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 30 m/s. The masses of the two objects are 3.0 and 7.6 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.

Answer 1

Case A

when large-mass object is moving

m1 = 7.6 kg

m2 = 3.0 kg

v1 = initial velocity of m1 = 30 m/sec

v2 = 0, in case 1

So using momentum conservation:

Pi = Pf

m1v1 + m2v2 = (m1 + m2)*V

V = (m1v1 + m2v2)/(m1 + m2)

Using given values:

V = (7.6*30 + 3.0*0)/(7.6 + 3.0)

V = 21.51 m/sec = Final Speed of the two-object system

Part B

when small-mass object is moving

m1 = 7.6 kg

m2 = 3.0 kg

v1 = initial velocity of m1 = 0 m/sec

v2 = 30 m/sec, in case 2

So using momentum conservation:

Pi = Pf

m1v1 + m2v2 = (m1 + m2)*V

V = (m1v1 + m2v2)/(m1 + m2)

Using given values:

V = (7.6*0 + 3.0*30)/(7.6 + 3.0)

V = 8.49 m/sec = Final Speed of the two-object system

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