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Weekly Challenge 13: Comet Catastrophe

A weekly challenge: these are shorter problems aimed at Post-16 students or enthusiastic younger students.

Collision with a Vertical Spring

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

A small disc of mass $60\mathrm{g}$ is placed on top of a vertical spring, which can oscillate and has a spring constant $k = 6\mathrm{N/m}$. Initially the spring is at rest. From a distance $h = 0.8\mathrm{m}$ above the spring we release a small elastic bouncing ball of mass $10\mathrm{g}$.

The ball collides with the disc with a coefficient of restitution $ e = \frac{3}{4} $ and bounces back - up.

Find the maximum distance between the ball and the disc.


Possible extension: What about the maximum distance between the ball and the disc after the two objects have collided a second time? (Computationally heavy!)


For simplicity, you may assume that $ g = 10 \mathrm{m/s}^2$.