3.4.1.6
Total momentum is conserved in all collisions when no external force acts
Newton's Laws & Momentum — AQA A-Level Physics
Key Definition
Conservation of momentum — The total momentum before a collision equals the total momentum after the collision, provided no external resultant force acts on the system.
- Applies to collisions and explosions in closed (isolated) systems.
- A closed system has no external forces -- only internal forces between the objects.
- For two objects: m_A u_A + m_B $u_B = m_A v_A + m_B v_B$.
- If objects stick together after collision: (m_A + m_B) $v = m_A u_A + m_B u_B$.
- If one object is initially stationary, its initial momentum is zero.
Worked Example
Trolley A (0.80 kg) travels at 3.0 m s^-1 and hits stationary trolley B (1.60 kg). They stick together. Find the common velocityThe rate of change of displacement. A vector quantity. Measured in m s⁻¹..
Show Solution
1
Calculate momentum before
$$p_{\text{before}} = (0.80 \times 3.0) + (1.60 \times 0) = 2.4 \text{ kg m s}^{-1}$$
2
Apply conservation of momentumIn a closed system (no external forces), the total momentum before an event equals the total momentum after.
$$p_{\text{after}} = (0.80 + 1.60) \times v = 2.4v$$
$$2.4v = 2.4$$
$$v = 1.0 \text{ m s}^{-1}$$Answer
Common velocityThe rate of change of displacement. A vector quantity. Measured in m s⁻¹. = 1.0 m s$^{-1}$ in the original direction of A.