# A 3.0 kg mass moving to the right at 1.4 m/s collides in a perfectly inelastic collision with a 2.0 kg mass initially at rest. What will the velocity of the combined mass be after the collision?

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Zack M. Share
Aug 22, 2016

When analyzing inelastic collisions, we need to consider the law of conservation of momentum, which states that the total momentum, $p$, of the closed system is a constant. In the case of inelastic collisions, the momentum of the combined mass after the collision is equal to the sum of the momentum of each of the initial masses.

${p}_{1} + {p}_{2} + \ldots = {p}_{f}$

In our case we only have two masses, which makes our problem fairly simple. Lets plug in the formula for momentum; $p = m v$.

${m}_{1} {v}_{1} + {m}_{2} {v}_{2} = \left({m}_{1} + {m}_{2}\right) {v}_{f}$

To find the velocity of the combined mass we simply rearrange the terms.

${v}_{f} = \frac{{m}_{1} {v}_{1} + {m}_{2} {v}_{2}}{{m}_{1} + {m}_{2}}$

Plug in the values given in the problem.

 v_f = ((3.0"kg")(1.4 "m/s") + color(red)(cancel(color(black)((2.0"kg")(0"m/s")))^0))/(3.0 "kg"+2.0"kg")

${v}_{f} = .84 \text{m/s}$

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