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A bullet of mass 0.7 kg hits a block and gets stuck with it with a velocity of 30m/s. The block has a mass of 50 and it is hanging by a string of length 15m. 1. find the T of the oscillations 2. Max acceleration of object after the collision in this periodic motion. 3. How long does it take the object to come back to rest?

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Answer #1

1. System is a simple pendulum.

with L = 15 m

T = 2 pi sqrt( L / g)

T= 2 pi sqrt(15/9.8) = 7.77 s ......Ans

2. w = 2 pi / T = 0.808 rad/s

Applying momentum conservtion for the collision,

(0.7 x 30) + (50 x 0) = (50 + 0.7) v

v = 0.414 m/s ...this is the maximum velocity of oscillation.


and a_max = v_max w

a_max = 0.335 m/s^2 .....Ans

3. t = T / 4 = 7.77 / 4

(time taken from mean position to extreme position)

t = 1.94 s  

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