# An object, previously at rest, slides #1 m# down a ramp, with an incline of #pi/3 #, and then slides horizontally on the floor for another #3 m#. If the ramp and floor are made of the same material, what is the material's kinetic friction coefficient?

##### 1 Answer

The coefficient of kinetic friction will be

#### Explanation:

This problem is most easily done by conservation of energy.

Two energy forms are involved:

A change in gravitational potential energy:

Frictional heating:

where

Before we can continue, we need to be aware of a couple of complications

We must express

Also, we must note that the normal force on an incline is not equal to mg, but to

With all that looked after, our equation becomes

(The first term is negative because the potential energy decreases.)

Notice that we can divide every term by mg, (including the right side of the equation)

So, inserting 1 m for