Question

You push a 2.0kg block against a horizontal spring, compressing the spring by 15 cm at which point the mass is at rest. Then you release the block, and the spring sends it sliding across a tabletop. It stops 75cm from where you released it. The spring constant is 200N/m. What is the block-table coefficient of kinetic friction?

Answer 1

To find the block-table coefficient of kinetic friction, use the work-energy principle and Hooke's Law to calculate the work done by the spring and the work done by the friction force.

Step-by-step explanation:

To find the block-table coefficient of kinetic friction, we need to consider the forces acting on the block. When the block is released, the only force acting on it is the friction force. We can use the work-energy principle to find the work done by the friction force.

The work done by the friction force is equal to the change in kinetic energy of the block. We can use the equation:

Work done by friction force = -change in kinetic energy

Since the block starts from rest and comes to a stop, the change in kinetic energy is equal to the initial kinetic energy of the block. We can write this as:

Work done by friction force = -initial kinetic energy

The initial kinetic energy of the block is equal to the work done by the spring in compressing it. We can use Hooke's Law to find the work done by the spring:

Work done by the spring = (1/2)kx^2

where k is the spring constant and x is the compression of the spring.