Question

15. A car of mass m moving at a speed v, collides and couples with the back of a truck of mass 2m moving initially in the same direction as the car at a lower speed v. (a) What is the speed v, of the two vehicles immediately after the collision? (b) What is the change in kinetic energy of the car-truck system in the collision?

Answer 1

By conservation of momentum m_1 u_1 + m_2 u_2 = m_1 v_1 + m_2 v_2 mv_1 + 2mv_1 = (m + 2m)v_f V-f = v_1 + 2v_2/3 b) delta K = K_p - K_i = 1/2 (m + 2m) v^2_f - [1/2 mv^2_1 + 1/2 mV^2_2] 3m/2 (v_1 + 2v_2/3)^2 - [1/52 mv^2_1 + 1/2 mv^2_2] m/2 [3 (v^2_1 + 4v^2_2 = 4v_1 v_2)/9 - [v^2_1 + v^2_1] m/2 [V^2_1/3 + 4v^2_2/3 + 4V_1 v_2/3 - v^2_1 - v^2_2] = m/2 [4v_1 v_2/3 - 2v^2_1/3 + v^2_2/3] = m/6[4v_1 v-2 - 2v^2_1 + v^2-2]