Question

 A wooden box with a mass of 10.0 kg rest on a ramp that is incline at an angle of 25° to the horizontal. A rope attached to the box runs parallel to the ramp and then passes over a frictionless bully. A bucket with a mass of M hangs at the end of the rope. The coefficient of static friction between the ramp in the box is 0.50. The coefficient of Kinetic friction between the ramp in the box is 0.35. Suppose the Bucket has a mass of 2.0 kg. Part a. What is the friction force exerted on the box by the ramp? Part B does the box remain at rest relative to the ramp? 

Answer 1

In order to answer part a and b of question 3, it is necessary to determine the forces of the system.

A force diagram is shown below:

as you can notice, the friction force fr is opposite to the force mgsinθ and has the same direction that the tension T on the chord.

The friction force is given by: