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In the figure here, a solid brass ball of mass 0.102 g will roll smoothly along

ID: 1435685 • Letter: I

Question

In the figure here, a solid brass ball of mass 0.102 g will roll smoothly along a loop-the-loop track when released from rest along the straight section. The circular loop has radius R = 0.15 m, and the ball has radius r << R.
(a) What is h if the ball is on the verge of leaving the track when it reaches the top of the loop?
(b) If the ball is released at height h = 5R, what is the magnitude of the horizontal force component acting on the ball at point Q?

I already have the answer for part a correct, but I am not sure how to do part b.

Explanation / Answer

For part b)

applying energy conservation, let velocity at Q = v

then mg(h-R) = 0.5 mv2

v2 = 2g(h-R)

now horizontal force at Q is the centrifugal force, F = mv2/R

F = 2mg(h-R)/R

F = 2 x 0.102 x 10-3 x 9.8 x 4R/R

F = 8 x 10-3 N

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