A 5.00 -g bullet is fired horizontally into a 1.20 -kg...

A 5.00 -g bullet is fired horizontally into a 1.20 -kg wooden block resting on a horizontal surface. The coefficient of kinetic friction between block and surface is $0.20 .$ The bullet remains embedded in the block, which is observed to slide 0.230 $\mathrm{m}$ along the surface before stopping. What was the initial speed of the bullet?

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Key Concepts

Conservation of Linear Momentum

This principle states that in the absence of external forces, the total momentum of a system remains constant. In collision problems, especially in inelastic collisions where objects might stick together, the momentum before collision is equal to the momentum after collision, providing a way to relate the velocities of the colliding bodies.

Inelastic Collisions

In an inelastic collision, the colliding objects stick together after impact and kinetic energy is not conserved, even though momentum is. This concept is important for understanding how the bullet embeds into the block and how the subsequent motion is governed by the combined mass.

Work-Energy Principle

This principle relates the work done by forces (such as friction) to the change in kinetic energy of an object. When the block (with the embedded bullet) slides and eventually stops due to friction, the work done by friction equals the loss in kinetic energy, allowing us to relate frictional force, displacement, and initial kinetic energy.

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