Work

At home, "work" means anything tiring: homework, housework. In physics it has one exact meaning: work is done when a force moves something. No movement, no work.

Building the idea with wheat bags. Lifting one bag up 1 m takes some work. Lifting three bags up 1 m (one at a time or all together) takes 3 times the work. Lifting one bag up 3 m also takes 3 times the work. So work depends on how big the force is and how far it moves things.

Work = force × displacement in the direction of the force, or W = F × s. Always say which force does work on which object.

Work is measured in joules (J). 1 J is the work done when a force of 1 N moves something 1 m in its direction. (1 J = 1 kg m² s⁻².) On a force-displacement graph, the work is the area under the line: 10 N × 1 m = 10 J.

When is the work zero?

• No force.
• No displacement: pushing a wall that doesn't move, or holding a barbell still.
• Force at right angles to the movement: carrying a box while walking on flat ground (you hold it up; it moves forward).

You may still feel tired, because your muscles use energy, but no work is done on the object.

Positive or negative? Ask: what did each force want?

• If the object moved the way the force wanted, the work is positive: pushing a wheelchair forward; lifting a dumbbell.
• If it moved the opposite way, the work is negative: friction on a sliding box; a goalkeeper's hands stopping a ball.
• If it moved neither way the force wanted, the work is zero.

A tricky one: lowering a dumbbell slowly. Which way is your hand pushing? Still up, or the dumbbell would drop. But it moves down. Force up, movement down: your hand does negative work.

Work has no direction, only a size with a + or – sign. A goalkeeper stops a ball with a force of 200 N while her hands move back 15 cm: W = 200 × (–0.15) = –30 J.