Problem

A bullet of mass is fired into a stationary block of mass at some velocity . The block is attached to a wire (assume massless and infinitely rigid). The bullet-block system swings to a height .

Part 1: Explain why the conservation of energy cannot be applied before the collision?

Part 2: Determine in terms of , , and .

Part 3: Suppose the block is 100 times heavier than the bullet. If the bullet-block system swings to a height of 20 cm, what was the velocity of the bullet? Assume this setup is on Earth.

Ballistic pendulum.jpg

Solution

Part 1

Energy is only conserved in perfectly elastic collisions. Since this collision is inelastic, energy is not conserved prior to collision and during the collision. However, kinetic energy of the bullet-block system is conserved post collision, which is converted to gravitational potential energy.

Part 2

Conservation of momentum (before and during collision).

Conservation of energy (post collision).

From the conservation of momentum

Thus

Part 3

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