Question

Momentum and kinetic energy are both calculated from the mass and velocity of an object. If mass is conserved during a collision, explain how momentum may be conserved but not kinetic energy.

Answer 1

The momentum conservation can be understood in the following way. Consider two objects that collide with forces F1 and F2.
Using Newton's third law,
F1 = - F2 ...(1)
Also, the time taken by the object to exert the force is same as the the time taken by the other object.
t1 = t2 ...(2)
Multiplying (1) and (2),
F1t1 = -F2t2
F1 can be written as m1 x v1/t1 and F2 can be written as m2 x v2/t2
m1 (v1/t1) x t1 = - m2 (v2/t2) x t2
m1v1 = - m2v2 (Conservation of momentum)

During collisions, the kinetic energy can be converted into other forms of energy such as heat energy. So in some collisions, (inelastic) kinetic energy is not conserved.