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HELP: Original Lessons on Energy, Work, & Power

Site: Mountain Heights Academy OER
Course: Physics Q4
Book: HELP: Original Lessons on Energy, Work, & Power
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Date: Friday, 4 April 2025, 11:57 AM

Description

These are the original lessons on energy, work, and power from Q3.  Review as needed.

Table of contents

Introduction to Energy


These young children are very active. They seem to be brimming with energy. You probably know that lots of things have energy—from batteries to the sun. But do you know what energy is? Read on to find out.

Defining Energy

Energy is defined in science as the ability to move matter or change matter in some other way. Energy can also be defined as the ability to do work, which means using force to move an object over a distance. When work is done, energy is transferred from one object to another. For example, when the boy in the Figure below uses force to swing the racket, he transfers some of his energy to the racket.

Q: It takes energy to play tennis. Where does this boy get his energy?

A: He gets energy from the food he eats.

SI Unit for Energy

Because energy is the ability to do work, it is expressed in the same unit that is used for work. The SI unit for both work and energy is the joule (J), or Newton • meter (N • m). One joule is the amount of energy needed to apply a force of 1 Newton over a distance of 1 meter. For example, suppose the boy in the Figure above applies 20 Newtons of force to his tennis racket over a distance of 1 meter. The energy needed to do this work is 20 N • m, or 20 J.

Energy Has Many Forms

If you think about different sources of energy—such as batteries and the sun—you probably realize that energy can take different forms. For example, when the boy swings his tennis racket, the energy of the moving racket is an example of mechanical energy. To move his racket, the boy needs energy stored in food, which is an example of chemical energy. Other forms of energy include electrical, thermal, light, and sound energy. The different forms of energy can also be classified as either kinetic energy or potential energy. Kinetic energy is the energy of moving matter. Potential energy is energy that is stored in matter. You can learn more about the different forms of energy at this URL: http://www.eia.gov/kids/energy.cfm?page=about_forms_of_energy-basics

For an animation showing the different forms of energy used to ride a bike, go to this URL:http://www.childrensuniversity.manchester.ac.uk/interactives/science/energy/what-is-energy/

Q: Is the chemical energy in food kinetic energy or potential energy?

A: The chemical energy in food is potential energy. It is stored in the chemical bonds that make up food molecules. The stored energy is released when we digest food. Then we can use it for many purposes, such as moving (mechanical energy) or staying warm (thermal energy).

Q: What is an example of kinetic energy?

A: Anything that is moving has kinetic energy. An example is a moving tennis racket.

Summary

  • Energy is defined in science as the ability to move matter or change matter in some other way. Energy can also be defined as the ability to do work.
  • The SI unit for energy as well as work is the joule (J), or Newton • meter (N • m).
  • Energy exists in different forms, such as mechanical energy and chemical energy. Most forms of energy can also be classified as either kinetic energy or potential energy.

Vocabulary

  • energy: Ability to cause changes in matter, or ability to do work.


Work

The teens in the picture on the left are having fun playing basketball. The teen in the picture on the right is working hard studying for an exam. It’s obvious who is doing work—or is it? Would it surprise you to learn that the teens who are working are the ones who are having fun playing basketball, while the teen who is studying isn’t doing any work at all? The reason why has to do with how work is defined in physics.

Defining Work

Work is defined differently in physics than in everyday language. In physics, work means the use of force to move an object. The teens who are playing basketball in the picture above are using force to move their bodies and the basketball, so they are doing work. The teen who is studying isn’t moving anything, so she isn’t doing work. Not all force that is used to move an object does work. For work to be done, the force must be applied in the same direction that the object moves. If a force is applied in a different direction than the object moves, no work is done. The Figure below illustrates this point.

Q: If the box the man is carrying is very heavy, does he do any work as he walks across the room with it?

A: Regardless of the weight of the box, the man does no work on it as he holds it while walking across the room. However, he does more work when he first lifts a heavier box to chest height.

