One object is moving and one object is at rest. The two objects then collide in

Question

One object is moving and one object is at rest. The two objects then collide in a dimensional, completely inelastic collision. So the two objects stick together after the collision and move off with a common velocity. Momentum of the two-object system is conserved. The masses of the two objects are 5.00 kg and 8.50 kg, respectively. The speed of the moving object masses 5.00 kg before the collision is 22.5 m/sec. Find the final speed of the two-object system after the collision; Find the kinetic energy of the two-object system before the collision, Find the kinetic energy of the two-object system after the collision.

Explanation / Answer

Given m1= 5 kg and m2 = 8.5 kg

Before collision v_1i = 22.5 m/s and v_2i = 0

From conservation of momentum m1 v_1i + m2 v_2i = (m1 + m2) v_f

                            v_f = 5 * 22.5 /( 5+8.5) = 8.33 m/s

K.E before collision = 1/2 * 5 * (22.5)2 = 1265.6 J

K.E after collision = 1/2 (5+8.5) * (8.33)2 = 468.37 J

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