents four priority categories. Must have, Should have, Could have, and Won’t have. This structure is key to managing stakeholder expectations and ensuring that a project team focuses on the most crucial elements first, setting a clear path for project progression.

The MoSCoW Categories

In the ‘ Must have ‘ category, you find the key activities that are essential to your project . These are non-negotiable and pivotal for the project’s success. This category often comprises items that, if omitted, would make the project irrelevant or non-compliant with essential criteria like legal standards or core objectives.

Should Have

Moving to the ‘ Should have ‘ category, we encounter important elements that, while not critical to the project’s existence, greatly enhance its value and effectiveness . These are features that stakeholders strongly desire, and their inclusion could significantly enhance the project’s outcome . However, their absence wouldn’t label the project a failure.

The ‘ Could have ‘ category is where you place desirable but less critical elements . These are often enhancements that would be nice to include but aren’t vital to the project’s success . The inclusion of these elements is usually subject to resource availability and project timelines.

The ‘ Won’t have ‘ category is often misunderstood but is crucial for setting realistic boundaries. It includes elements that, although potentially beneficial, are beyond the scope of the current project phase or constraints. This clear demarcation helps manage expectations and focus on what’s achievable within the project’s constraints.

How to Apply the MoSCoW Method: A Step-by-Step Guide

Implementing the MoSCoW Method in a project requires a systematic approach, ensuring that all aspects of the project are considered and aligned with the prioritization framework. Here’s a detailed look into each step of implementing this method:

Step 1: Gather Requirements

The first step in the MoSCoW method requires gathering a list of the tasks , activities, features, or requirements you need to prioritize in your project. For this step, you should engage with all relevant stakeholders , including project sponsors, end-users, and technical teams. This ensures that the requirements reflect a wide range of perspectives and needs.

To help decide the categorize of each task in a later step you should understand the overall goals of the project . You will also need to gain an understanding of technical, business, time, and resource constraints right from the start. This helps in setting realistic expectations for what can be achieved.

Step 2: Categories Each Requirement

The next step is to, as a team with the relevant stakeholders, run a categorization session . Doing this with the stakeholders involved will help to gain buy-in and support for the project as well as a shared understanding of priorities.

Each requirement’s placement in the MoSCoW categories should be a subject of discussion. Different stakeholders may have varying views on what is a ‘ Must have ‘ or ‘ Should have ‘, and these need to be reconciled.

For each decision, documenting the rationale behind the categorization can be valuable, especially for future reference or when explaining decisions to others not involved in the process.

Step 3: Review and Adjust

You will need to ensure the decisions of the categories are balanced and achievable within the scope once all are allocated. You may find that you still have too many must-haves and should-haves that either some activities need to be downgraded or a consideration to go back to decision-makers and create a case for more resources of time to achieve what is needed.

Step 4: Use as a Guiding Tool

You should continue to use the MoSCoW prioritization to inform decisions throughout the project lifecycle. This helps maintain focus on what’s most important . Prioritization can guide where to allocate resources and effort, especially when under constraints.

Step 5: Update as Necessary

Finally, regularly revisit the MoSCoW categorization , especially after major milestones or significant changes in the project environment. Also, be prepared to adjust the priorities in response to new information, stakeholder feedback, or changes in the external environment.

Implementing the MoSCoW Method is an exercise in strategic planning and adaptive management. It begins with a comprehensive gathering of project requirements, engaging a broad spectrum of stakeholders to ensure a multifaceted view of the project’s needs. The heart of the process lies in the collaborative categorization of these requirements, balancing differing perspectives to establish a shared priority framework.

As the project progresses, this method serves as a dynamic guide, directing resources and decision-making effectively. Regularly revisiting and adjusting these priorities ensures the project stays aligned with evolving objectives and constraints, making MoSCoW an indispensable tool for successful project management.

Kuhn, J., 2009. Decrypting the MoSCoW analysis. The workable, practical guide to Do IT Yourself , 5 .
Ahmad, K.S., Ahmad, N., Tahir, H. and Khan, S., 2017, July. Fuzzy_MoSCoW: A fuzzy based MoSCoW method for the prioritization of software requirements. In 2017 International Conference on Intelligent Computing, Instrumentation and Control Technologies (ICICICT) (pp. 433-437). IEEE.

