Question

An object of mass M travels along a horizontal air track at a constant speed v and collides elastically with an object of identical mass that is initially at rest on the track. Which of the following statements is true for the two objects after the impact? 

(A) The total momentum is Mv and the total kinetic energy is ½Mv²

(B) The total momentum is Mv and the total kinetic energy is less than ½ Mv² 

(C) The total momentum is less than Mv and the total kinetic energy is ½Mv² 

(D) The momentum of each object is ½Mv 

(E) The kinetic energy of each object is ¼Mv²

Answer 1

Correct option (A) The total momentum is Mv and the total kinetic energy is ½ Mv²

Since it is an elastic collision, the energy after must equal the energy before, and in all collisions momentum before equals momentum after. So if we simply find both the energy before and the momentum before, these have the same values after as well. p = Mv, K = ½ Mv².