Calculate energy changes from work done

Physics · Work done

The force is fixed at 350 N. Drag the bar to change the distance moved in the direction of the force. The work done is the energy transferred, so it shows in joules and in kilojoules.

Predict, then check

The bar above held the force still. Now change both.

A crate is pulled with a force over some distance. Now double the force AND double the distance. What happens to the work done?

What you need to know

• A force making an object move does work on it. The work done is the energy transferred, measured in joules (J).
• No movement, no work: push a car that won't budge and no work is done on it.
• Have a goJay spends all lunchtime shoving a brick wall, sweating hard. The wall doesn't move. Jay says he did loads of work on it. Is he right?

  No. No work was done on the wall.

  Work needs the force to make the object move. The wall stayed put, so no energy was transferred. Feeling tired isn't the same as doing work.

• Use E = F × d: E in joules, F in newtons, d in metres moved in the direction of the force.
• Have a goA force of 20 N moves a box 5 m in the direction of the force. How much work is done?

  100 J

  Multiply, don't add: E = F × d = 20 × 5 = 100, and it's in joules because work done is energy transferred.

• Work done is directly proportional to force and to distance, so doubling both gives four times the work.
• Pushing a crate up a slope: the person's chemical store loses energy; the crate's gravitational store and the surroundings' thermal store gain it.
• Pull the crate along a level floor instead and the gravitational store gains nothing, because the height stays the same.
• Friction warms the surfaces, the surfaces warm the air, and the energy spreads out into the surroundings: it dissipates.
• Energy is never created or destroyed, only transferred, so the total is the same before and after a transfer.
• Have a goA person's chemical store loses 500 J pushing a crate up a slope. The crate's gravitational store gains 300 J. How much energy goes to the thermal store of the surroundings?

  200 J

  Energy is only transferred, never destroyed, so the 500 J that left the chemical store must turn up elsewhere: 300 J + 200 J.

• Convert before you calculate: 7.2 kN is 7200 N, 120 cm is 1.2 m, and 1 kJ is 1000 J.

The big picture

Work is done when a force makes an object move, and the work done is the energy transferred, measured in joules. Calculate it with E = F × d, converting units first, and follow the energy between stores as it moves.

⚠ Watch out

Putting the numbers straight into E = F × d without converting. Using 7.2 kN as 7.2 instead of 7200 N, or 120 cm as 120 instead of 1.2 m, gives an answer that is wrong by a factor you'd never guess.

Memory hook

No movement, no work. Then newtons × metres: convert first, calculate second.

Check yourself

Without looking back: a crate is dragged along a level floor. Which store loses energy, which gains it through friction, and which gains nothing? Why?