A 9.59-g bullet, moving horizontally with an initial speed v 0 , embeds itself i

Question

A 9.59-g bullet, moving horizontally with an initial speed v0, embeds itself in a 1.45-kg pendulum bob that is initially at rest. The length of the pendulum is L = 0.829 m. After the collision, the pendulum swings to one side and comes to rest when it has gained a vertical height of 12.4 cm. (a) Is the kinetic energy of the bullet-bob system immediately after the collision greater than, less than, or the same as the kinetic energy of the system just before the collision?

Explain.

(b) Find the initial speed of the bullet.
m/s

(c) How long does it take for the bullet-bob system to come to rest for the first time?

Explanation / Answer

a) inelatic collision so less than

b)

after collision convservation of energy

1/2 mv^2 = m g h

v = sqrt(2*g*h) = sqrt(2*9.81*.124)= 1.56 m/s

conservation of momentum during collision

9.59E-3*v = (9.59E-3+1.45)*1.56

v=237.4 m/s

c)time = T/4 = 2*pi*sqrt(L/g)/4 = 2*pi*sqrt(0.829/9.81)/4= 0.457 s

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