Skip to content

Physics · Ch 4 — Work, Energy and Power

Perfect inelastic collision

4.4.3

Perfect inelastic collision

In a perfectly (completely) inelastic collision, the two bodies stick together permanently on impact and move off as one, sharing a single common velocity vv. Momentum conservation alone (no kinetic-energy condition applies here, since kinetic energy is not conserved) is enough to determine this common velocity:

m1u1+m2u2=(m1+m2)v⟹v=m1u1+m2u2m1+m2m_1u_1 + m_2u_2 = (m_1+m_2)v \quad\Longrightarrow\quad \boxed{v = \frac{m_1u_1+m_2u_2}{m_1+m_2}} …

Figure 4.17Perfect inelastic collision in one dimension

What this figure shows. Before the collision, masses m1 and m2 approach each other (or one catches up to the other) along a straight line with velocities u1 and u2. After the collision the two masses have coalesced into a single combined body that moves off with one shared common velocity v, illustrating that momentum -- not kinetic energy -- is the quantity whose conservation determines the outcome of a perfectly inelas …