Question

prove that the total Momentum of two object remains constant before and after their collision

Answer 1

when two or more bodies act upon one another there total momentum remains constant or conserved provided no external forces are acting. it can also be stated as momentum can never be created or destroyed.suppose 2 bodies- a truck and a car are moving in same direction having mass m1 and m2 respectively.if initial velocity of both are U1 and U2 then the truck and the car collide for short time t. due to which their velocity change into V1 and V2 respectively.

Total momentum before collision=m1u1+m2u2
after =m1v1+m2u2
acceleration=v1-u1/t
car a2=v2-u2/t
force exerted by truck on car f1=m2(v2-u2)/t
(from Newton 2 law f=ma)
"f2" car on a truck f2=m1(v1-u1)/t
•f1=-f2
m2(v2-u2)/t = - m1(v1-u1)/t
m2v2-m2u2= -m1v1+m1u1
m1v1+m2v2= m1u1+m2u2
This proved that momentum remains constant...

Answer 2

The law of momentum conservation can be stated as follows. For a collision occurring between object 1 and object 2 in an isolated system, the total momentum of the two objects before the collision is equal to the total momentum of the two objects after the collision.