Consider an isolated system consisting of two masses, each of which has a velocity vector in two dimensions. When these two masses collide the total momentum of the system is conserved.

Question

(a) Show that if the total momentum of the system is conserved then the component momenta are also conserved.

(b) Given that the total momentum is conserved, can we also conclude that the total kinetic energy is conserved for this collision? Explain.

Answer 1

If Vector A + Vector B = Vector C
then orthogonal components of the vectors also add.
If V = A + B
then
Vx = Ax + Bx
and
Vy = Ay + By
and
Vz = Az + Bz
and as many more dimensions as our tensor occupies ")

(b) NO !!!!!
It is only conserved in an elastic collision
Energy is NOT a vector for one thing.
If two blocks of the same mass come at each other from opposite directions at the same speed and stick, the resulting kinetic energy is ZERO
(By the way the momentum was conserved because it was mv-mv = 0 to start with)