Want to know exactly how to do this?

Question

A similar question will probably be on exam, & want to be sure I know how to do it. There is no equivalent problem in the textbook:

A light horizontal spring has a spring constant of 135 N/m. A 2.18 kg block is pressed against one end of the spring, compressing the spring 0.101 m. After the block is released, the block moves 0.287 m to the right before coming to rest.

What is the coefficient of kinetic friction between the horizontal surface and the block? Acceleration of gravity is 9.81 m/s^2.

Answer 1

This is an energy problem. The equation would be

1/2kx^2 - (mu)mgd = 0

This is the initial potential energy minus the work done by a non-conservative force equals the final kinetic energy, which is zero. Mu is the coefficient of kinetic friction, k is the spring constant, x is the displacement of the spring, m is the mass of the block, g is the gravitational constant and d is the distance it travels. So, solving for mu would give

mu = kx^2/(2mgd)