Solving for the Coefficient of Kinetic Friction: An In-Depth Explanation

[Vinegar]

Homework Statement

Homework Equations

PE=mgh, KE=1/2mv^2

The Attempt at a Solution

In picture.

What's confusing me is how to find the kinetic friction without its coefficient. I've attempted multiple solutions on paper, and I can't get anywhere with it. I know that at the bottom of the ramp, the KE is equivalent to the PEi of the ramp, and I know the distance it stops at.

I just need an in-depth explanation of the steps taken to solve for the coefficient. If I can find this, I'm set. I'm great at physics, but I am having trouble grasping this concept. Help is appreciated!

 

[cepheid]

Welcome to PF!

What's confusing me is how to find the kinetic friction without its coefficient. I've attempted multiple solutions on paper, and I can't get anywhere with it. I know that at the bottom of the ramp, the KE is equivalent to the PEi of the ramp, and I know the distance it stops at.

I just need an in-depth explanation of the steps taken to solve for the coefficient. If I can find this, I'm set. I'm great at physics, but I am having trouble grasping this concept. Help is appreciated!

Since you know the suitcase's kinetic energy at the bottom of the ramp (from conservation of energy), you know how much work has to be done in order to bring it to a stop. You also know over what distance this work was done. Therefore, you can solve for the frictional force that must have done said work on the suitcase. Once you know the frictional force, you can easily solve for the coefficient of kinetic friction, since you know everything else (aside from the coefficient itself) that that frictional force depends on.