Question

A box of mass 0.200 kg is given an initial speed of 2 m/s up a ramp with an angle of θ = 45° from the horizontal. The coefficients of friction between the box and ramp are μs = .7 and μk = .5 a) How far up the ramp does the box go before it comes to rest? b) Does it start to slide down the ramp after it gets to its maximum distance up the ramp?

Answer 1

Part A

Let the distance travelled be .

Then, the box would have travelled a height .

To do this, the box would have needed initial energy equal to the sum of the potential energy it would gain, and the energy it would lose due to friction.

Here

The work due to friction will be the friction force times the distance travelled along the slope. The friction force will be equal to the normal force times the coefficient of kinetic friction.

and the kinetic energy will be

Putting in our values and solving for , we get

Part B

For it to slide down, the component of its weight along the ramp must be greater than the force of static friction.

Since , we can directly compare these two without calculation.

It will slide down.