A block of mass m is at rest at the top of a ramp of vertical height h . The blo

Question

A block of mass m is at rest at the top of a ramp of vertical height h. The block starts to slide down the frictionless ramp and reaches a speed v at the bottom. If the same block were to reach a speed 2v at the bottom, it would need to slide down a frictionless ramp of vertical height _____.

h1

1.41h

2h

3h

4h

6h

A block of mass m is at rest at the top of a ramp of vertical height h. The block starts to slide down the frictionless ramp and reaches a speed v at the bottom. If the same block were to reach a speed 2v at the bottom, it would need to slide down a frictionless ramp of vertical height _____. h1 1.41h 2h 3h 4h 6h

Explanation / Answer

Since the first incline is frictionless, there is no energy loss in coming down.

4 times as high. By conservation of energy, PEi = KEf, mgh = (1/2) mv2.

h is proportional to v2.   If v doubles, v2 quadruples, and so does h.

Hence the answer is 4h

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