# 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?

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")

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