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: This content can also be viewed on the site it originates from. 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.
Good Day Momentum is the tendency of an object to continue moving. The mathematical formula of momentum is (momentum = mass × velocity) This means, heavier object have bigger momentum compared to lighter or smaller object considering if they are moving at the same velocity. Example: Two objects with different mass running at the same velocity 20 m/s east and heavy object has 50 kg mass and lighter object has 25 kg mass. Which has greater momentum? Heavy object Lighter Object m (mass) 50 kg 25 kg v (velocity) 20 m/s 20 m/s p (momentum) ? ? Momentum (heavy object) Momentum (Light Object) p = mv p = mv = 100 kg × 10 m/s = 50 kg × 10 m/s = 1000 kg.m/s = 500 kg.m/s Greater momentum Lesser momentum Bigger object are usually heavy, which have greater momentum compared to smaller object that are lighter |
Which of the two vehicles a car and a bus have a greater momentum when traveling at the same velocity?
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