Work, Force, and Distance

Work is directly related to both the force applied to an object and the distance the object moves. It can be represented by the equation:

Work = Force × Distance

The unit for work is the Joule abbreviated with the letter J

This equation shows that the greater the force that is used to move an object or the farther the object is moved, the more work that is done. You can see a short video introduction to work as the product of force and distance below:

To see the effects of force and distance on work, compare the weight lifters in the Figure below. The two weight lifters on the left are lifting the same amount of weight, but the one on the bottom is lifting the weight a greater distance. Therefore, this weight lifter is doing more work. The two weight lifters on the bottom right are both lifting the weight the same distance, but the weight lifter on the left is lifting a heavier weight, so she is doing more work.

Summary

  • In physics, work is defined as the use of force to move an object. For work to be done, the force must be applied in the same direction that the object moves.
  • Work is directly related to both the force applied to an object and the distance the object moves. It can be represented by the equation: Work = Force × Distance.

Vocabulary

  • work: Use of force to move an object; calculated as force multiplied by distance.

Practice

At the following URL, review the meaning of work by reading the first two paragraphs of the article. Then do the quick quiz. Be sure to check your answers and read the explanations.

http://www.physicsclassroom.com/Class/energy/u5l1a.cfm

Review

  1. How is work defined in physics?
  2. Write the equation that relates work to force and distance.
  3. Assume that a friend hands you a heavy book to hold as he turns the combination lock on his locker. Which of you does more work?

Power


Did you ever sweep a floor with a broom, like the woman in the picture on the left? It can take a lot of effort to do the job. But if you use an electric vacuum cleaner, like the woman in the picture on the right, you can do the same work more easily and quickly. That’s because the vacuum cleaner provides more power.

What Is Power?

Power is a measure of the amount of work that can be done in a given amount of time. Power can be represented by the equation:

\mathrm{Power=\frac{Work}{Time}}

In this equation, work is measured in joules (J) and time is measured in seconds (s), so power is expressed in joules per second (J/s). This is the SI unit for power, also known as the watt (W). A watt equals 1 joule of work per second. You’re probably already familiar with watts. Light bulbs and small appliances such as microwave ovens are labeled with the watts of power they provide. For example, the package of light bulbs in the Figure below is labeled “14 watts.”

Q: Assume you have two light bulbs of the same type, such as two compact fluorescent light bulbs like the one pictured in the Figure above. If one light bulb is a 25-watt bulb and the other is a 60-watt bulb, which bulb produces brighter light?

A: The 60-watt bulb is more powerful, so it produces brighter light.

Compared with a less powerful device, a more powerful device can either do more work in the same time or do the same work in less time. For example, compared with a low-power microwave oven, a high-power microwave oven can cook more food in the same time or the same amount of food in less time.

Calculating Power from Work and Time

Power can be calculated using the formula above if the amount of work and time are known. For example, assume that a microwave oven does 24,000 joules of work in 30 seconds. Then the power of the microwave is:

\text{Power}=\frac{\text{Work}}{\text{Time}}=\frac{24000 \ \text{J}}{30 \ \text{s}}=800 \ \text{J/s, or } 800 \ \text{W}

Q: Another microwave oven does 5,000 joules of work in 5 seconds. What is its power?

A: The power of the other microwave oven is:

\text{Power}=\frac{5000 \ \text{J}}{5 \ \text{s}}=1000 \ \text{J/s, or } 1000 \ \text{W}

Q: Which microwave oven will heat the same amount of food in less time?

A: The 1000-watt microwave oven has more power, so it will heat the same amount of food in less time.

Calculating Work from Power and Time

You can also calculate work if you know power and time by rewriting the power equation above as:

Work = Power × Time

For example, if you use a 1000-watt microwave oven for 20 seconds, how much work does it do? First express 1000 watts in J/s and then substitute this value for power the work equation:

Work = 1000 J/s × 20 s = 20,000 J

You can watch a video about calculating work and power at this URL:

http://www.brightstorm.com/science/physics/energy-and-momentum/power/

Horsepower

Sometimes power is measured in a unit called the horsepower. For example, the power of car engines is usually expressed in horsepowers. One horsepower is the amount of work a horse can do in 1 minute. It equals 745 watts of power. Compare the horsepowers in the two Figures below

This team of three horses provides 3 horsepowers of power.

