Discussion
If a solid elastomer ball of weight 100 g is allowed to free fall from a height of 10 m and it rebounds back to a height of 8 m, the hysteresis loss is
Answer: C
The hysteresis loss is 1.96 J.
The energy lost in the impact is the difference between the potential energy at the drop height and at the rebound height. It is dissipated as heat by internal friction in the rubber, which is what hysteresis means:
\[ \begin{aligned} \Delta E &= mg(h_{1} - h_{2}) = 0.1 \times 9.8 \times (10 - 8) \\ &= 1.96\ \text{J} \end{aligned} \]
9.80 J is the full potential energy at 10 m, and 19.60 J doubles it. 0.98 J would be the loss for a 1 m drop in height. The rebound resilience here is 8/10 = 80 percent.
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