You are watching: The momentum of an object depends on which two quantities
The very first semester of an undergraduate physics course invariably spends a lot of time ~ above two large ideas: The inert principle and also the work energy principle. Both attend to forces exhilaration on one object, which often leads students to think they room similar. In a way, lock are, and they beat a huge duty in practically everything girlfriend learn throughout an advent to physics.
Before I provide you a an excellent physics inquiry that offers these ideas, I will go over them in a super-brief physics lesson. First, the inert principle states that a net force transforms the inert of an item where the momentum is the product of mass and also velocity. Working in one dimension to avoid dealing with vectors, I have the right to write it prefer this:
If you consult her introductory physics textbook, you'll view that this is basically the same as Newton's 2nd Law, which says that the net force is equal to the product of mass and also acceleration (where acceleration represents the readjust in velocity). You can rewrite the momentum principle to fix for the adjust in momentum (which is useful). It looks favor this:
Trust me, you'll find this equation advantageous in just a tiny bit.
OK, now for the second huge idea, the work power principle. It states that, for a solitary particle, the work done on an item is same to the change in kinetic energy. Work is defined as the product that a force in the direction of a displacement. I can write this as:
Just to be clear, Δr to represent the displacement (how far the force pushes something) and θ represents the angle in between the force and the direction the thing moves. Similar to the inert principle, I have the right to rewrite this so that looks a bit an ext useful:
Let's take a 2nd and look in ~ these 2 ideas. 2 things distinguish the inert principle indigenous the work energy. First, it is technically a vector equation since the momentum of an object depends upon its direction the movement. Second, the inert principle counts upon the adjust in time (this is important). The work energy principle depends only on displacement, not time.
A inquiry of two Vehicles
OK. Currently to my great physics question. Intend a heavy truck and also a light auto start v the same momentum (if it renders you happy, we can say the truck has actually a mass three times the of the car). Both vehicles have the same pressure acting on lock to bring them come a stop. I beg your pardon one stops first?
If you want to take it a moment to think around this, I'll wait.
I'm tho waiting.
OK, hope you have response by now. If you like, you can check with friend to watch what lock think. However, due to the fact that I'm not there and also you aren't here, ns will just share two typical answers civilization provide.
Answer number 1: The light car stops first. Since it has lower mass, the pressure acting top top it results in bigger acceleration. This, in turn, causes the car to slow down much more quickly since the truck has a huge mass and also a tiny acceleration.
Answer number 2: They prevent in the exact same amount that time. Yes, it's true that the auto has a lower mass and a higher acceleration. However, the starts through a much larger velocity since the two vehicles have actually the same beginning momentum. In the end, both vehicles will have the same force with the same readjust in momentum. According to the momentum principle, they must have the same readjust in time.
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Clearly, prize number 2 is correct. The cars stop at the exact same time since they begin with the same momentum. Just for fun, let's develop a numerical calculation for this. Of course, that requires some actual values for the fixed of the two vehicles, the starting momentums, and the protecting against force. We'll say the car has a fixed of 10 kg (it's a really tiny car) and the truck has a mass of 30 kg (three time the massive of the tiny car). The initial momentum is 20 kg*m/s and the stopping force is 2 newtons.