Question

One object is at rest, and another is moving. The two collide in a one-dimensional, completely inelastic collision. In other words, they stick together after the collision and move off with a common velocity. Momentum is conserved. The speed of the object that is moving initially is 22 m/s. The masses of the two objects are 3.2 and 8.0 kg. Determine the final speed of the two-object system after the collision for the case (a) when the large-mass object is the one moving initially and the case (b) when the small-mass object is the one moving initially.

(a) v_f =  

(b) v_f =  

Answer 1

Let m1 = 3.2kg and m2 = 8kg.

(a) When m2 is moving initally, the initial speed of m2 is v2 = 22m/s and that of m1 is v1 = 0m/s. Let vf be their final speed after inelastic collision. In an inelastic collsion, momentum is conserved. Applying law of consevation of momentum,

So when the larger mass is moving initially, the final velocity of the system after inelastic collision is 15.71m/s.

(b) When m1 is moving initally, the initial speed of m1 is v1 = 22m/s and that of m2 is v2 = 0m/s. Let vf be their final speed after inelastic collision. Applying law of consevation of momentum

So when the smaller mass is moving initially, the final velocity of the system after inelastic collision is 6.28m/s.