University of North Carolina at Chapel Hill
Newton's Laws Basics - Example 4


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welcome to our final example video discussing the basics of Newton's laws. In this video, we're going to consider a scenario that happens a lot, and it always has the same result. Let's say we have a truck here. It's probably something like a couple tons. We have a two ton truck and it is going to challenge mosquito. Okay, And then the question we want to ask ourselves is how much force is exerted on the truck by the mosquito when the mosquito hits the windshield and how much force exists exerted by the mosquito on the truck. So force of truck on mosquito and the force of the mosquito on the truck. How much are these two quantities? And how do they compare to each other? In particular is what we're interested in. Um, let's go ahead and decides the masses then, eh? So we're going to say that the mass of the truck, if it's approximately two tons, that's about 2000 pounds. It turns out that there are approximately £2.2 in 1 kg, and then we'll say that our mosquito here has a mass on the order of will say, uh, 20 mg something like that. So that's equal to 20 times 10 to the negative six kilograms. Okay, so now that we have our masses figured out and we could say, Well, I know that I've got this force It's I know that the force of the truck on the mosquito is going thio affect the mass of the mosquito multiplied by the acceleration of the mosquito and the force of the map of the mosquito on the truck. It's going to be equal to the mass of the truck multiplied by the acceleration of the truck. And what Newton's third law tells us, because this is really a Newton's third law problem. It tells us that these forces have to be equal and opposite. That means they're opposite directions, but they're the same magnitude. So that's odd, because this is a truck hitting mosquito on mosquito hitting the truck. How could the mosquito possibly hit the truck with the same force that the truck is hitting the mosquito? Well, let's let's look at this here we plug things and we have mass of the mosquito. Acceleration of the mosquito has to be equal to negative mass of the truck times the acceleration of the truck. Let's consider the ratio here of our different quantities the acceleration of the mosquito, the acceleration of truck. First of all, this ratio. We expect this to be very, very large because we think, well, the mosquitoes going to accelerate. Ah, lot more due to this collision than the truck is. And then we set this equal. It's gonna be equal to We'll just put the negative on that side, the mass of the truck divided by the mask of the mosquito. And this is a very large ratio here. So we have something that's on the order of 10 to the 3 kg, and here we have something that's on the order of 10 to the negative 6 kg. So we're gonna have something on the order of 10 to the nine is our ratio, which is a much larger acceleration. And because the acceleration of the mosquito is so much larger than the acceleration of the truck, this actually turns out to be true that the force of the truck on the mosquito is equal to the opposite of the force of the mosquito on the truck. Because of the very disparate masses here they have, very. They have very different accelerations, even though the forces are the same. This is one of these concepts that students really struggle with, generally speaking toe. Understand? How is it that that this could possibly true, that the forces can be equal on each other? Well, the forces are equal on each other because it's not that the masses it saying the masses are different doesn't say that the forces have to be different. It just says that the accelerations would have to be different. Or more precisely, it says that this has to be true, that the ratio of the accelerations has to be equal to the ratio of the masses. And this is something we need to keep a very close eye on in the coming videos. We're going to look a lot at this in the context of how do we draw free body diagrams, a free body diagram for the mosquito in a free body diagram for the truck, and this will help us to see how these reactionary forces work

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