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Preventing a Block from Sliding down an Inclined Plane

What is the minimum value of a force acting on a resting block to prevent the block from slipping down on an inclined plane?

See the figure below.


A block of 8 kg of mass rests on an incline with 37° of the slope. The coefficient of static friction between the block an the plane is 0.2 and the coefficient of kinetic friction is 0.1. Use cos 37° = 0.8, sin 37° = 0.6 and g = 10 m/s2 for the three questions below:
a) What is the minimum value of the force F that will prevent the box from sliding down the inclined plane?
b) What is the minimum value of F that will start the box moving up the inclined plane?
c) What is the value of F to get the box move up with a constant velocity?

Discussion
All of the three questions above in the same condition. ΣF = 0. Sketch the free diagram of forces for each question first and then apply the condition of ΣF = 0.

a) minimum value of the force F that will prevent the block from sliding down the inclined plane



b) the minimum value of F that will start the block moving up the inclined plane



c) the value of F the block moves up with a constant velocity



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