Work, Energy and Power
Three everyday words that mean something exact in physics. Each lab below has sliders. Move them and watch the numbers and graphs change. No maths background needed.
A force moves something over a distance. Measured in joules (J).
The ability to do work. It uses the same unit as work, the joule (J).
How fast work gets done. Measured in watts (W). 1 W means 1 joule every second.
How big is a joule? Lifting a small apple (about 100 g) up by 1 metre takes roughly 1 J.
Work happens when a force moves something
In daily life, "work" means any effort. In physics, work happens only when a force makes an object move. Push a box across the floor and you do work. Push a wall that never moves and you do none, however tired you get.
Three things decide how much work you do:
- Force F in newtons (N): how hard you push.
- Distance d in metres (m): how far the object moves.
- Angle theta : the direction of your push compared with the direction the box moves.
Only the part of the push that points along the motion counts. That part is F x cos theta . Push straight along the motion (theta = 0 degrees) and all of it counts.
Push a box
W = F x d x cos thetaThe shaded area in the graph is the work: force along the motion x distance.
Energy is the ability to do work
An object has energy when it can make things happen. Two kinds matter first.
- Kinetic energy (KE) belongs to anything that moves.
- Potential energy (PE) is stored by height. A book on a high shelf can fall and hit something.
Energy is measured in joules, the same unit as work. Doing work on an object changes its energy.
Kinetic energy: the energy of motion
KE = 1/2 x m x v^2The curve gets steeper as speed rises. Speed is squared, so it counts twice.
Potential energy depends on mass, height and the pull of gravity. Gravity's strength is written g. On Earth it is 9.8 m/s^2, meaning a falling object gains 9.8 m/s of speed every second.
When the ball below falls, its PE turns into KE. The total never changes. This rule is called conservation of energy .
Drop a ball
PE = m x g x hPower is how fast the work gets done
Two people carry the same box up the same stairs. Both do the same work. The one who finishes in half the time has twice the power.
Power = work / time. One watt is one joule of work every second. An old 100 W light bulb turns 100 joules of electrical energy into light and heat each second.
Race a 100 W machine
P = W / tThe steepness of each line is its power. Steeper means more work per second.
Work changes energy
Push a cart from rest on a smooth floor. The work you do goes straight into its kinetic energy, so W = KE . This link is called the work-energy theorem.
From the energy you can find the final speed. From the time the push takes you can find the power.
Push a cart from rest
W = F x d = KEAt every point, the kinetic energy equals the work done so far.
Four quick questions
You push a wall with 500 N for a whole hour and it never moves. How much work did you do?
Zero joules. The distance is 0, so W = F x d = 0. Pushing is tiring for your muscles, but no work is done on the wall.
A car doubles its speed. What happens to its kinetic energy?
It becomes 4 times bigger, because speed is squared. Try it in the kinetic energy lab: 10 m/s, then 20 m/s.
Two people lift identical boxes to the same shelf. One takes 5 s and the other 10 s. Who does more work, and who has more power?
They do the same work. The person who takes 5 s has twice the power, because P = W / t.
You carry a heavy bag sideways along a corridor. Your arms hold it up. Do your arms do work on the bag?
No. The upward force is at 90 degrees to the sideways motion, and cos 90 degrees = 0. Set the angle to 90 degrees in the work lab to see it.
Summary table
| Quantity | Symbol | Unit | Formula |
|---|---|---|---|
| Force | F | newton (N) | F = m x a |
| Work | W | joule (J) | W = F x d x cos theta |
| Kinetic energy | KE | joule (J) | KE = 1/2 m v^2 |
| Potential energy | PE | joule (J) | PE = m g h |
| Power | P | watt (W) | P = W / t |
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