Sphere of Fear
Solution:
a) To find the normal forces acting on the motorcycle at both the top and the bottom of the vertical circular path we start with the free body diagram for each position.
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We can now write the respective equations for each position. Note that the velocity must be converted from km/h to m/s, and that the radius, not the diameter is required.
b) To successfully complete the loop, the minimum velocity at the top would be that at which the normal force would equal zero, thus requiring only the weight of the motorcycle to provide the centripetal force.
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