Two identical ball bearings in contact with each other and resting on a frictionless table are hit head-on by another ball bearing of the same mass moving initially with a speed $V$. If the collision is elastic, which of the following figure is a possible result after collision ?
Two identical ball bearings in contact with each other and resting on a frictionless table are hit head-on by another ball bearing of the same mass moving initially with a speed $V$. If the collision is elastic, which of the following figure is a possible result after collision ?
It can be observed that the total momentum before and after collision in each case is constant.
For an elastic collision, the total kinetic energy of a system remains conserved before and after collision.
For mass of each ball bearing $m,$ we can write:
Total kinetic energy of the system before collision:
$=\frac{1}{2} m V^{2}+\frac{1}{2}(2 m) 0$
$=\frac{1}{2} m V^{2}$
case $(i)$
Total kinetic energy of the system after collision
$=\frac{1}{2} m \times 0+\frac{1}{2}(2 m)\left(\frac{V}{2}\right)^{2}$
$=\frac{1}{4} m V^{2}$
Hence, the kinetic energy of the system is not conserved in case (i).
Case $(ii)$
Total kinetic energy of the system after collision:
$=\frac{1}{2}(2 m) \times 0+\frac{1}{2} m V^{2}$
$=\frac{1}{2} m V^{2}$
Hence, the kinetic energy of the system is conserved in case (ii).
Case $(iii)$ Total kinetic energy of the system after collision:
$=\frac{1}{2}(3 m)\left(\frac{V}{3}\right)^{2}$
$=\frac{1}{6} m V^{2}$
Hence, the kinetic energy of the system is not conserved in case (iii).
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