Intermediate · 12 min
Pulleys and mechanical advantage
Calculate force and distance trade-offs in an ideal pulley system.
A machine can change the required force
A pulley can change the direction of an applied force, and a movable pulley system can reduce its magnitude. In an ideal arrangement with massless rope and frictionless pulleys, rope tension is the same throughout one continuous rope. If n parallel vertical rope sections support a load, their upward forces add. For steady lifting, n × tension balances the load's weight. Count supporting sections, not simply the number of pulleys.
Worked example
A 60 N load is supported by three vertical sections of an ideal rope. Required rope tension = 60 ÷ 3 = 20 N
The distance trade-off
An ideal machine does not create energy. If its force advantage is n, the pulling end moves n times as far as the steadily rising load in this arrangement. Input work equals output work. Real pulleys have friction and mass, so the required effort can be greater. Mechanical advantage is load force divided by effort force; it is not a percentage.
Worked example
With a force advantage of 2, raising a load by 0.4 m requires pulling 0.8 m of rope. For a 100 N load, ideal effort is 50 N; both work values are 40 J.
Check the work on both sides
- For an ideal system with force advantage 2 lifting an 80 N load through 0.3 m, find the effort force and pulling distance.
- Calculate effort work and load work separately. Explain why the reduced force does not reduce the ideal energy required.