What it means to "do work"
- Work is done whenever a force moves the object it is acting on through a distance in the direction of that force
- If the force does not move the object, no work has been done. Pushing on a stationary wall for ten minutes transfers no energy to the wall, no matter how tired your arms feel
- "Doing work" is just the mechanical pathway in different language. The amount of work done equals the amount of energy transferred between stores:
energy transferred = work done
- Both quantities are measured in joules (J); 1 J = 1 N m (one newton acting through one metre)
Sign of the energy transfer
- If a force acts in the same direction as the motion, the object gains energy (usually into its kinetic store, sometimes into gravitational potential if it is being lifted)
- If a force acts in the opposite direction to the motion, the object loses energy; in everyday cases this is friction or drag dissipating energy as heat into the surroundings
- Lifting a 5 kg sack of flour onto a kitchen shelf does work against gravity and fills the sack's gravitational potential store; sliding a box across a carpet does work against friction and dumps that energy into the thermal stores of the carpet and the box
The work-done equation
W = F × d
- where:
- W = work done (J or N m)
- F = force acting on the object (N)
- d = distance the object moves in the direction of the force (m)
- Use SI units throughout (newtons and metres); the result then comes out in joules
Example — a sledge is dragged along level snow with a rope pulling at 85 N along the line of travel. After 12 m of pulling, how much work has the rope done on the sledge?
- W = F × d = 85 × 12 = 1020 J
Example — a delivery van rolls to a stop over 18 m while its brakes push back on it with a constant 1200 N force. Find the work that the brakes do on the van during the stop.
- W = F × d = 1200 × 18 = 21 600 J
- The braking force opposes the motion, so this is the energy that has been removed from the van's kinetic store and dissipated as heat in the brake discs