Work moves along the lever

The idea

The work done on one end of a lever is transferred to the other end, so F1 × d1 = F2 × d2: the end with the smaller force moves through the larger distance.

Press a long bar

Pressing the end of a long bar down a long way lifts a heavy stone just a little.

Where do you think the work you do at your end goes?

• It is passed to the other end
• It disappears
• It is stored in the bar for ever

Move the effort end

The load is 60 N and rises 10 cm (examples). Choose how far the effort end moves.

Little force, long way

The work done at the effort end was passed to the load end. Where the force was smaller, the end moved through a larger distance. F1 × d1 stayed equal to F2 × d2.

The work done on one end of a lever is transferred to the other end: F1 × d1 = F2 × d2. The end with the smaller force moves through the larger distance.

Notes

F1 × d1 = F2 × d2: the work on one end is transferred to the other; the end with the smaller force moves the larger distance.

Check yourself

A load end is pushed with F2 = 60 N through d2 = 0.1 m. What is the work F2 × d2, in J?

Answer: 6 J

F2 × d2 = 60 N × 0.1 m = 6 J.

The load end does 6 J of work. The effort end uses a force F1 = 15 N. Through what distance d1 does it move, in m?

Answer: 0.4 m

d1 = 6 J ÷ 15 N = 0.4 m.

In a lever, which end moves through the larger distance?

What happens to the work done on one end of a lever?

• The end with the larger force. Since F1 × d1 = F2 × d2, the larger force acts through the smaller distance.
• The end with the smaller force — correct. Yes!
• Both ends move the same distance. If the forces differ, the distances differ, since F1 × d1 = F2 × d2.
• It is lost completely. The work done on one end is transferred to the other end.
• It is doubled at the other end. The two works are equal: F1 × d1 = F2 × d2.
• It is transferred to the other end — correct. Yes!