A block slides on a rough 45 degree incline. The coefficient of friction is µk what is the ratio of acceleration when the block accelerates down the incline to the acceleration when the block is projected up the incline

= (1 - μ)/μ

Explanation:

Always draw a diagram!

Up the incline:

= maximum friction

= μk

k = R = mg.cos(45) = mg.sin(45)

Resolution of forces parallel to the slope:

F (Fp in the diagram) = force of propulsion

g = gravity

μ.mg.cos(45)

Down the decline:

Resolution of forces:

μ.mg.cos(45)

Then, find the ratio:

Potentially, there is no need to consider F in this situation, in which case:

= (1 - μ)/μ