# A box with an initial speed of #2 m/s# is moving up a ramp. The ramp has a kinetic friction coefficient of #8/7 # and an incline of #( pi )/4 #. How far along the ramp will the box go?

##### 1 Answer

The box will travel

#### Explanation:

This problem is most easily done by conservation of energy.

Three energy forms are involved:

A change in kinetic energy:

A change in gravitational potential energy:

Frictional heating:

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

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

Also,