when two bodies of equal masses collide elastically with each other then they will move perpendicular to each other
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a) Suppose two masses m1 and m2 are going elastic collision (Coefficient of restitution e = 1 for elastic collision). The initial speed of both masses are u1 and u2respectively. And the final speed of both masses are v1 and v2 respectively.
So the expression for their final velocities after an elastic collision is given as,
v1=(m1−m2m1+m2)u1+(2m2m1+m2)u2
and,
v2=(2m1m1+m2)u1+(m2−m1m1+m2)u2
so by using these two equations we can say that if the mass of two bodies are same we get,
v1=u2v2=u1
this shows that when two bodies of same masses collide with each other then they merely exchanges their speeds.
(b) Similarly, by using these two equation we can say that if one lighter mass elastically collides with the heavier mass at rest then after collision the lighter mass will move with same velocity but the direction will be reversed whereas the heavier mass will still remains at rest.
So the expression for their final velocities after an elastic collision is given as,
v1=(m1−m2m1+m2)u1+(2m2m1+m2)u2
and,
v2=(2m1m1+m2)u1+(m2−m1m1+m2)u2
so by using these two equations we can say that if the mass of two bodies are same we get,
v1=u2v2=u1
this shows that when two bodies of same masses collide with each other then they merely exchanges their speeds.
(b) Similarly, by using these two equation we can say that if one lighter mass elastically collides with the heavier mass at rest then after collision the lighter mass will move with same velocity but the direction will be reversed whereas the heavier mass will still remains at rest.
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