# Momentum and Collisions

Let's say that there's a car parked in the middle of an airfield. It's a decent size for a car, and conveniently, there's a couple big line of cones making a lane directly towards the side of the car. Somebody sees this setup, and decides to hop into their dump truck, and drive quickly down the lane, and into the side of the car. Who wins?

The dump truck. Obviously. Why? It has more mass, and therefore more inertia. But it also has more speed, and therefore more momentum.

As you should all know by now, momentum is equal to the mass of an object multiplied by its velocity, or p = mv

This means that the car, if it weighed 1 metric ton, or 1000 kg, multiplied by it's initial velocity 0 m/s, had an initial momentum of 0 kg*m/s

The dump truck, if it weighed 2.5 metric tons, or 2500 kg, multilplied by it's initial velocity 25 m/s, had a p_{o} = (2500 kg) * (25 m/s) = 62,500 kg*m/s

The law of conservation of momentum, assuming that there's no outside forces acting on the system, states that the momentum of the system before the collision is equal to the momentum of the system after the collision, or in this case, p_{car} +p_{truck} = p_{car + truck} since the car and truck stick together after the collision.

Now we can substitute in for momentum. (0 kg*m/s) + (62,500 kg*m/s) = v_{f} * (m_{car} + m_{truck}) or (62,500 kg*m/s) = v_{f} * (3500 kg)

If you solve for v_{f}, you get v_{f} = 18 m/s

After the collision, when the car sticks to the dump truck, the dump truck moves much slower than it originally was, even though it's fairly difficult to see in the clip. TV shows tend to like fast cuts and replays, which make it hard to appreciate the science.

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