Work and Potential Energy on a Sliding Block with Friction?

Question

A block of weight w sits on a plane inclined at an angle theta. The coefficient of kinetic friction between the plane and the block is mu.
A force F is applied to push the block up the incline at constant speed.

What is the change in potential energy of the block, DeltaU, as it moves a distance L down the incline?
answer in terms of some or all of the following: mu, w, theta, L.

What is the work W done by the applied force of magnitude F?
answer in terms of some or all of the following: mu, w, theta, L.

What is the work W_f done on the block by the frictional force?
answer in terms of some or all of the following: mu, w, theta, L.

Answer 1

The potential energy depends only on the height of the block. Draw the triangle of horizontal distance as one leg, ramp as the hypotenuse. You can then see how to calculate the change in vertical elevation. The potential energy of a mass is given by m*g*h, where g = accel of gravity = 9.8m/sec^2

Work done by a constant force is F*s, where s is the distance over which the force acts. This is the work done to overcome friction. That must be added to the change in potential energy (energy = work) to get the total work done by the force.

As said above, the work done by friction is F*s.

Answer 2

You will benefit from drawing a diagram on a piece of paper with all the different variables with their directions.

To start, PE = force x vertical height = weight x vertical height

You can express the vertical height in terms of sine theta and L...

Hope this helps!