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  • 8.4: Solving Problems Involving Conservation of Linear Momentum in Collisions

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    When solving problems for elastic collisions, it is important to remember that the kinetic energy is conserved. Therefore, the total kinetic energy at the start of the collision must equal the total kinetic energy at the end of the collision. We can write this as \frac{1}{2}m_1 v_1^2 + \frac{1}{2}m_2 v_2^2 = \frac{1}{2}m_1 v_1^{'2} + \frac{1}{2}m_2 v_2^{'2}

    Moreover, we know that momentum must be conserved in the collision. Therefore, the total momentum at the start of the collision must equal the total momentum at the end of the collision. That is, for two objects (object one and two) colliding, we can write \frac{1}{2}m_1 v_1 + \frac{1}{2}m_2 v_2 = \frac{1}{2}m_1 v_1^{'} + \frac{1}{2}m_2 v_2^{'} . Using conservation of momentum, we can usually set up these problems so we only have to solve for one unknown.