A ballistic pendulum is a block of wood (mass M) suspended on a string of length

Question

A ballistic pendulum is a block of wood (mass M) suspended on a string of length l. A bullet (mass rn) is shot horizontally at the block and embeds itself into the wood, making the block swing, like a pendulum. One then measures the max angle theta that pendulum swings to from the vertical before it swings back, and uses that angle to determine the original speed of the bullet. Which quantities are conserved (for the system consisting of bullet and block) as the bullet embeds itself into the block of wood and as the pendulum swings from its initial rest position at the bottom to its max angle. Briefly justify why. Find a general expression for the initial speed of the bullet given m, M, l and theta. You measure m = 2g, M = 2 kg, l = 1 m and theta = 4 degree. What is was the bullet's speed?

Explanation / Answer

a) i) angular momentum will be conserved as there is no impulsive torque

ii) energy is conserved as there is no any friction or air drag.

b) by energy conservation, 0.5*(M+m)V^2= (m+M) g*l*(1-cos theta)

V = sqrt[2gl(1-cos theta)]

now by momentum conservation initially,

mv = (M+m)V

v = [(M+m)/m]*sqrt[2gl(1-cos theta)]

c) v =  [(2+0.002)/0.002]*sqrt[2*9.8*1(1-cos 4 degree)]

= 218.7 m/s answer

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