(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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The picture speaks for itself. I'm asked to find the minimum velocty that this bead should be given so that it will reach point B.

2. The attempt at a solution

I've solved this question using energy conservation with a "new gravity": [tex] g_{eff}=g+a [/tex] , so that:

[tex] 0.5mV^{2}=m(g+a)(2R) \to V=2 \sqrt{(g+a)R} [/tex]

and this is the right answer.

However, supposing I want to solve this question using Newton's 2nd law in an accelerating frame, so:

[tex] m \vec {a}_{rel} = \vec{F}_{real} - m \vec{a}_{frame} [/tex]

If i take the positive values to be in the direction of the relative acceleration, i'll obtain:

[tex] m \frac{V^{2}}{R} = mg + ma \to V= \sqrt {(g+a) R } [/tex] ?!?!?!?!

Why is that? Am I missing something?

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# Bead on a hoop+accelerating elevator

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