Comparing the momenta of two objects requires you to think about both the mass and the velocity of the objects. Let’s compare the momenta of several objects.

We learned in the last lesson that the momentum of an object is found by multiplying the mass times the velocity of the object. The sign of the momentum comes as a result of the direction of the velocity.

# Comparing the momenta of two objects

To compare the momenta of two objects, simply find the momenta of each. The tricky part about this is that sometimes you find that a small object can have a larger momentum than a large object. This occurs when the smaller object has a larger velocity.

## Two objects with different masses but the same velocity

For example, lets compare the momenta of a small car and a large truck. According to Google, the mass of a Volkswagen Beetle is around 3100 pounds. This converts to a mass of roughly 1400 kg. Google also lists the weight of a school bus as around 10,000 pounds. This converts to about 4500 kg. (Note: I’ve rounded these numbers a bit so that they are easier to compare.)

If both are moving the same speed, it should be fairly obvious that the bus will have the larger momentum. For example, if both are moving 10.0 m/s in the positive direction, we find their momenta to be…

\(\color{black}{ p_{car} = 1400 \text{ kg} \times 10.0 \text{ m/s} = \text{14,000 kg m/s}}\)

\(\color{black}{ p_{bus} = 4500 \text{ kg} \times 10.0 \text{ m/s} = \text{45,000 kg m/s}}\)

## Two objects with different masses and different velocities

Now suppose that the car is moving faster than the bus. In this case, the mass of the bus might not be enough to make the momentum of the bus larger.

Suppose that the car is moving at 40.0 m/s, while the bus is still moving at 10 m/s. In this case, we find the momenta to be…

\(\color{black}{ p_{car} = 1400 \text{ kg} \times 40.0 \text{ m/s} = \text{56,000 kg m/s}}\)

\(\color{black}{ p_{bus} = 4500 \text{ kg} \times 10.0 \text{ m/s} = \text{45,000 kg m/s}}\)

In this case, the car has a larger momentum than the bus. This happens because of the larger velocity of the car.

### Think about the following…

- Is there any way for a stationary object to have a larger momentum than a moving object?
- If two identical objects are moving in opposite directions with the same speed, which has the larger momentum?
- How could two objects with different masses have the same momentum?