Simple machines

Simple machines such as levers, pulleys, gears, ramps and wheels-and-axles make jobs easier by changing the size or direction of a force. A machine that lets you use a smaller force always makes you move further, so you never get more work out than you put in.

Key facts

  • The six simple machines: lever, pulley, wheel and axle, inclined plane (ramp), wedge, screw.
  • Mechanical advantage (MA) = load ÷ effort.
  • Lever: effort × distance from pivot = load × distance from pivot.
  • A pulley system with n supporting ropes: effort = load ÷ n (ideally), but you pull n times as much rope.
  • Gears: the gear with fewer teeth turns faster; meshing gears turn in opposite directions.
  • Ramp (no friction): effort × length = load × height. Efficiency = useful work out ÷ work in.

Worked examples

Example 1

A crowbar has the load 10 cm from the pivot and the effort 90 cm from it. What effort lifts a 450 N stone?

  1. The effort pushes down on the long end.
  2. Moments about the pivot balance: effort × its distance = load × its distance. E × 90 = 450 × 10
  3. Divide. E = 4500 ÷ 90 = 50 N

Answer: 50 N

Example 2

A pulley system with 4 supporting ropes lifts a 1200 N load by 1.5 m. Find the effort and how much rope is pulled.

  1. Four rope sections hold up the bottom pulley. They share the load equally.
  2. Each section carries a quarter of the load, and the effort equals the tension in the rope. effort = 1200 ÷ 4 = 300 N
  3. To raise the load 1.5 m, each of the 4 sections must shorten by 1.5 m. rope pulled = 4 × 1.5 = 6 m
  4. Check: work in = work out. 300 × 6 = 1800 J = 1200 × 1.5

Answer: 300 N; 6 m

Example 3

A 40-tooth gear turns 6 times and drives a 15-tooth gear. How many turns does the small gear make?

  1. The big gear turns 6 times. Every tooth that passes the meeting point pushes one tooth of the small gear. 6 × 40 = 240 teeth
  2. One turn of the small gear uses 15 teeth. It turns the opposite way. 240 ÷ 15 = 16 turns

Answer: 16 turns