1. What Is the Law of Conservation of Momentum?
The law of conservation of momentum states that:
“In a closed system with no external forces, the total momentum before an interaction is equal to the total momentum after the interaction.”
This means momentum cannot be created or destroyed. It can only be transferred from one object to another.
1.1. Understanding a Closed System
A closed system is one where no external forces (like friction or pushes from outside) act on the objects involved. Only internal forces act between the objects.
2. Momentum Before and After Interaction
When two objects collide or push each other, they may change their individual momenta, but the total momentum of both together stays the same.
2.1. Mathematically
For two objects A and B:
Before collision: \( p_1 = m_A v_{A1} + m_B v_{B1} \)
After collision: \( p_2 = m_A v_{A2} + m_B v_{B2} \)
Law: \( p_1 = p_2 \)
2.2. Why Momentum Remains Constant
When two objects interact, the forces they apply on each other are equal and opposite (Newton’s third law). These internal forces cancel out, so total momentum stays unchanged.
3. Simple Examples of Conservation of Momentum
This law appears in many simple real-life scenarios, especially where two objects interact.
3.1. Example 1: Two Skaters Pushing Apart
When two skaters standing still push each other, they move in opposite directions. Even though each one gains momentum, their total momentum remains zero, just like before pushing.
3.2. Example 2: Collision Between Two Balls
If a moving ball hits a stationary ball, part of its momentum may transfer to the second ball. The first ball slows down or changes direction, but the combined momentum stays the same.
3.3. Example 3: Gun and Bullet
When a gun fires a bullet, the bullet goes forward and the gun recoils backward. The forward momentum of the bullet equals the backward momentum of the gun, keeping total momentum conserved.
4. Real-Life Applications
The law of conservation of momentum helps explain many natural and technological processes.
4.1. Examples
- Rocket propulsion — gases expelled downward carry momentum, and the rocket moves upward.
- Car collisions — momentum calculations help understand impact forces.
- Billiards — the way one ball transfers motion to another follows momentum conservation.
5. Problem-Solving Using Momentum
Momentum conservation makes solving collision problems easier because we only equate total momentum before and after interaction.
5.1. Simple Numerical Example
A 2 kg object moving at 3 m/s hits a 1 kg object at rest.
Total momentum before collision:
\( p = (2)(3) + (1)(0) = 6 \text{ kg·m/s} \)
If after collision they stick together, their common velocity is:
\( v = \dfrac{6}{3} = 2 \text{ m/s} \)