By：Tao Steven Zheng (鄭濤)

【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.

【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