Question

prove that in one dimensional elastic collision elastic collision between two bodies the energy transfer is Maximum when their masses are equal.​

Answer 1

In any collision, momentum is conserved. This means

m1u1+m2u2=m1v1+m2v2

For a perfectly elastic collision, kinetic energy is also conserved

m1u21+m2u22=m1v21+m2v22

Solving these equations simultaneously (v1 and v2 are the variables)

v1=u1(m1−m2)+2m2u2m1+m2;v2=u2(m2−m1)+2m1u1m1+m2;

when m1=m2, these reduce to

v1=u2;v2=u1;

You can check out what happens for other cases as well (m1>>m2 or u2=0, etc.)

If you look at it from the point of view of forces, you will see the same force act on both objects, in opposite directions. This will cause an acceleration depending on the mass of the object (F=ma), but only for the tiny instant that the two are in contact. Now, for example, considering equal masses, the force would decelerate the first object to some velocity, and accelerate the second object to the same velocity (because both have equal masses, and the force acts for an equal amount of time). From the momentum equations, we find that the velocities are swapped.

Important point to remember: Force is not velocity. The same force can produce different accelerations and hence different velocities for different masses.

hope it helps you ❤️

Answer 2

Answer:

In one dimensional elastic collision between two bodies, the energy transfer is maximum, when there masses are equal because, the mass of a body determines how impact or thrust it is going to provide, on the object it is hitting.

Explanation:

When there are two bodies, with similar masses colliding with each other, then in that case the transfer of energy form both the bodies are near about equal, and according to newtons third law, both object will get a back thrust from there colliding object, causing maximum energy transfer, at that point of time.