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A roller coaster is designed such that riders experience "weightlessness" as they go round the top of a hill whose radius of curvature is . The speed of the car at the top of the hill is between:

  1. A
    and
  2. B
    and
  3. C
    and
  4. D
    and

Solution & Step-by-step Explanation

At the top of the hill, the forces acting on the rider are gravity () downwards and the normal force () upwards. The net centripetal force is:

For weightlessness, the normal force :

Given and taking :

If we take :

Thus, the speed is between and .

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A roller coaster is designed such that riders experience "weightlessness" as they go round the top of a hill whose radius of curvature is . The speed of the car at the top of the hill is between:
A
and
B
and
C
and
D
and

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Circular MotionWeightlessnessMechanics

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