Conservation of Momentum

Momentum measures how hard it is to stop something moving — it depends on both mass and velocity. When objects in a closed system collide or push off each other, momentum can transfer from one object to another, but the total amount never changes. That's why a fast, heavy ball can send a light resting ball flying, while barely slowing down itself.

p = m · v

• p — momentum (kg·m/s): how much motion an object carries
• m — mass (kg): how much matter the object has
• v — velocity (m/s): how fast the object moves, and in which direction

A 3 kg cart moving at 4 meters per second crashes into a stationary 1 kg cart, and they stick together. How fast do they move after the collision?

• m₁ = 3 kg
• v₁ = 4 m/s
• m₂ = 1 kg

1. m₁ · v₁ + m₂ · v₂ = (m₁ + m₂) · v
2. 3 kg · 4 m/s + 1 kg · 0 m/s = (3 kg + 1 kg) · v

v = 3 m/s

The same 3 kg cart moving at 4 meters per second now crashes into a heavier 3 kg cart at rest, sticking together. What is their speed after the collision?

• 3 m/s
• 6 m/s
• 2 m/s

Two identical 2 kg carts roll toward each other, each at 3 meters per second, collide head-on, and stick together. What is their momentum right after the collision?

• Zero
• 12 kilogram meters per second
• 6 kilogram meters per second