Conservation of Momentum

We can calculate momentum by using the equation:

Momentum = Mass × Velocity

  • p = m × v

When a system is not affected by any external forces, the total momentum before an event is equal to the total momentum after the event. We call this conservation of momentum.

Example

A van with a mass of 2,000 kg is travelling at 25 m/s. It collides with a stationary car, which has a mass of 1,200 kg. After the collision, the two cars move together.

Calculate the velocity of the van and car together after the collision.

Step 1: Calculate the total momentum before the collision.

p = m × v

Momentum of the van before the collision = 2,000 × 25 = 50,000 kg m/s

Momentum of the car before the collision = 1,200 × 0 = 0 kg m/s

Total momentum before = 50,000 + 0 = 50,000 kg m/s

Step 2: Calculate the total momentum after the collision.

As momentum is conserved in this system, the total momentum after the collision remains 50,000 kg m/s.

Step 3: Calculate the total mass after the collision

Total mass = Mass of van + Mass of car

= 2,000 + 1,200

Total mass = 3,200 kg

Step 4: Calculate the combined velocity after the collision

By rearranging p = m × v, we get v = p ÷ m

Velocity after the collision = 50,000 ÷ 3,200 = 15.63 m/s (rounded to 2 decimal places)

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