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Work, W = Fd

Energy and power · level 5, lesson 1 of 6

A question to start

You push a heavy cart across a habitat floor. Then you lean on a wall for ten minutes until your arms ache. In physics, only one of these is "work". Which, and why?

The idea

A force does work when it moves something in the direction of the force. The work done is

\[W = F d,\]

where \(F\) is the force in newtons and \(d\) the distance moved along the force, in metres. Work is measured in joules: \(1 \text{ J} = 1 \text{ N m}\).

Work is how a force passes energy on. When you push the cart, the energy you put in equals the work you do. Where does it go? Into the cart's kinetic energy, or, if friction holds it to a steady speed, into heat.

Fd

No movement, no work. Leaning on a wall, your muscles get tired, but the wall does not move, so you do no work on the wall. (Your muscles still burn food energy, turning it into heat.)

On Mars, the work to push something along depends on the force needed. On wheels, getting a cart moving takes the same work as on Earth (mass does not change). Sliding it against friction takes less work, because friction is only 0.38 as big.

Worked examples

1. Pushing a cart. 80 N for 15 m: \(W = 80 \times 15 = 1{,}200\) J.

2. Dragging a sled on Mars. A 60 kg sled of equipment on a surface with \(\mu = 0.3\). Friction \(= 0.3 \times 60 \times 3.71 = 67\) N. Pulling it 50 m at a steady speed: \(W = 67 \times 50 = 3{,}340\) J. On Earth: \(8{,}830\) J.

3. Lifting. Lifting a 2 kg box by 1.5 m on Mars at a steady speed needs a force equal to its weight, 7.42 N: \(W = 7.42 \times 1.5 = 11.1\) J.

Try it

  1. A force of 25 N pushes a box 4 m. How much work is done?
  2. How much work do you do holding a heavy bag still for a minute?
  3. A crane lifts 500 kg by 10 m on Mars. How much work does it do?
  4. How much work does it do lifting the same load by the same height on Earth?
Answers
  1. \(25 \times 4 = 100\) J.
  2. None on the bag: it does not move.
  3. \(500 \times 3.71 \times 10 = 18{,}550\) J.
  4. \(500 \times 9.81 \times 10 = 49{,}050\) J.

Common mistake

"Tiring work must be physics work." Physics work needs movement along the force. Holding something still is tiring, but does no work on the object.

Where it leads