A Sliding Block Question - Answer

A Sliding Block Question - Answer = B

The block takes more time to slide down the incline plane than it took to slide up. Since it started with some initial velocity (Vo) and ended its upward trip with zero final velocity, its average velocity was Vo/2. (As we assume uniform deceleration due to friction and gravity.) So the time up would be, t = d/(Vo/2).

However, the block loses energy going up and down due to friction (kinetic energy is converted into heat energy), thus when it slides back down its final kinetic energy (and final velocity) will be less then the initial kinetic energy (and initial velocity) as it started up the ramp.

Since for the downward trip the block starts at zero velocity and ends with Vf , its average velocity down is Vf/2, which is less than its average velocity up (since Vf is less than Vo), so the trip down take longer than the trip up the incline.

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