a) Assuming that f=N, show that the coefficient of (rolling) friction for the car moving down the inclined plane with a constant speed is gived

a) Assuming that f=μN, show that the coefficient of (rolling) friction for the car moving down the inclined plane with a constant speed is gived by μ=m ² /mc cosθ. Use symbols, not numbers.

b)Prove that θ is equal to μk when the blcok sldies down the incline with a constant speed?(use symbols not numbers)

b2) if θ is the maximum angle of inlcline just before the blcok moves, what is μs in term of θ?

c)suppose that the blcok were made to move up the inclined plane with a uniform speed by suspending masses on a string over the pulley. Derive an equation for the coefficient of kinetic friction for this case in terms of the suspended masses, the mass of the block, and the angle of decline. (neglect friction and mass of pulley)