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Simple Machines

13 min read

Machines make work easier

A machine is a device that makes work easier. It can reduce the force needed, change the direction of a force or increase speed. Simple machines include the lever, pulley, inclined plane (ramp), wheel and axle, screw and gear. A machine does not save work: to use a smaller force you move it a longer distance.

A fixed pulley only changes the direction of the force. A two-pulley system halves the effort; a lever with a long effort arm can cut it even more.

Pulleys

A pulley is a wheel with a rope over it. A fixed pulley only changes the direction of the force. A movable pulley shares the load between two ropes, so the effort is about half the load but you must pull twice as much rope. A block and tackle uses several pulleys and gives a bigger velocity ratio.

Pulley systemsThree pulley arrangements: a single fixed pulley that only changes the direction of the force, a single movable pulley that halves the effort, and a block and tackle with four supporting ropes.LFixed pulleyMA = 1, changes directionLMovable pulleyMA = 2, VR = 2LBlock and tackleVR = 4 (four supporting ropes)
The effort moves twice as far as the load.

Mechanical advantage, velocity ratio and efficiency

MA tells how many times the machine multiplies your force. VR is what it would multiply in a perfect machine. Efficiency compares the two.
Try itTest a pulley system

A pulley system has a velocity ratio set by its number of rope sections. You lift a load with an effort. How efficient is it?

Worked exampleEfficiency of a pulley system

A pulley system has VR = 4. An effort of 160 N lifts a load of 480 N. Find the MA and the efficiency.

  1. MA.
  2. Efficiency.

Answer: MA = 3 and efficiency = 75%.

The inclined plane

A ramp (inclined plane) lets you raise a load by a smaller force over a longer distance. It is easier to push a heavy drum up a long ramp than to lift it straight up. Friction on the slope wastes some of the work, so the efficiency is below 100%.

A block on an inclined planeA block on a slope with four forces: weight pulling straight down, the normal reaction pushing out at right angles to the slope, an effort pulling it up the slope and friction acting down the slope against the motion.W (weight)R (normal)effortfrictionθ
A long, gentle slope has a big velocity ratio, so the effort needed is small.

The three classes of lever

The three classes of leverThree levers. In a first-class lever the pivot is between the load and the effort. In a second-class lever the load is between the pivot and the effort. In a third-class lever the effort is between the pivot and the load.First classloadeffortpivotcrowbar, see-saw, scissorsSecond classloadeffortpivotwheelbarrow, bottle openerThird classloadeffortpivottweezers, fishing rod
Classes of lever
ClassPivot, load, effortExamples
Firstpivot between load and effortsee-saw, scissors, crowbar
Secondload between pivot and effortwheelbarrow, nutcracker
Thirdeffort between pivot and loadtweezers, a fishing rod, your forearm
Check yourself A machine has MA = 5 and VR = 8. What is its efficiency?
Check yourself Which is a second-class lever?

Key terms

Load
The force the machine overcomes.
Effort
The force you apply to the machine.
Mechanical advantage
Load divided by effort.
Velocity ratio
Distance moved by the effort divided by distance moved by the load.
Efficiency
Useful work out as a percentage of work in.

Summary

  • Machines change the size or direction of a force; they do not save work.
  • MA = load ÷ effort; VR = effort distance ÷ load distance.
  • Efficiency = MA ÷ VR × 100% and is always less than 100%.
  • A movable pulley halves the effort but doubles the distance; a ramp has VR = slope length ÷ height.
Forces in Equilibrium Motion in a Straight Line