This big tractor provides 180 horsepowers of power.

Q: If the team of horses and the tractor do the same amount of work plowing a field, which will get the job done faster?

A: The tractor will get the job done faster because it has more power. In fact, because the tractor has 30 times the power of the six-horse team, ideally it can do the same work 30 times faster!

Summary

  • Power is a measure of the amount of work that can be done in a given amount of time. Power equals work (J) divided by time (s).
  • The SI unit for power is the watt (W), which equals 1 joule of work per second (J/s).
  • Power can be calculated from work and time using the equation: .
  • Power may be measured in a unit called the horsepower. One horsepower is the amount of work a horse can do in 1 minute, which equals 745 watts of power.
    • \text{Power} = \text{Force} \times \text{velocity}

Vocabulary

  • power: Measure of the amount of work that can be done in a given amount of time.
  • watt (W): SI unit for work, equal to 1 joule of work per second.

Practice

At the following URL, review what power means and how it is calculated. Then do the first four Check Your Understanding problems. Be sure to check your answers and read the explanations. For an extra challenge, try to do the last two Check Your Understanding problems.

http://www.physicsclassroom.com/Class/energy/u5l1e.cfm

Review

  1. What is power? What is the SI unit for power?
  2. How much power does a toaster have if it does 21,000 joules of work in 30 seconds?
  3. How much work can be done in 30 seconds by a 1000-watt microwave oven?
  4. Lamar’s mom has a car with a 182-horsepower engine. How many watts of power is that?

Potential Energy

This diver has just jumped up from the end of the diving board. After she dives down and is falling toward the water, she’ll have kinetic energy, or the energy of moving matter. But even as she is momentarily stopped high above the water, she has energy. Do you know why?

Stored Energy

The diver has energy because of her position high above the pool. The type of energy she has is called potential energy. Potential energy is energy that is stored in a person or object. Often, the person or object has potential energy because of its position or shape.

Q: What is it about the diver’s position that gives her potential energy?

A: Because the diver is high above the water, she has the potential to fall toward Earth because of gravity. This gives her potential energy.

Gravitational Potential Energy

Potential energy due to the position of an object above Earth’s surface is called gravitational potential energy. Like the diver on the diving board, anything that is raised up above Earth’s surface has the potential to fall because of gravity. You can see another example of people with gravitational potential energy in the Figure below. 

Gravitational potential energy depends on an object’s weight and its height above the ground. It can be calculated with the equation:

Gravitational potential energy (GPE) = weight × height

Consider the little girl on the sled, pictured in the Figure above. She weighs 140 Newtons, and the top of the hill is 4 meters higher than the bottom of the hill. As she sits at the top of the hill, the child’s gravitational potential energy is:

GPE = 140 N × 4 m = 560 N • m

Notice that the answer is given in Newton • meters (N • m), which is the SI unit for energy. A Newton ∙ meter is the energy needed to move a weight of 1 Newton over a distance of 1 meter. A Newton • meter is also called a joule (J).

Q: The gymnast on the balance beam pictured in the Figure above weighs 360 Newtons. If the balance beam is 1.2 meters above the ground, what is the gymnast’s gravitational potential energy?

A: Her gravitational potential energy is:

GPE = 360 N × 1.2 m = 432 N • m, or 432 J


On Earth, an object's weight can be calculated as weight = mass x acceleration due to gravity.  So the formula for gravitational potential energy can also be written as GPE = mgh.  This formula is useful to remember, since we are often given an object's mass instead of its weight.


Elastic Potential Energy

Potential energy due to an object’s shape is called elastic potential energy. This energy results when an elastic object is stretched or compressed. The farther the object is stretched or compressed, the greater its potential energy is. A point will be reached when the object can’t be stretched or compressed any more. Then it will forcefully return to its original shape.

Look at the pogo stick in the Figure below. Its spring has elastic potential energy when it is pressed down by the boy's weight. When it can’t be compressed any more, it will spring back to its original shape. The energy it releases will push the pogo stick—and the boy—off the ground. You can see how a pogo stick spring compresses and then returns to its original shape in the animation at this URL:

http://en.wikipedia.org/wiki/File:Pogoanim.gif

Q: The girl in the Figure below is giving the elastic band of her slingshot potential energy by stretching it. She’s holding a small stone against the stretched band. What will happen when she releases the band?

