A block is projected up a rough 37° incline. It stops and then returns to the starting point. If the time to go up is half the time to come down, find μ.
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A block is projected up a rough 37° incline. It stops and then returns to the starting point. If the time to go up is half the time to come down, find μ.

G1 Physics · Accepted Answer

The deceleration while moving up is g(sin37° + μcos37°), whereas the acceleration while coming down is g(sin37° - μcos37°). For the same distance, time-up/time-down = √(downward acceleration/upward acceleration) = 1/2, hence upward acceleration = 4downward acceleration. Solving gives μ = (3/5)tan37° = 9/20.