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 27 m/s. The masses of the two objects are 3.4 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.

Explanation / Answer

The initial speed of the object is vi = 27m/s

the mass of the larger body m1 = 3.4 kg

the mass of the second body m2 = 7.6 kg

since the collision is inealstic collision

So, from law of conservation of momentum

           m2vi = (m1 + m2) vf

therefore the final speed

       vf = m2vi / (m1 +m2)

           = (7.6kg)(27) / (7.6+3.4)

           = 18.65 m/s

(b) For smaller mass

        vf = m1vi / (m1 + m2)

            = (3.4)(27) / (7.6 + 3.4)

            = 8.34 m/s

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