arXiv preview of The Paper-Stack Trampoline

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The Problem

A steel ball dropped onto a thicker cushion should bounce less: more material usually means more energy dissipated during the impact. We investigated whether this intuition always holds for a stack of ordinary A4 printer paper.

Our Approach

My collaborators and I measured the coefficient of restitution (e) of a steel ball dropped onto stacks containing different numbers (N) of paper sheets. We compared the impact dynamics with the acoustic travel time through the stack and repeated the experiments while changing the gas surrounding the sheets.

Key Findings

The coefficient of restitution does not simply decrease as the stack becomes thicker:

• It first decreases as sheets are added.
• It then rises to a pronounced maximum.
• It finally decreases again toward a minimum.

The maximum appears when the acoustic round-trip time through the stack matches the contact time of the impact. When the contact is set by the stack itself, the result recovers the classical bar-impact condition, where the stack-to-ball mass ratio is of order one.

What Makes the Stack a Trampoline?

Bar-impact theory predicts only a weak recovery and does not explain why the surrounding gas matters. The recovery is large for paper stacks, but the maximum disappears when the stack is evacuated. This shows that the air trapped between the sheets, rather than the paper alone, gives the stack its trampoline-like behavior.