Solution to Question 15

Physics Solution: The Juggler Problem

1. Analyzing the Load

We need to determine if the juggler can cross a bridge with a maximum safe load of 50 kgf.
Data:

Mass of Juggler: $ M = 47 $ kg
Mass of one ball: $ m = 2 $ kg
Number of balls: $ n = 5 $
Bridge Limit: $ 50 $ kgf

2. Calculating Average Force

The juggler believes that by keeping balls in the air, the load on the bridge decreases. However, physics dictates that the average normal force exerted by the ground (bridge) over a period of time must equal the total weight of the system.

To keep balls in the air, the juggler must impart upward impulses. The reaction force to these impulses adds to his weight. Averaged over time, the force $ F_{avg} $ is:

$$ F_{avg} = \text{Weight of Juggler} + \text{Total Weight of Balls} $$ $$ F_{avg} = 47 + (5 \times 2) = 47 + 10 = 57 \text{ kgf} $$

Since $ 57 \text{ kgf} > 50 \text{ kgf} $, the average load exceeds the bridge’s capacity. Furthermore, the peak force during the “throw” phase would be even higher than the average.

Final Answer

The juggler is incorrect. The bridge will break because the average load is (c) 57 kgf.