Question

Two identical objects A and B of mass M move on a one-dimensional, horizontal air track. Object B initially moves to the right with speed v_o. Object A initially moves to the right with speed 3v_o, so that it collides with object B. Friction is negligible. Express your answers to the following in terms of M and v_o.

a. Determine the total momentum of the system of the two objects.

b. A student predicts that the collision will be totally inelastic (the objects stick together on collision). Assuming this is true, determine the following for the two objects immediately after the collision. 

i. The speed

ii. The direction of motion (left or right)

When the experiment is performed, the student is surprised to observe that the objects separate after the collision and that object B subsequently moves to the right with a speed 2.5v_o 

c. Determine the following for object A immediately after the collision.

i. The speed 

ii. The direction of motion (left or right) 

d. Determine the kinetic energy dissipated in the actual experiment. 

Answer 1

(a) p_tot = M(3v_o) + (M)(v_o) = 4mv_o

(b) (i) Apply momentum conservation perfect inelastic. p_before = p_after

4Mvo = (m₁ + m₂)v_f 4Mv_o = (2M) v_f v_f = 2v_o

(ii) Since they are both moving right they would have to be moving right after

(c) i) Apply momentum conservation p_before = p_after

4Mv_o = m₁v_1f + m₂v_2i 4M_vo = Mvaf + M(2.5vo) vaf = 1.5 vo

(ii) As before, the would have to be moving right.

(d) ∆K = Kf – Ki = (½ mavaf + ½mbvbf2) – ( ½mavai2 + ½mbvbi2) = 4.25 Mvo2 – 5Mvo2 = – 0.75Mvo2.