In Figure 11-32, a solid brass ball of mass m and radius r will roll without slipping along the loop-the-loop track when released from rest along the straight section. For the following answers use g for the acceleration due to gravity, and m, r, and R, as appropriate, where all quantities are in SI units.(adsbygoogle = window.adsbygoogle || []).push({});

(a) From what minimum height h above the bottom of the track must the marble be released to ensure that it does not leave the track at the top of the loop? (The radius of the loop-the-loop is R. Assume R > r.)

(b) If the marble is released from height 6R above the bottom of the track, what is the magnitude of the horizontal component of the force acting on it at point Q?

For part a I came up with the equation

mgh = (1/2)mv^{2}+ (1/2)mv^{2}+ 2mgR

gh = (7/10)v^{2}+ 2gR

I think that's right, but I can't figure out how to solve for v. I'm guessing that It has something to do with centripetal force.

Part b probably needs an answer from part a. The horizontal component of the force is the normal force (= centripetal force?).

Help please.

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# Homework Help: Cons. of energy with rotational motion

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