# Pulley Puzzle

In the pulley puzzle diagram below, there is a pulley attached to a scale. One side of the pulley is attached to a weight and the other side is attached to the ground.

If the scale reads 100g, does the weight weigh 50g, 100g, or 200g?

Assume the pulley and rope has no weight (the scale is already adjusted to account for these), and that the whole system is in equilibrium (nothing is moving).

Note: this puzzle is best solved with a bit of basic physics knowledge, but there is also an intuitive solution, so give it a shot.

#### Solution

50g

Physics Solution

Let’s say the weight weighs x. So it exerts x downward force on the rope. Since the system is in equilibrium, we know the rope must be exerting x upward force on the weight.

Tension force is constant along the length of a rope, so the rope is also exerting x upward force on the ground. Since the system is in equilibrium, we know the ground must then be exerting x downward force on the rope.

Therefore the total downward force on the scale is 2x (x from the weight and x from the ground), which is equal to 100g. So the weight must weigh 50g.

Intuition Solution

Since nothing is moving, the ground must be pulling on the rope with the same force as the weight is pulling on the rope. This means we can just replace the ground with another identical weight. Clearly the scale now has two identical weights attached to it, so if it reads 100g, each weight must weigh 50g.