Question

what is your full conservation of momentum equation for 2 objects colliding inelastically

Answer 1

In the inelastic collision, the objects stick to each other or move in the same direction. The total kinetic energy in this form of collision is not conserved but the total momentum and energy are conserved. During this kind of collision, the energy is transformed into other energy forms like heat and light. Since during the phenomenon the two masses follow the law of conservation of momentum and move in the same direction with same the same speed v we have:

m1u1 + m2u2 = (m1+ m2)v

v= (m1u1 + m2u2)/(m1+ m2)

The kinetic energy of the masses before the collision is : K.E1 = 1/2 m1u21 + 1/2 m2u22

While kinetic energy after the collision is: K.E2 = 1/2 (m1+ m2) v2

But according to the law of conservation of energy: 1/2 m1u21 + 1/2 m2u22 = 1/2 (m1+ m2) v2 + Q

‘Q’ here is the change in energy that results in the production of heat or sound.