Conservation of momentum
Newton's Laws & Momentum - OCR A-Level Physics
Key Definition
Conservation of momentum
In a closed system (no external resultant force), the total momentum before an event equals the total momentum after the event.
In a closed system (no external resultant force), the total momentum before an event equals the total momentum after the event.
$$m_1 u_1 + m_2 u_2 = m_1 v_1 + m_2 v_2$$
- This applies to ALL interactions: collisions, explosions and separations
- It follows from Newton's third lawWhen two objects interact, the forces they exert on each other are equal in magnitude, opposite in direction, and act on different objects.: equal and opposite forces act for the same time, producing equal and opposite impulses
- A closed systemA system where no external forces act, so total momentum is conserved. means no external resultant force acts. Internal forces between objects within the system can act
- Choose a positive direction before writing equations. Objects moving in the negative direction have negative momentum
Common Mistake
MEDIUM
Students often: A common slip: forgetting include the sign of velocityThe rate of change of displacement. A vector quantity. Measured in m s⁻¹. when objects move in opposite directions, causing momentum not to be conserved in the calculation.
Instead: Define a positive direction first. If object A moves right at +5 $m s^{-1}$ and object B moves left, assign B's velocityThe rate of change of displacement. A vector quantity. Measured in m s⁻¹. as -3 $m s^{-1}$. Keep signs consistent throughout.
Instead: Define a positive direction first. If object A moves right at +5 $m s^{-1}$ and object B moves left, assign B's velocityThe rate of change of displacement. A vector quantity. Measured in m s⁻¹. as -3 $m s^{-1}$. Keep signs consistent throughout.