The “ballistic pendulum” is a device used for measuring the speed that bullets t

Question

The “ballistic pendulum” is a device used for measuring the speed that bullets travel in a laboratory. A pendulum is built out of a cable with length L and a clay block of mass M, and allowed to hang straight down. A bullet of mass m is shot into the clay block. The bullet lodges in the block and the block swings up until the pendulum makes an angle of with the vertical. By measuring how large this angle is, technicians can work backward and find the initial velocity v0 of the bullet.

Find an expression for v0 in terms of M, m, L, and .

Explanation / Answer

m vo = ( M + m ) V
= [ m / ( M + m ) ] vo
hmax is h = L ( 1 - cos ) and by balance of engergy at the lowest point and at the highest point we have

( 1/2 ) ( M + m ) V2 = ( M + m ) g h
V2 = 2 g h
V = ( 2 g h )
V = [ 2 g L ( 1- cos ) ]
[ m / ( M + m ) ] vo = [ 2 g L ( 1- cos )]
vo =    [ ( M + m ) / m]   [ 2 g L ( 1- cos ) ]

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