A frictionless inclined plane, which is at an angle to the h...

Question

A frictionless inclined plane, which is at an angle to the horizontal, is connected to a rough horizontal table. Block B is initially stationary at the base of the inclined plane. Block A is released from rest at the top of the inclined plane. After sliding down, A collides inelastically with B, and the two blocks stick together, then slide on the horizontal table. The inclined plane has a height , and both blocks have the same mass. The coefficient of kinetic friction between the combined blocks and the table is 0.2. What is the maximum distance L the combined blocks travel on the table? (Take g=10 m/s²)

To solve the problem, we analyze the system in three parts:

1. Block A's descent on the incline

2. Inelastic collision of blocks A and B

3. Sliding of the combined blocks on the rough table

Find the velocity of Block A at the bottom of the incline

The potential energy of Block A at height is converted to kinetic energy as it slides down the frictionless incline.

Using conservation of energy:

Substitute and :

Block A's velocity at the bottom is .

Apply conservation of momentum for the inelastic collision

The total momentum before and after the collision is conserved. Let be the mass of each block, and be the velocity of the combined system after the collision:

Substitute :

The combined blocks move with a velocity after the collision.

Analyze the motion of the combined blocks on the rough table

The friction force

Click "Show Answer" to reveal the answer and analysis

Physics

Question

Options

Answer & Analysis

Answer

Analysis

Want More Practice Questions?