Elastic and Inelastic Collisions Worked Examples Cheat Sheet

Key Facts

• Momentum is calculated with $p = mv$, where $p$ is momentum, $m$ is mass, and $v$ is velocity.
• For an isolated collision system, total momentum is conserved: $m_1v_{1i} + m_2v_{2i} = m_1v_{1f} + m_2v_{2f}$.
• Kinetic energy is calculated with $KE = \frac{1}{2}mv^2$, and it is always zero or positive.
• In an elastic collision, both $m_1v_{1i} + m_2v_{2i} = m_1v_{1f} + m_2v_{2f}$ and $\frac{1}{2}m_1v_{1i}^2 + \frac{1}{2}m_2v_{2i}^2 = \frac{1}{2}m_1v_{1f}^2 + \frac{1}{2}m_2v_{2f}^2$ are true.
• In a perfectly inelastic collision, the objects stick together, so $m_1v_{1i} + m_2v_{2i} = (m_1 + m_2)v_f$.
• The final velocity for a perfectly inelastic collision is $v_f = \frac{m_1v_{1i} + m_2v_{2i}}{m_1 + m_2}$.
• Kinetic energy lost in a collision can be found with $\Delta KE = KE_f - KE_i$, and an inelastic collision has $\Delta KE < 0$.
• In one-dimensional elastic collisions, the relative speed relationship is $v_{1i} - v_{2i} = -(v_{1f} - v_{2f})$.

Vocabulary

Momentum

Momentum is the quantity of motion of an object, calculated by $p = mv$.

Impulse

Impulse is the change in momentum caused by a force acting over time, written as $J = \Delta p$.

Elastic collision

An elastic collision is a collision in which both total momentum and total kinetic energy are conserved.

Inelastic collision

An inelastic collision is a collision in which total momentum is conserved but total kinetic energy decreases.

Perfectly inelastic collision

A perfectly inelastic collision is a collision where objects stick together and move with the same final velocity.

Isolated system

An isolated system is a group of objects with no significant net external impulse during the collision.