Question

Sata and prove conservation of linear momentum

Answer 1

Hii your answer below.

If no external forces act on the system of two colliding objects, the vector sum of the linear momentum of each body remains constant.

Let two balls of masses m1 and m2 move in the same direction with velocities u1 and u2 respectively. And after bumping their velocities become v1 and v2.

Now, initial momentum of the first ball=m1u1.

And, final momentum of the first ball=m1v1.

Therefore, change in their momentum=m1v1–m1u1.

Thus, rate of change of their momentum=(m1v1–m1u1)/t.

Similarly, initial momentum of the second ball=m2u2.

And, final momentum of the second ball=m2v2.

So, change in momentum=m2v2–m2u2.

And, rate of change of momentum=(m2v2–m2u2)/t.

By Newton's third law of motion,

F1=–F2

or (m1v1–m1u1)/t = –{(m2v2–m2u2)/t} (by Newton's 2nd law of motion)

or m1u1+m2u2 = m1v1+m2v2(proved).