Multiple Collisions in Tube!

Classical Mechanics Level 2

Inside a smooth circular tube of radius 5 m, a small ball A moves at speed 10 m/s and strikes another ball B with double the mass located at a diametrically opposite point, as shown in the figure. If the coefficient of restitution is 0.5 and the time when the second collision occurs is $n \pi$ , find $n$ .

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1 solution

Fiki Akbar
Nov 7, 2017

From conservation of linear momentum (vertical direction at point of impact), $m u = mu' + 2m v' \:.$ From definiton of coefficient of restitution, we get $u' = v' - \frac{u}{2} \:,$ and subtituting into first equation, we have $v'=\frac{u}{2}$ and $u' =0$ .

Therefore, the second collision will occur at the same point with the first collision, hence ball B will take the full circle before second collision occur. Then, $T = \frac{2\pi R}{v'} = \frac{4\pi R}{u} = 2\pi \:\mathrm{s}\:.$

Multiple Collisions in Tube!

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