Collisions and Conservation of Momentum

When two objects bump into each other, they collide. In collisions, the total momentum of all objects stays the same, as long as no external forces (like strong friction) act during the impact.

Momentum recap

Momentum measures “how hard it is to stop something.” It depends on mass and speed:

$$p = m v$$ where p is momentum (kg m/s), m is mass (kg), and v is velocity (m/s). Velocity has direction, so momentum does too.

Conservation of momentum

In a closed system (no net external force):

$$\text{total momentum before} = \text{total momentum after}$$

For two objects 1 and 2, with velocities u before and v after:

$$m_1 u_1 + m_2 u_2 = m_1 v_1 + m_2 v_2$$

Choose one direction as positive (e.g. right is +). Use negative for the opposite direction.

Types of collisions

• Elastic: total kinetic energy is also conserved. These are rare in everyday life.
• Inelastic: objects may stick or deform; kinetic energy decreases (some becomes heat, sound). Total momentum still stays the same.

Explosions are like “reverse collisions”: objects push apart from rest. Total momentum is still zero before and after (equal and opposite).

Common misconceptions

• “Momentum disappears if objects stick.” False: momentum is conserved; kinetic energy may decrease.
• “Heavier always means more momentum.” Not always; speed matters too ($p = mv$).
• “Direction does not matter.” Momentum is a vector; use plus and minus correctly.

Real-world links: bumper cars, sports tackles, and car crashes all show momentum transfer. Sound, heat, and bending parts show kinetic energy is not always conserved.