Q: What types of projects is the MoSCoW method best suited for?

A: The MoSCoW method is versatile and can be used for various types of projects, ranging from software development and website redesign to manufacturing and logistics. It’s particularly useful for projects with multiple stakeholders and those that require a clear understanding of task priority.

Q: How often should the MoSCoW list be reviewed and updated?

A: The frequency of reviewing the MoSCoW list depends on the project’s complexity and how often its circumstances change. For fast-paced projects, a weekly or bi-weekly review might be necessary. For more stable projects, a monthly review could suffice.

Q: Can the MoSCoW method be integrated with other project management techniques?

A: Absolutely! The MoSCoW method can be used in conjunction with other project management methodologies like Agile, Scrum, or Lean Six Sigma. It serves as a prioritization tool that can easily be incorporated into other frameworks to make them even more effective.

Q: What should I do if stakeholders disagree on the categorization of tasks?

A: If there’s disagreement on task categorization, it’s useful to have a facilitated discussion to reach a consensus. You can also use a weighted scoring system to quantitatively assess each task’s importance, which can help in making more objective decisions.

Q: Are there any tools or software that can help in applying the MoSCoW method?

A: While the MoSCoW method can be applied using simple tools like whiteboards and Post-It notes, there are also specialized project management software that offer built-in MoSCoW categorization features. These tools can be particularly helpful for larger or more complex projects.

Daniel Croft

Daniel Croft is a seasoned continuous improvement manager with a Black Belt in Lean Six Sigma. With over 10 years of real-world application experience across diverse sectors, Daniel has a passion for optimizing processes and fostering a culture of efficiency. He's not just a practitioner but also an avid learner, constantly seeking to expand his knowledge. Outside of his professional life, Daniel has a keen Investing, statistics and knowledge-sharing, which led him to create the website www.learnleansigma.com, a platform dedicated to Lean Six Sigma and process improvement insights.

Free Lean Six Sigma Templates

Improve your Lean Six Sigma projects with our free templates. They're designed to make implementation and management easier, helping you achieve better results.

Was this helpful?

IMAGES

Mechanical Energy: Problem Solving Lecture
Mechanical Energy Problem Solutions
How to Calculate Total Mechanical Energy
Mechanical Energy Problem Solutions
Mechanical Energy Problem Solutions
Physics 1 Total Mechanical Energy Solutions

