A block slides down a rough ramp (with friction) of height h . The block started

Question

A block slides down a rough ramp (with friction) of height h . The block started at rest. It reaches a speed v at the bottom of the ramp. Would the height of the ramp needed to reach a speed of 2v be more than, less than, or the same as the height in the frictionless case?

A) The rough ramp would need the same height to reach a speed 2v as in the frictionless case.

B) The rough ramp would need more height to reach a speed 2v than in the frictionless case.

C) The rough ramp would need less height to reach a speed 2v than in the frictionless case.

D) We would need to know the coefficient of friction to compare the height of need by the rough ramp to the height needed in the frictionless case.

Explanation / Answer

Here ,

as the acceleration on a rough incline is given as

a = g * (sin(theta)- u * cos(theta))

on a frictionless surface ,

a = g * sin(theta)

Now, for the height needed for velocity to be 2v on the frictionless surface , we need the value of u and theta , but it will be less than the rough incline

hence , correct option is

B) The rough ramp would need more height to reach a speed 2v than in the frictionless case.

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