A: The elastic band will spring back to its original shape. When that happens, watch out! Some of the band’s elastic potential energy will be transferred to the stone, which will go flying through the air.

Other Forms of Potential Energy

All of the examples of potential energy described above involve movement or the potential to move. The form of energy that involves movement is called mechanical energy. Other forms of energy also involve potential energy, including chemical energy and nuclear energy. Chemical energy is stored in the bonds between the atoms of compounds. For example, food and batteries both contain chemical energy. Nuclear energy is stored in the nuclei of atoms because of the strong forces that hold the nucleus together. Nuclei of radioactive elements such as uranium are unstable, so they break apart and release the stored energy.

Work and Energy are Related

Work and energy are related, which you probably guessed since they are both measured in Joules or Newton-meters.  If you do work on an object, then the object gains energy.  You can see this in action when you do work to lift an object and the object gains gravitational potential energy.  The amount of work done on the object is equal to the object's increase in energy.  So if I do 50 J of work to lift an object from the ground, the object now has 50 J of gravitational potential energy.

Summary

  • Potential energy is energy that is stored in a person or object.
  • Gravitational potential energy is due to the position of an object above Earth’s surface. The object has the potential to fall due to gravity. Gravitational potential energy depends on an object’s weight and its height above the ground (GPE = weight x height).
  • Elastic potential energy is due to an object’s shape. It results when an elastic object is stretched or compressed. The more it is stretched or compressed, the greater its elastic potential energy is.
  • Chemical energy and nuclear energy are other forms of potential energy.

Vocabulary

  • potential energy: Stored energy an object has because of its position or shape.

Practice

Do the animation at the following URL, and then answer the questions below.

http://www.classzone.com/books/ml_science_share/vis_sim/mem05_pg69_potential/mem05_pg69_potential.html

  1. Which paint can has greater potential energy after the painter carries it up the ladder? Why is this can’s potential energy greater?
  2. How could the painter give the other can more potential energy?

Review

  1. What is potential energy?
  2. Compare and contrast gravitational and elastic potential energy, and give an example of each.
  3. The diver on the diving board in the opening picture weighs 500 Newtons. The diving board is 5 meters above the ground. What is the diver’s gravitational potential energy?
  4. Why does food have potential energy?

Kinetic Energy

What could these four photos possibly have in common? Can you guess what it is? All of them show things that have kinetic energy.  

Defining Kinetic Energy

Kinetic energy is the energy of moving matter. Anything that is moving has kinetic energy—from atoms in matter to stars in outer space. Things with kinetic energy can do work. For example, the spinning saw blade in the photo above is doing the work of cutting through a piece of metal.

Calculating Kinetic Energy

The amount of kinetic energy in a moving object depends directly on its mass and velocity. An object with greater mass or greater velocity has more kinetic energy. You can calculate the kinetic energy of a moving object with this equation:

\mathrm{Kinetic\; Energy\; (KE)=\frac{1}{2} mass \times velocity^2}

This equation shows that an increase in velocity increases kinetic energy more than an increase in mass. If mass doubles, kinetic energy doubles as well, but if velocity doubles, kinetic energy increases by a factor of four. That’s because velocity is squared in the equation.

Let’s consider an example. The Figure below shows Juan running on the beach with his dad. Juan has a mass of 40 kg and is running at a velocity of 1 m/s. How much kinetic energy does he have? Substitute these values for mass and velocity into the equation for kinetic energy:

\text{KE}=\frac{1}{2} \times 40 \ \text{kg} \times (1\frac{\text{m}}{\text{s}})^2=20 \ \text{kg} \times \frac{\text{m}^2}{\text{s}^2}=20 \ \text{N} \cdot \text{m}, or 20 \ \text{J}

Notice that the answer is given in joules (J), or N • m, which is the SI unit for energy. One joule is the amount of energy needed to apply a force of 1 Newton over a distance of 1 meter.