COMMENTS

Mechanical Energy Problem Solutions
I cancelled out the initial kinetic energy because: KE i = ½ mv f2. KE i = (½) (3.5) (0 2) = 0 J. I cancelled out the final potential energy because: PE f = mgh f. PE f = (3.5) (9.8) (0) = 0 J. (Note: In many of these problems I could cancel out mass but did not since it was provided) Since I did not cancel out mass I could answer the ...
9.2 Mechanical Energy and Conservation of Energy
Assume that no energy is lost to friction. At any point in the ride, the total mechanical energy is the same, and it is equal to the energy the car had at the top of the first rise. This is a result of the law of conservation of energy, which says that, in a closed system, total energy is conserved—that is, it is constant. Using subscripts 1 ...
Work, Energy, and Power Problem Sets
Determine Ima's kinetic energy at the top of the loop. b. Determine Ima's potential energy at the top of the loop. c. Assuming negligible losses of energy due to friction and air resistance, determine Ima's total mechanical energy at the bottom of the loop (h=0 m). d. Determine Ima's speed at the bottom of the loop. Audio Guided Solution
Work, Energy, and Power Problem Sets
Problem Set WE8: Total Mechanical Energy. Use mass, speed, and height values to calculate the total amount of mechancial energy possessed by an object. Includes 5 problems. Problem Set WE9: Work and Kinetic Energy 1. Use the work-energy theorem to calculate either the work or the kinetic energy. All problems are highly scaffolded.
How to Calculate Total Mechanical Energy
How to Calculate Total Mechanical Energy. Step 1: Read the problem and identify all variables given within the problem as well as all forms of energy. Step 2: Using the equation for total ...
Energy Equations Basics: Total Mechanical Energy (TME)
Solving for different variables using the Total Mechanical Energy equation using algebra.
Lesson 41: Total Mechanical Energy
Lesson 41: Total Mechanical Energy. A large number of questions you will do involve the Total Mechanical Energy of a system. Total mechanical energy is just the kinetic plus potential energy. As long as there are no outside forces unaccounted for, we know that the totals before and after will be equal. E k + E p = E k ' + E p '.
Conservation of Mechanical Energy Problems and Solutions
At maximum height, (the final position) the kinetic energy is. Kf = ½ mvf2 = ½ (1. 50 kg) (16. 6 m/s) 2 = 206 J. In this problem there are only conservative forces (namely, gravity). The mechanical energy is conserved: Ki + Ui = Kf + Uf. We already found the initial kinetic energy of the snowball: Ki = 300 J.
Mechanical energy
Answer: When mechanical energy is conserved in a system (no non-conservative forces like friction), the total energy at the beginning is equal to the total energy at the end. This principle allows us to relate the potential and kinetic energies at different points in time, simplifying the problem-solving process.
PDF Energy Problem Solving Techniques
Energy Problem Solving. Consider the inclined plane problem that was just worked, but add a spring at the bottom of the incline. The spring will be compressed a distance Δx and then released. Find the velocity of the box when it rises back to where it was first compressed a height of Δh.
Conservation of Energy
Conservation of Energy in general. Throughout the first half of the 19^\text {th} 19th century, engineers realized that thermal heat was another form of energy, capable of mechanical work. By 1850, the law of conservation of energy was formally stated for the first time, as the first law of thermodynamics.
9.1 Work, Power, and the Work-Energy Theorem
The subscripts 2 and 1 indicate the final and initial velocity, respectively. This theorem was proposed and successfully tested by James Joule, shown in Figure 9.2.. Does the name Joule sound familiar? The joule (J) is the metric unit of measurement for both work and energy. The measurement of work and energy with the same unit reinforces the idea that work and energy are related and can be ...
8.3 Conservation of Energy
We found the speed directly from the conservation of mechanical energy, without having to solve the differential equation for the motion of a pendulum (see Oscillations). We can approach this problem in terms of bar graphs of total energy. Initially, the particle has all potential energy, being at the highest point, and no kinetic energy.
Mechanical Energy
The total mechanical energy of Lee Ben Fardest is the sum of the potential and kinetic energies. The two forms of energy sum up to 50 000 Joules. Notice also that the total mechanical energy of Lee Ben Fardest is a constant value throughout his motion. There are conditions under which the total mechanical energy will be a constant value and ...
Calculating Total Mechanical Energy
A body of mass 0.5 kg is hanging at the end of a spring with an original length of 0.3 m. The increase in the length due to the body is 0.1m. Find out the total mechanical energy if the spring ...
How to Solve Conservation of Energy Problems
Example Problem 1 - Solving Conservation of Energy Problems. ... Therefore, it has gained 0.33 Joules of kinetic energy because the total mechanical energy was conserved. Since is started with ...
Total Mechanical Energy Problem
Total mechanical energy is useful in solving problems because it allows us to analyze the motion of an object by considering its energy instead of individual forces. By using the conservation of energy principle, we can solve for unknown variables, such as velocity or height, without needing to know the specific forces acting on the object.
Fact-checking Donald Trump's rally in Bozeman, Montana
Trump took the stage later than expected at his Friday night rally in Bozeman, Montana, after a mechanical problem forced his plane to divert 140 miles east to Billings. The plane landed without ...
MoSCoW Method of Prioritization explained
Meaning and acronym of the MoSCoW Method. Moscow is an acronym made up of the first letters. The two Os have been added to make the word 'moscow' readable, they don't have any meaning themselves. The M stands for 'Must haves', S for 'Should haves', C for 'Could haves' and W for 'Won't haves' or 'Would haves'. Figure ...
Equation Overview for Work, Energy, and Power Problems
Work, Energy and Power: Problem Set Overview There are 20 ready-to-use problem sets on the topic of Work, Energy, and Power. The problems target your ability to use equations related to work and power, to calculate the kinetic, potential and total mechanical energy, and to use the work-energy relationship in order to determine the final speed, stopping distance or final height of an object.
The MoSCoW Method
The MoSCoW method is a simple and highly useful approach that enables you to prioritize project tasks as critical and non-critical. MoSCoW stands for: Must - These are tasks that you must complete for the project to be considered a success. Should - These are critical activities that are less urgent than Must tasks.
MoSCoW Method
The MoSCoW Method is a prioritization tool that helps professionals in managing their time and effort.. To do so, it proposes to classify the importance of the different characteristics of a product (or a Project) according to their importance. Its name is an acronym of the 4 Prioritization Categories proposed (adding two "o"):. M ust Have.; S hould Have.; C ould Have.
Guide: MoSCoW Method
Step 1: Gather Requirements. The first step in the MoSCoW method requires gathering a list of the tasks, activities, features, or requirements you need to prioritize in your project. For this step, you should engage with all relevant stakeholders, including project sponsors, end-users, and technical teams. This ensures that the requirements ...

