The diagram below shows a pulley arrangement :
If the free end of the string moves through a distance x, find the distance by which the load is raised.
Topic: Machines, levers and pulleys
Answer
For the pulley arrangement shown, the velocity ratio is 2.
Velocity ratio = distance moved by the effort ÷ distance moved by the load VR = d_E ÷ d_L
2 = x ÷ d_L d_L = x ÷ 2
The load is raised through a distance of x/2.
Count the strands supporting the movable pulley — that number is the velocity ratio. Here two strands share the load, so VR = 2.
The effort always moves the greater distance, so the load must rise by LESS than x. An answer of 2x would mean the load moves further than the effort, which no machine does. That check catches the inverted answer instantly.
The trade-off is the whole point of a machine: the effort is halved, so the distance is doubled. Energy in equals energy out, in an ideal system.