## Coming To Equilibrium: Pulleys And Heavy Weights - Question of the Week 2/2 - 2/6

A pulley system can be used to lift heavy objects using a smaller force. A typical one is shown in the photo below.

In this case, a heavy object is placed on the hook below the lower pulley, and a presumably lighter force is applied to the hook at the left just inside the left support on the frame.

The question this week is how much force applied to the rope at the left is required to balance a weight put onto the hook below the movable pulley. Note that this system is in equilibrium; the small black block hanging above the hook on the rope at the left exactly balances the weight of the movable pulley.

Two kilograms of mass placed on the hook at the left will exactly balance how much mass hanging from the hook below the pulley?

• (a) 1 kg.
• (b) 2 kg.
• (c) 4 kg.
• (d) 8 kg.

The answer is (c): the two-kilogram mass on the hook at the left exactly blances four kilograms of load on the moving pulley at the right. This is seen in the photograph at the left below and the detail of the weights at the right.

This system obeys the general law of pulleys: the weight that can be supported by the lifting force is proportional to the ratio of the number of ropes supporting the load to that for the lifting force. Here the ratio is two to one, as seen in the photograph.