Question

A box sits on a 30o incline as shown below, and is coasting up the ramp...

A box sits on a 30o incline as shown below, and is coasting up the ramp with an initial speed of 5.0 m/s. The coefficient of kinetic friction between the box and the ramp is 0.25. Determine the acceleration of the box on the way up. How long will it take for the box to come to rest? How far up the ramp will it travel before coming to rest?

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Answer #1

The situation can be visualized as

From the diagram

and

Now, let us assume the box travels a distance of l on the ramp before stopping. So, the work done by the force of friction on the box is

The total energy of the system when the box is at the bottom of the incline is

The vertical height of the box at a distance l can be given using trigonometry

So, when the box is at that position, the total energy of the system is

The work-energy theorem gives us

So, the box would travel a distance of 1.78 m along the ramp.

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