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Homework Statement Both object A and B have mass M and are moving. An object with mass of m and moving with velocity u collide with the object B elastically. (m < M) Find the following after m collide with B 1) Velocity of m after bouncing back 2) Velocity of B Then m collide with A and bounce...

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Oh! I should estimate the equation into ##1 + (\alpha_2 - \alpha_1) \Delta T## ##r_1 = \frac{d}{(\alpha_2 - \alpha_1) \Delta T}## Is that correct?

From these equations ##r_1 \theta = L_0 (1 + \alpha_1 \Delta T)## ##r_2 \theta = L_0 (1 + \alpha_2 \Delta T)## Then substitute ##r_2## with ##r_1 + d## ##\frac{r_1 + d}{r_1} = \frac{1}{1+(\alpha_1 - \alpha_2) \Delta T}## Where am I going wrong?

##\frac{d}{r_1} = \frac{-(\alpha_1 - \alpha_2) \Delta T}{1 + (\alpha_1 - \alpha_2) \Delta T}## Then ##r_1 = (\frac{1}{(\alpha_2 - \alpha_1) \Delta T} - 1) d## Is that correct?

Then it should be 1/(1 - α2ΔT)(1 + α1ΔT) and then 1/(1+(α1 - α2)ΔT) Is that correct?

Thank you. Which mean r1 is equal to d/((α2 - α1)ΔT) What about the estimation? Or do I have to estimate them before the calculation?

Then the difference should be d. And the ratio should be (r1 + d)/r1 or (1 + α2ΔT)/(1+α1ΔT) Is that correct?

The difference is d(2 + α1ΔT + α1ΔT)/2 because of the width expansion. Is that correct?

Thank you very much.

Oh! I forgot about that. 1/2m(2gh) = 1/2mv2 + mg(2R) v2 = 2g(h - 2R) Then mg = mv2/R g = (2g(h-2R))/R h/R = 5/2 Then use v at point B to calculate distance from O after landing using projectile. Is that correct?

I have another question. v at point B is equal to v and point O?

There are the gravitational force and centripetal force which are mg and mv2/R. Reaction force = 0 means the centripetal force (from object to center) is equal to gravitational force. Is that correct?

I just read about the centripetal force on wikipedia. The formula is F = mv2/R which v2/R is the centripetal acceleration. How can I use this to solve this problem?