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A simple pendulum is suspended from a peg on a vertiacl wall. The pendulum is pulled away from the wall to horizontal position and released . the ball hits the wall coefficient of restitution being 2/√5 . what is the minimum number of collisions after which the amplitude of oscillations becomes less than 60 degrees

A simple pendulum is suspended from a peg on a vertiacl wall. The pendulum is pulled away from the wall to horizontal position and released . the ball hits the wall coefficient of restitution being 2/√5 . what is the minimum number of collisions after which the amplitude of oscillations becomes less than 60 degrees

Grade:11

1 Answers

Arun
25750 Points
6 years ago
Dear Anita
 
By the definition of coefficient of restitution, the velocity after each impact is $ \frac{2}{\sqrt{5}}$ of the velocity before it. Hence, the Kinetic energy after impact is $ \frac{4}{5}$ of that before.

To make amplitude $ \leq 60^0$, the maximum potential energy (and hence, the total energy) should be halved.

Observe that $ \left( \frac{4}{5}\right)^4<\frac{1}{2}$, and so, $ N=4$
 
Regards
Arun (askIITians form expert)

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