Momentum is a measurement of inertia in motion. When a mass has velocity, it has momentum. Momentum is calculated by the equation

momentum = mass x velocity

momentum = mv

This conservation of momentum example problem illustrates the principle of conservation of momentum after a collision between two objects.

### Problem:

Consider a 42,000 kg train car travelling at 10 m/s toward another train car. After the two cars collide, they couple together and move along at 6 m/s. What is the mass of the second train car?

In a closed system, momentum is conserved. This means the total momentum of the system remains unchanged before and after the collision.

Before the collision, the total momentum was the sum of the momentums of both train cars.

The first car’s (blue freight car) momentum is

momentum_{Blue} = mv

momentum_{Blue} = (42,000 kg)(10 m/s)

momentum_{Blue} = 420,000 kg·m/s

The second car’s (tanker car) momentum is

momentum_{tanker} = mv

momentum_{tanker} = m(0 m/s)

momentum_{tanker} = 0 kg·m/s

Add these two together to get the total momentum of the system prior to collision.

Total momentum = momentum_{Blue} + momentum_{tanker}

Total momentum = 420,000 kg·m/s + 0 kg·m/s

Total momentum = 420,000 kg·m/s

After the collision, the two cars couple together into one mass. This new mass is

mass_{Blue} + mass_{tanker}

42,000 kg + mass_{tanker}

The velocity the new pair of cars is traveling is 6 m/s. Because momentum is conserved, we know the total momentum of the cars after the collision is equal to the momentum prior to the collision.

Total Momentum = 420,000 kg·m/s

Total Momentum = mv

Total momentum = (42,000 kg + mass_{tanker})·(6 m/s)

420,000 kg·m/s = (42,000 kg + mass_{tanker})·(6 m/s)

Divide both sides by 6 m/s

70,000 kg = 42,000 kg + mass_{tanker}

Subtract 42,000 kg from both sides

70,000 kg – 42,000 kg = mass_{tanker}

28,000 kg = mass_{tanker}

### Answer

The mass of the second car is equal to 28,000 kg.

Remember, the momentum of a system is conserved. The momentum of the individual masses may change, but the *net* momentum of the system does not change.