Question

derive the mathmatical formula of conservation of momentum​

Answer 1

Let us consider a situation wherein: a truck of mass m1, velocity u1 and its momentum = m1u1 and a car of mass m2, velocity u2 and its momentum m2u2; are moving in the same direction but with different speeds. Therefore, total momentum=m1u1 + m2u2.

Now suppose the car and truck collide for a short time t, their velocities will change. So now the velocity of the truck and car become v1 and v2 respectively. However, their mass remains the same. Hence, now the total momentum = m1v1 + m2v2

Acceleration of car (a) = (v2–u2)/t

Also, F = ma

F1 = Force exerted by truck on the car

F1 = m2(v2–u2)/t

Acceleration of truck =(v1–u1)/t

F2 = m1(v1–u1)/t and F1 = –F2

m2(v2– u2)/t = –m1(v1– u1)/t

m2v2–m2u2 = –m1v1+m1u1

or m1u1+m2u2 = m2v2+m1v1