Mechanical Energy Problem Solutions

3. How much gravitational potential energy does a 35 kg boulder have when 30 meters off the ground?

First Law of Thermodynamics

Second Law of Thermodynamics

JEE-IIT-NCERT Physics & Math

Post a Comment for "Conservation of Mechanical Energy Problems and Solutions"

Share this:

Conservation of Energy

The Conservation of Kinetic Energy

This problem is posted in connection to the upcoming collaboration party hosted by me! Interested people may come forward (just ping me on slack).

8.3 Conservation of Energy

Systems with a Single Particle or Object

Conservation of Energy

Problem-Solving Strategy

Example 8.7

Significance

Example 8.8

Check Your Understanding 8.8

Example 8.9

Check Your Understanding 8.9

Systems with Several Particles or Objects

Total Mechanical Energy Problem

Related to Total Mechanical Energy Problem

2. How is total mechanical energy calculated?

3. Is total mechanical energy conserved?

4. What happens to total mechanical energy when work is done on a system?

5. How is total mechanical energy useful in solving problems?

Similar threads

Hot Threads

Recent Insights

Stand up for the facts!

I would like to contribute

Our Sources

Browse the Truth-O-Meter

MoSCoW Method of Prioritization explained

What is the MoSCoW Method of Prioritization?

Origin and advantages of the MoSCoW Method

Meaning and acronym of the MoSCoW Method

The requirements when you start with the MoSCoW Method

M – Must haves

S – Should haves

C – Could haves

W – Won’t haves (and would haves)

How to reach deadlines using the MoSCoW Method of Prioritization?

It’s Your Turn

More information

Patty Mulder

Related ARTICLES

DevOps methodology explained

RASCI Chart explained including an example

Learning Management System (LMS)

Stage Gate Process by Robert Cooper explained

Test Driven Development (TDD)

Feature Driven Development Methodology (FDD)

Gantt Chart explained plus template

Prince2 Methodology: Phases and Principles

Responsibility Assignment Matrix: the Basics and Template

Leave a Reply Cancel reply

BOOST YOUR SKILLS

POPULAR TOPICS

ABOUT TOOLSHERO

Mechanics: Work, Energy and Power

Mechanical, Kinetic and Potential Energies

Work-Energy Connection

Habits of an Effective Problem-Solver

Additional Readings/Study Aids:

Watch a Video

What is the MoSCoW Method?

Four Prioritization Categories

MoSCoW Method example

Why is the MoSCoW Method important?

When should you use the MoSCoW Method?

MoSCoW Method examples

A Wallet - MoSCoW Method example

Making a Cake - MoSCoW Method example

Designing a Poster - MoSCoW Method example

Summarizing

Log in with your credentials

Guide: MoSCoW Method

What is the MoSCoW Method?