A 2.0 -kg block of wood rests on a long tabletop. A 5.0 -g...

A $2.0$ -kg block of wood rests on a long tabletop. A $5.0$ -g bullet moving horizontally with a speed of $150 \mathrm{~m} / \mathrm{s}$ is shot into the block and lodges in it. The block then slides $270 \mathrm{~cm}$ along the table and stops. ( $a$ ) Find the speed of the block just after impact. ( $b$ ) Find the friction force between block and table assuming it to be constant.

Key Concepts

Conservation of Momentum in Inelastic Collisions

This concept refers to the principle that, in the absence of external forces, the total linear momentum of a system remains constant during a collision, even if the collision is inelastic. In an inelastic collision, some kinetic energy is converted into other forms of energy, but the momentum before the collision equals the momentum after. This principle is used to determine the speed of the combined mass (block plus bullet) immediately after the collision.

Work-Energy Principle

The work-energy principle states that the work done by all forces acting on an object equals the change in its kinetic energy. In scenarios where friction is the only significant force doing work over a distance, this principle can be applied to relate the kinetic energy lost (due to friction) to the work done by friction, allowing one to compute the friction force when the distance and initial kinetic energy are known.

Friction Force

Friction force is a resistive force that acts opposite to the direction of motion, dissipating kinetic energy as an object moves over a surface. In problems involving sliding motion (like a block coming to rest on a table), a constant friction force is typically assumed, and its magnitude can be determined by calculating the work required to dissipate the initial kinetic energy over the distance traveled.

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