Why does a moving car have more momentum than a car moving at the same speed?

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LAWS OF MOTIONINERTIAMOMENTUMFIND OUT MORE

Dynamics is the study of how objects move when forces act on them. Normally objects stay still or move along at a steady pace. They resist changes in their motion because of their INERTIA. Once they start moving, they tend to carry on doing so because of their MOMENTUM. Most types of everyday movement can be explained by just three simple LAWS OF MOTION. These were originally worked out by English physicist Sir Isaac Newton.

Newton’s three laws of motion (often called Newton’s laws) explain how forces make objects move. When the forces that are acting on an object are balanced, there is no change in the way it moves. When the forces are unbalanced, there is an overall force in one direction. This changes the object’s speed or the direction in which it is moving. Physicists call a change in speed or direction an acceleration.

An object will stay still or move along at a steady pace unless a force acts on it. For example, a rocket on a launchpad remains in place because there is no force acting on it to make it move.

When a force acts on an object, it makes the object change speed or move in a different direction. When the rocket’s engines fire, the force they produce lifts the rocket up off the launchpad and into the air.

When a force acts on an object, the object pulls or pushes back. This reaction is equal to the original force but in the opposite direction. As the hot gases shoot down from the engines, an equal force pushes the rocket up.

Newton’s three laws of motion enabled him to produce a complete theory of gravity, the force that dominates our Universe, and to explain why the Moon circles round Earth. Newton also made major discoveries about optics (the theory of light) and explained how white light is composed of many colours.

Newton’s first law explains that objects remain where they are or move along at a steady speed unless a force acts on them. This idea is known as inertia. The greater the weight (or mass) of an object, the more inertia it has. Heavy objects are harder to move than light ones because they have more inertia. Inertia also makes it harder to stop heavy things once they are moving.

As a car accelerates, passengers are thrown backwards; when a car brakes or crashes, passengers are thrown forwards. In both cases, this is because the inertia caused by their mass resists the change in movement. During crash-tests, dummies that weigh the same as a human body are used to help test safety belts and airbags.

Moving objects carry on moving because they have momentum. The momentum of a moving object increases with its mass and its speed. The heavier the object and the faster it is moving, the greater its momentum and the harder it is to stop. If a truck and a car are travelling at the same speed, it takes more force to stop the truck because its greater mass gives it more momentum.

A foal is smaller and has less mass than a horse. When a foal and a horse gallop along together at the same speed, the horse has more momentum because of its greater mass. This means that it is easier for the foal to start moving, stop moving, and change direction than the horse. The momentum of a moving object is equal to its mass times its velocity.

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Let's take a second and look at these two ideas. Two things differentiate the momentum principle from the work energy. First, it is technically a vector equation because the momentum of an object depends upon its direction of movement. Second, the momentum principle depends upon the change in time (this is important). The work energy principle depends only on displacement, not time.

A Question of Two Vehicles

OK. Now to my great physics question. Suppose a heavy truck and a light car start with the same momentum (if it makes you happy, we can say the truck has a mass three times that of the car). Both vehicles have the same force acting on them to bring them to a stop. Which one stops first?

If you want to take a moment to think about this, I'll wait.

I'm still waiting.

OK, hopefully you have an answer by now. If you like, you can check with friends to see what they think. However, since I'm not there and you aren't here, I will just share two common answers people provide.

Answer number 1: The light car stops first. Since it has lower mass, the force acting on it results in larger acceleration. This, in turn, causes the car to slow down more quickly because the truck has a large mass and a small acceleration.

Answer number 2: They stop in the same amount of time. Yes, it's true that the car has a lower mass and a higher acceleration. However, it starts with a much larger velocity since the two vehicles have the same starting momentum. In the end, both vehicles will have the same force with the same change in momentum. According to the momentum principle, they must have the same change in time.

Clearly, answer number 2 is correct. The cars stop at the same time because they start with the same momentum. Just for fun, let's create a numerical calculation for this. Of course, that requires some actual values for the mass of the two vehicles, the starting momentums, and the stopping force. We'll say the car has a mass of 10 kg (it's a really small car) and the truck has a mass of 30 kg (three times the mass of the tiny car). The initial momentum is 20 kg*m/s and the stopping force is 2 newtons.

A plot of the x-velocity for the car and the truck looks like this:

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You can see that the car does indeed start with a higher velocity, but both cars stop at the same time. Yes, this is a plot of velocity vs. time instead of distance vs. time for a very particular reason.

Another Question About Stopping Vehicles

Now for the next (and more interesting) question. Using the same situation we examined above, which vehicle stops in the shortest distance and why? Figure it out and explain your answer. I'll wait.

Really, you should answer this one. Take your time.