A ballistic pendulum is a device that was used to measure the speeds v of bullet

Question

A ballistic pendulum is a device that was used to measure the speeds v of bullets before electronic timing devices came along. It consists of a large block of wood, whose mass M is 5.4 kg. hanging from two long pairs of cords. A m=9.5g bullet is fired into the block, coming quickly to rest. The block + bullet then swing upward, their center of mass rising a vertical distance of h=6.3 cm before the pendulum comes momentarily to rest at the end of its arc.

How much is the energy lost once the pendulum gets to it the maximum height?

Explanation / Answer

Applying energy conservation to find speed of block after collision,

PEi + KEi = PEf+ KEf

0 + ( M + m) v^2 /2 = (M + m) g h + 0

v= sqrt(2 g h) = sqrt(2 x 9.8 x 0.063 )

v = 1.11 m/s

Applying momentum conservation,

(9.5 x 10^-3)v0 + (5.4 x 0) = (5.4 + 0.0095) (1.11)

v0 = 632.7 m/s

Ki = (9.5 x 10^-3) (632.7)^2 / 2

Ki = 1901.77 J  

Kf = (5.4 +0.0095) (1.11^2) / 2

= 3.33 J  

Energy lost = Ki - Kf = 1898 J ........ANs

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