Assume the collision between the bullet and block is a perfect inelastic collisi

Question

Assume the collision between the bullet and block is a perfect inelastic collision. Obtain an expression for the velocity of the block-bullet system after the bullet is lodgcd in the block, but before the pendulum swings upwards. Express in terms ofM,m, and v_0. What is the change in vertical position, call it h, for the bullet-block system as they reach theta_max, in terms of L and theta_max ? Use your answers to a), b) and another fundamental principle of physics to obtair an expression for the initial velocity of the bullet in terms of L, g, M, m and theta_max.

Explanation / Answer

Since the collision is inelastic, KE of the system will not be conserved. Of course the total energy of system is conserved.

a) Conserving momentum we have

mvo= (M+m)v => v= mvo/(M+m)

b) h= L(1-cosmax)

c)Once the bullet sticks to the mass M, the system will behave as a pendulum with mass M+m which is given a velocity v(as determined in part 1).

Applying conservation of energy to this new system,

Initial KE + initial PE = final KE +final PE

0.5x(M+m)(mvo/(M+m))2 + 0 = 0 + (M+m)g(L-Lcosmax)

=> vo= (2gL(1-cosmax))0.5(M+m)/m -----(1)

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