Two 0.85m -long pendulums hang side by side. The masses of the pendulum bobs are

Question

Two 0.85m -long pendulums hang side by side. The masses of the pendulum bobs are 50g and 70 g . The lighter bob is pulled aside until its string is horizontal and is then released from rest. It swings down and collides elastically with the other bob at the bottom of its arc. To what height does the lighter bob rebound? Express your answer to two significant figures and include the appropriate units. To what height does the heavier bob rebound? Express your answer to two significant figures and include the appropriate units.

Explanation / Answer

Let v be the velocity of the lighter bob at the bottom just before collision.

v=sqrt(2gh)=4.08m/s

Conserving momentum, (v2 be the velocity of lighter pendulum after collision)

4.08*50=-50v2+70v1.

Also, since it is an elastic collision,

velocity of separation=velocity of approach,

v1+v2=v=4.08

v1=3.4m/s

v2=0.68m/s

a)Height achieved by the lighter bob=sqrt(v2/2g)=0.154m

b)Height achieved by the heavier bob=sqrt(v2/2g)=0.768m

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