Question

A ball of negligible size and mass 0.75 kg is initially given a velocity Uble-16 m/s to the left relative to the cart in which it is carried. The cart has a mass 6 kg, and is initially also moving, with a velocity of te 0.3 m/s to the left. The coefficient of restitution between the ball and walls A and B is 0.8.Neglect friction. Figure 1) igure 1 of 1 b/c

a) Determine the velocity of the ball just after it strikes A, indicating the direction with a sign (with positive indicating a velocity to the right).

b) Determine the velocity of the cart immediately after the ball strikes A and has rebounded, indicating the direction with a sign (with positive indicating a velocity to the right).

c) If one half of the length of the cart (in which the ball is moving is   1.2 m, and the ball is initially at the center of the cart, determine the total time needed for the ball to strike A, rebound, then strike B, and rebound and then return to the center of the cart. Express your answer in terms of some or all of the variables v0, m, M, 1.2, and e.

Answer 1

At the first collision (left arrow^+) sigma mv_1 = sigma mv_2 MV_c_0 + mv_0 = mv_b + mv_c 6 (0.3) + 0.75 (1.6) = 0.75 v_b + 6 v_c { from data v_h l c = 1.6, v_c = 0.3, n = E } 0.75 v_b + 6 v_c = 3 (1) (leftarrow^+) e = v_c - v_b/v_c_0 + v_0 0.8 = v_c - v_b/0.3 + 1.6 v_c - v_b = 1.58 (2) solve (1) + (2) 0.75 v_b + 6 v_c = 3 - 6 v_b + 6 v_c = 9.48/6.75 v_b = -6.48 v_b = -0.96 m/s rightarrow velocity of ball then v_c = 1.55 - 0.96 v_c = 0.62 rightarrow velocity of cart Relative velocity in the cart