One object is at rest, and another is moving. The two collide in a one-dimension

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 26 m/s. The masses of the two objects are 2.7 and 8.2 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.

Explanation / Answer

given Vi = 26 m/s and M = 8.2kg and m = 2.7 kg

a)

Vf = ViM / ( m + M )

= 26 X 8.2 / ( 2.7 + 8.2 )

Vf = 213.2 / 10.9

Vf = 19.55 m/s

b)

Vf = Vim / ( m + M )

Vf = 26 X 2.7 / ( 2.7 + 8.2 )

Vf = 70.2 / 10.9

Vf = 6.44 m/s

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