What about Juan’s dad? His mass 80 kg, and he’s running at the same velocity as Juan (1 m/s). Because his mass is twice as great as Juan’s, his kinetic energy is twice as great:

\text{KE}=\frac{1}{2} \times 80 \ \text{kg} \times (1 \frac{\text{m}}{\text{s}})^2=40 \ \text{kg} \times \frac{\text{m}^2}{\text{s}^2}=40 \ \text{N} \cdot \text{m}, or 40 \ \text{J}

Q: What is Juan’s kinetic energy if he speeds up to 2 m/s from 1 m/s?

A: By doubling his velocity, Juan increases his kinetic energy by a factor of four:

\text{KE}=\frac{1}{2} \times 40 \ \text{kg} \times (2 \frac{\text{m}}{\text{s}})^2=80 \ \text{kg} \times \frac{\text{m}^2}{\text{s}^2}=80 \ \text{N} \cdot \text{m}, or 80 \ \text{J}

Summary

  • Kinetic energy (KE) is the energy of moving matter. Anything that is moving has kinetic energy.
  • The amount of kinetic energy in a moving object depends directly on its mass and velocity. It can be calculated with the equation: \text{KE}=\frac{1}{2}\text{mass} \times \text{velocity}^2.

Vocabulary

  • kinetic energy: Energy of moving matter.

Review

  1. What is kinetic energy?
  2. The kinetic energy of a moving object depends on its mass and its
    1. volume.
    2. velocity.
    3. distance.
    4. acceleration.
  3. The bowling ball in the Figure below is whizzing down the bowling lane at 4 m/s. If the mass of the bowling ball is 7 kg, what is its kinetic energy?

Work-Energy Theorem

Watch the following video for an introduction to the Work-Energy Theorem:



Watch the following video for an example of a calculation involving the Work-Energy Theorem:

Watch the following video to see an example of how to algebraically manipulate the Work-Energy Theorem:

After you have completed this part of the lesson, you can check the associated box on the main course page to mark it as complete

Conservation of Energy

Key Equations

\sum E_{\text{initial}} = \sum E_\text{final} \; \; \text{The total energy does not change in closed systems}

Guidance
Energy is conserved in a closed system. That is, if you add up all the energy of an object(s) at one time it will equal all the energy of said object(s) at a later time. A closed system is a system where no energy is transferred in or out. The total energy of the universe is a constant (i.e. it does not change). The problems below do not consider the situation of energy transfer (called work). So friction and other sources where energy leaves the system are not present. Thus, one simply adds up all the potential energy and kinetic energy before and sets it equal to the addition of the total potential energy and kinetic energy after.

Example 1

Billy is standing at the bottom of a ramp inclined at 30 degrees. Billy slides a 2 kg puck up the ramp with an initial velocity of 4 m/s. How far up the ramp does the ball travel before it begins to roll back down? Ignore the effects of friction.

Solution

The potential energy of the puck when it stops at the top of it's path will be equal to the kinetic energy that it was initially rolled with. We can use this to determine the how high above the ground the puck will be above the ground when it stops, and then use trigonometry to find out how far up the ramp the puck will be when it stops.

PE_i + KE_i &= PE_f + KE_f && \text{start with conservation of energy}\\0 + \frac{1}{2}mv^2 &= mgh + 0 && \text{take out the energy terms we know will be zero and substitute the equations for potential and kinetic energy.}\\\frac{1}{2}v^2 &= gh && \text{simplify the equation}\\h&=\frac{v^2}{2g} && \text{solve for h}\\h&=\frac{(4\;\text{m/s})^2}{2*9.8\;\text{m/s}^2} && \text{substitute in the known values}\\h&=0.82\;\text{m}\\

Now we can find the distance up the ramp the ball traveled since we know the angle of the ramp and the height of the ball above the ground.

\sin(30)&=\frac{h}{x}\\x&=\frac{h}{\sin(30)}\\x&=\frac{0.82\;\text{m}}{\sin(30)}\\x&=1.6\;\text{m}\\


Watch the following videos for examples of setting up problems using conservation of energy: