English:Work, Energy, and Power
Work, Energy, and Power
Introduction
Work, Energy, and Power are closely connected ideas in physics. In this Grade 7–8 aiMOOC, you will learn how forces transfer energy, how moving and raised objects store energy, and how power describes the rate at which energy is transferred.
You meet these ideas every day. Lifting a backpack, riding a bicycle, climbing stairs, stretching a spring, using an electric motor, and riding a roller coaster all involve work, energy, or power.
The image above reminds you that energy can appear in different forms. In this course, the main focus is on mechanical energy: kinetic energy and potential energy. You will also connect mechanical energy to thermal, chemical, and electrical energy.
Learning Goals
By the end of the course, you should be able to:
- Work: Explain when a force does mechanical work and calculate work for simple cases.
- Energy: Describe energy as a quantity that can be stored and transferred.
- Kinetic energy: Explain how mass and speed affect the energy of motion.
- Potential energy: Explain how position or deformation can store energy.
- Power: Calculate and compare rates of energy transfer.
- Conservation of energy: Trace energy changes in real systems and explain the effects of friction.
Core Ideas
Work: Energy Transfer by a Force
In physics, work is done when a force causes an object to move through a distance and the force has a component in the direction of that movement. For the simple situations in this course, when force and motion are in the same direction:
Work = force × distance
The symbol form is W = F × d.
Force is measured in newtons (N), distance in metres (m), and work in joules (J). One joule is the work done when a force of one newton moves an object one metre in the direction of the force.
Example: You push a box with a force of 20 N through 3 m in the direction of the push. The work done is 20 × 3 = 60 J.
If the object does not move, the force does no mechanical work on that object. Also, a force perpendicular to the motion does no work in the direction of travel. This is why the physics meaning of work is more specific than the everyday meaning.
A pulley system can reduce the force needed to lift a load, but then you usually pull the rope through a greater distance. In an ideal machine without friction, the trade-off keeps the total work the same.
Energy: The Ability to Cause Change
Energy is a measurable quantity that can be stored and transferred. Energy and work use the same SI unit, the joule.
When work is done on an object, energy can be transferred to or from that object. Energy can also be transferred by heating, electrical processes, and radiation.
Kinetic Energy
Kinetic energy is the energy an object has because it is moving. For an object of mass m moving at speed v:
Kinetic energy = 1/2 × mass × speed²
The symbol form is KE = 1/2 mv².
This formula shows two important patterns. A more massive object has more kinetic energy at the same speed. Speed has an even stronger effect because it is squared: if speed doubles, kinetic energy becomes four times as large.
Example: A 2 kg cart moving at 4 m/s has KE = 1/2 × 2 × 4² = 16 J.
Potential Energy
Potential energy is stored energy associated with position or arrangement. Two common examples are gravitational potential energy and elastic potential energy.
Near Earth's surface, the change in gravitational potential energy can be estimated using:
Gravitational potential energy = mass × gravitational field strength × height
The symbol form is GPE = mgh.
For many school calculations, you may be told to use g = 10 N/kg as an approximate value near Earth's surface.
Example: A 3 kg object raised 2 m gains about 3 × 10 × 2 = 60 J of gravitational potential energy.
A stretched rubber band or compressed spring can store elastic potential energy. When released, some of this stored energy can become kinetic energy.
Conservation of Energy
The law of conservation of energy states that energy cannot be created or destroyed. It can be transferred between objects and transformed from one form to another.
In a pendulum, gravitational potential energy is greatest near the highest points and kinetic energy is greatest near the bottom. In an ideal system with no air resistance or friction, the total mechanical energy stays constant as energy changes between these two forms.
The FuseSchool video above reviews conservation of energy. As you watch, identify where energy is stored at the start of each example and where it is transferred later.
Mechanical Energy and Roller Coasters
Mechanical energy is the total of an object's kinetic energy and potential energy in the situation being studied.
At the top of a roller-coaster hill, the car has more gravitational potential energy. As it moves downhill, gravitational potential energy decreases while kinetic energy increases. The car speeds up because energy is being transformed.
Real roller coasters are not frictionless. Wheels, bearings, and air resistance transfer some mechanical energy into thermal energy and sound.
This does not mean energy has disappeared. The total energy is still conserved, but less of it remains as useful mechanical energy.
Power: How Fast Energy Is Transferred
Power describes how quickly work is done or energy is transferred.
Power = work ÷ time
The symbol form is P = W / t. You can also use P = E / t when you know the amount of energy transferred.
Power is measured in watts (W). One watt means one joule of energy transferred each second.
Example: If a student does 120 J of work in 3 s while climbing stairs, the average power is 120 ÷ 3 = 40 W.
Two people can do the same amount of work but have different power. The person who completes the work in less time produces greater average power.
The Khan Academy video above connects work, energy transfer, and power. Pause after each worked example and explain in your own words what is being transferred and how quickly.
Putting Work, Energy, and Power Together
The three ideas form a useful chain:
Force acting through a distance → work done → energy transferred
Energy transferred over a time interval → power
A motor can do work by lifting a load. The energy supplied to the motor is transferred into gravitational potential energy of the load, while some energy may also become thermal energy and sound. A higher-power motor can transfer the same amount of useful energy in less time.
The Crash Course Physics video above gives a broader overview. Some parts go beyond Grade 7–8, so focus on the central relationship among force, work, energy change, and time.
Energy Transformations, Friction, and Efficiency
Friction and Dissipation
Friction often changes organized mechanical energy into less useful thermal energy in objects and their surroundings. For example, bicycle brakes become warm because kinetic energy is transferred into thermal energy.
When scientists say that energy is dissipated, they mean that it has spread into the surroundings and is less available for a useful purpose. The energy has not been destroyed.
Efficiency
Efficiency compares the useful energy output of a device or process with the total energy input.
Efficiency = useful energy output ÷ total energy input × 100 percent
If a machine receives 200 J of energy and transfers 150 J usefully, its efficiency is 150 ÷ 200 × 100 percent = 75 percent. The remaining 50 J is still present, often as thermal energy or sound.
The FuseSchool video above gives examples of useful and wasted energy transfers. Try drawing an energy-flow diagram for one example from the video.
Energy Recovery in Technology
Some technologies are designed to capture energy that would otherwise be dissipated. Regenerative braking and flywheel systems can store part of a vehicle's kinetic energy during braking and reuse it during later acceleration.
The photograph shows a kinetic-energy recovery flywheel system developed for motor racing. It is a real-world example of engineers trying to make energy transfers more useful.
Worked Examples
Example 1: Work Done Pushing a Cart
A student pushes a cart with a constant force of 15 N for 4 m in the direction of motion.
Work = force × distance = 15 × 4 = 60 J.
The student transfers 60 J of energy by mechanical work.
Example 2: Comparing Kinetic Energy
A 1 kg ball moves at 2 m/s.
KE = 1/2 × 1 × 2² = 2 J.
If the same ball moves at 4 m/s, its kinetic energy becomes:
KE = 1/2 × 1 × 4² = 8 J.
Doubling the speed made the kinetic energy four times as large.
Example 3: Lifting and Power
A student transfers 600 J of energy while climbing stairs in 5 s.
Power = energy ÷ time = 600 ÷ 5 = 120 W.
If another student transfers the same 600 J in 10 s, the average power is 60 W. Both transfer the same energy, but the first student transfers it faster.
Common Misconceptions
Misconception: If you feel tired, you must be doing mechanical work on an object.
Correction: You can use chemical energy in your body even when the object does not move. In physics, mechanical work on the object requires displacement caused by a force.
Misconception: A powerful machine always uses more total energy.
Correction: Power describes a rate. A high-power machine may simply transfer the same amount of energy in a shorter time.
Misconception: Friction destroys energy.
Correction: Friction transforms mechanical energy into thermal energy and sometimes sound. Total energy is conserved.
Misconception: A motionless object has no energy.
Correction: It may have potential energy because of its height, shape, chemical composition, or another stored-energy condition.
Interactive Tasks
Quiz: Test Your Knowledge
When is mechanical work done on an object in the simplest case studied here? (A force moves the object in the direction of the force) (!A force acts but the object stays still) (!The object has mass but no force acts) (!Time passes while the object remains still)
What is the SI unit of work and energy? (Joule) (!Watt) (!Newton) (!Metre)
A 10 N force moves a box 5 m in the same direction. How much work is done? (50 joules) (!2 joules) (!15 joules) (!500 joules)
Which kind of energy is associated with motion? (Kinetic energy) (!Gravitational potential energy) (!Chemical energy) (!Elastic potential energy)
If the speed of an object doubles while its mass stays the same, what happens to its kinetic energy? (It becomes four times as large) (!It becomes two times as large) (!It stays the same) (!It becomes half as large)
Which change increases gravitational potential energy near Earth's surface? (Raising an object higher) (!Lowering an object) (!Stopping a moving object) (!Reducing the object's height)
What does conservation of energy mean? (Energy changes form but the total amount is conserved) (!Energy disappears when friction acts) (!Energy is created by powerful machines) (!Energy exists only in moving objects)
What does power measure? (How quickly energy is transferred) (!How much mass an object has) (!How far an object has moved) (!How warm an object becomes)
A device transfers 100 J of energy in 5 s. What is its average power? (20 watts) (!5 watts) (!95 watts) (!500 watts)
Why do real machines have efficiencies below 100 percent? (Some input energy is transferred into less useful forms) (!Some energy is destroyed completely) (!The law of conservation of energy stops applying) (!All input energy remains stored forever)
Memory Game
| Work | Energy transferred when a force causes displacement |
| Joule | SI unit used for energy and mechanical work |
| Kinetic | Energy associated with motion |
| Potential | Stored energy associated with position or arrangement |
| Power | Rate at which energy is transferred |
| Watt | SI unit equal to one joule per second |
Drag and Drop
| Match the correct terms. | Topic |
|---|---|
| Force times distance | Simple expression for mechanical work |
| Mass and speed | Quantities that determine kinetic energy |
| Mass height and gravity | Quantities used for gravitational potential energy |
| Energy divided by time | Simple expression for power |
| Useful output divided by total input | Basis for calculating efficiency |
Match each phrase to the physics idea it describes, then explain one match in a complete sentence.
