On a horizontal track, Cart F of mass 0.40kg is moving to the right at 2.5m⋅s−1. Ahead of it is Cart G of mass 0.60kg at rest. Cart H, of mass 0.20kg, is also at rest further down the track and does not interact with the collision. Cart F collides elastically with Cart G. Immediately after the collision, Cart F reverses direction and moves leftward.
Neglect friction for all carts.
(a) Taking only Carts F and G as the system, write the principle that constrains their motions during the very short collision interval.
(b) Determine the magnitude and direction of the velocity of Cart F immediately after its collision with Cart G.
(c) Determine the velocity (magnitude and direction) of Cart G immediately after the collision.
(d) Using your answers, calculate the speed of the center of mass of the three-cart collection (F, G, and H) both before and after the collision, and explain how your results are consistent with the behavior of Cart H.