Simple Machines

How can a small child balance a grown-up on a see-saw, or lift a heavy load with one hand? Try a lever and some pulleys to find out.

Machine
Left moment
98.1 N·m
Right moment
73.6 N·m
Result
Tips left
Tilt
0°

The maths, live

Left moment M = m × g × dM = 10 × 9.81 × 1.00 = 98.1 N·m
Right moment M = m × g × dM = 5 × 9.81 × 1.50 = 73.6 N·m
Balanced when m₁ × d₁ = m₂ × d₂10 × 1.00 = 10.00 ≠ 5 × 1.50 = 7.50

Can a 5 kg block balance a 20 kg block? Move it further from the pivot and see.

How it works

A force that turns something round a pivot makes a moment: moment = force × distance from the pivot. A see-saw balances when the moments on both sides are equal, m₁ × d₁ = m₂ × d₂. Otherwise it tips towards the side with the bigger moment, so a light mass far out can balance a heavy mass close in.

In a pulley system the load hangs from several ropes that share the weight, so the effort you need is the load divided by the number of supporting ropes. There is a catch: you have to pull that many times more rope. Work in (effort × rope pulled) equals work out (load × height lifted), so a machine makes a job easier but never saves energy.

Try this

  1. Put 10 kg at 1 m on the left. Where must 5 kg go on the right to balance it?
  2. Lift a 100 kg load with each pulley system. How much effort does each one need?
  3. Lift the load 0.5 m with 4 ropes. How much rope do you pull?