Crossword Puzzle
| Joule | Which unit measures work and energy? |
| Watt | Which unit measures power? |
| Kinetic | Which type of energy belongs to a moving object? |
| Potential | Which type of energy can be stored because of position? |
| Friction | Which interaction often changes mechanical energy into thermal energy? |
| Efficiency | Which idea compares useful output with total input? |
LearningApps
Cloze Text
Open-Ended Tasks
Easy
- Energy diary: Record five energy transformations you observe during one day and label the starting and ending energy forms.
- Work experiment: Use a spring scale or teacher-approved force meter to pull a light object across a measured distance and calculate the work done.
- Motion poster: Create a poster showing how changing mass and changing speed affect kinetic energy, using your own examples and diagrams.
- Power explanation video: Record a one-minute video explaining the difference between energy and power using a safe everyday example.
Standard
- Stair-power investigation: With teacher supervision, measure a safe vertical height and climbing time, estimate the gain in gravitational potential energy, and compare average power for repeated trials.
- Pendulum study: Build a small safe pendulum, observe where it moves fastest and slowest, and explain the changes between potential and kinetic energy.
- Home energy audit: Compare the power ratings of several household devices without opening or modifying them, then explain which devices transfer energy fastest when operating.
- Roller-coaster model: Design a paper or digital roller-coaster diagram and annotate where gravitational potential energy, kinetic energy, friction, and thermal energy are important.
Advanced
- Pulley investigation: Build or examine a teacher-approved pulley setup and test the trade-off between force and pulling distance while comparing the work done.
- Engineering research: Research regenerative braking or flywheel energy storage and create an infographic showing the energy transfers and possible efficiency benefits.
- Energy interview: Interview an engineer, technician, science teacher, or sports coach about where work, energy, and power matter in their field, then compare the interview with physics definitions.
- Power project: Design a fair test comparing the average power of two safe human-powered tasks, identify variables and measurement uncertainty, analyze your data, and present the results.
Learning Assessment
- Work and energy reasoning: A student pushes a heavy wall for 30 seconds and feels tired, but the wall does not move; explain the difference between the student's energy use and the mechanical work done on the wall.
- Energy transformation analysis: Trace the energy changes of a bicycle moving downhill and then braking, including gravitational potential, kinetic, thermal, and sound energy.
- Power comparison: Two students do the same amount of work climbing identical stairs in different times; determine who has greater average power and justify your answer.
- Kinetic energy transfer: Explain why speed is especially important in kinetic energy and predict the effect of doubling speed without using simple recall alone.
- Efficiency problem: A machine receives 500 J of input energy and provides 350 J of useful output; calculate the efficiency and explain where the remaining energy may have gone.
- Engineering transfer: Choose a real device such as an elevator, bicycle, crane, or electric fan and explain how work, energy transfers, power, friction, and efficiency are connected in its operation.
Evidence of Learning
| Area | Evidence you can produce |
|---|---|
| Knowledge | Accurate explanations of work, kinetic energy, potential energy, power, conservation of energy, friction, and efficiency |
| Calculation skills | Correct use of units and simple formulas for work, kinetic energy, gravitational potential energy, power, and efficiency |
| Scientific reasoning | Clear predictions and explanations about how changing force, distance, mass, speed, height, or time affects a system |
| Investigation skills | Safe measurements, organized data, fair-test choices, and discussion of uncertainty |
| Products | Diagrams, posters, videos, reports, models, or presentations that show energy transfers accurately |
| Transfer | Application of the ideas to unfamiliar examples such as sports, transport, machines, amusement rides, and household devices |
OERs on the Topic
Explore these English Wikipedia articles for further reading:
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