2. A bullet of mass m and initial velocity v 0 passes through a block of mass M

Question

2. A bullet of mass m and initial velocity v0 passes through a block of mass M suspended by an unstretchable, massless string of length L from an overhead support. It emerges from the collision on the far side traveling at v1 < v0. This happens extremely quickly (before the block has time to swing up) and the mass of the block is unchanged by the passage of the bullet (the mass removed making the hole is negligible, in other words). After the collision, the block swings up to a maximum angle max and then stops. Find max.

Explanation / Answer

here,

let the block of the speed after the collision is v m/s

Now, for the bullet block collision

Using conservation of momentum

m * (v0 - v1) = M * v

v = m *(v0 - v1)/M ...(1)

Now, for the block , using conseravtion of energy

m*g*L(1 - cos(thetamax)) = 0.5 * M * v^2 ...(2)

from equation (1) and (2)

thetamax = arccos( 1 - m * (v0 - v1)^2 / (2 * M * g * L))

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