Anderson Video - Momentum: Bird vs Bug

Professor Anderson
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>> Hello class. Professor Anderson here. Let's try our hawk versus bug problem, right? We're big fans of hawks these days. Hopefully that hawk will get out of the classroom that it was locked in earlier. So let's take a look at this picture. And the idea is the following. We're going to have a hawk that's flying to the right. I don't know how to draw a bird, but we'll see what it looks like. That's not right. OK. There's my hawk. It's a fish bird. [ Laughter ] OK and it's moving to the right at V hawk initial. And then there is a bug here that is flying along. I guess if it's flying it's got to have some wings on it, right? It's flying along at V bug initial. OK? There's a mass of the hawk. There is a mass of the bug. And what's going to happen is the hawk's going to eat the bug. So this is the before picture. And in the after picture, the hawk is going to eat the bug. Let's see if I can draw the hawk almost the same. Alright. Got a little fatter, I guess. [Laughter] Now the bug's in the hawk's belly. Not so happy about it, OK? And the whole thing is moving in this direction with some V final, which we don't know yet. But we want to find out what that is. So, this is what type of collision? Is it elastic or inelastic? What do you guys think? [Inaudible student replies] Inelastic, right? Any time two things stick together, that is inelastic. When you hear that word inelastic, think like clay. Right? Clay is kind of sticky. Any time things stick together, that's inelastic. Elastic is like a super ball, right? If things bounce off each other, that's an elastic collision. And in this case, if the bug had bounced off the bird's beak, that would be elastic. Alright. Let's take a look at conservation momentum -- all one dimension, so we're only worried about X. So what do we have initially? Initially we have the mass of the hawk times the speed of the hawk going to the right. We have the mass of the bug times the speed of the bug going to the left. That is our P initial. P final in the X direction is the mass of the hawk plus whatever is in its belly, the mass of the bug, times V final of the whole system. OK? They're stuck together and so we can combine the two masses because they're both moving at the same speed. And now we can just set them equal to each other And now we can just set them equal to each other and we can solve for Vf. What do we get? Vf is equal to m of the hawk V of the hawk minus m of the bug V of the bug all divided by mass of the hawk plus the mass of the bug. OK? That's what your solution looks like with all the variables still intact. And again, it's nice to hang onto the variables just to make sure it makes sense. So a second ago when we talked about the collision between two cars and we wanted the final velocity to be equal to zero, we had the mass of one was equal to the mass of the other. And their speeds were equal. If that was the case here, then mass of the hawk would equal the mass of the bug. Speed of the hawk would equal the speed of the bug. Numerator goes to zero. Final velocity is zero. OK? So if this bug was not a bug but a hawk, and they were flying at each other and they hit each other and stuck together, they would come to rest and they would fall out of the sky. Right? If the hawk is much, much more massive than the bug, what do you think's going to happen to the speed of the hawk? Chris? Hand Chris the microphone. >> Can you repeat the question, please? >> Let's say the hawk is huge. >> Yes. >> Alright? There was a hawk flying around not only in our classroom, but over my house the other day. Hawks are really big. Like, they're much bigger than sort of normal blackbirds and blue jays that are flying around. They're huge, right? Let's say the hawk is gigantic. OK? It's a particularly big hawk. And this thing is not a ladybug or something like that. Let's say it's like a mosquito. Do you think the hawk's going to slow down at all as it swallows the mosquito? >> No, it's -- yeah. The mass of the bug would be negligible. >> Negligible. So let's take a look at that condition. If the mass of the bug is much smaller than the mass of the hawk, then how would our equation change here? Vf would equal what? Well, if mass of the bug is small, we can ignore it compared to the mass of the hawk. And so we get mH VHi divided by mH because we're going to ignore that term on the bottom and we're going to ignore this term on the top. The m's now cancel out and we get VHi. The hawk doesn't change its speed. If it's moving at VHi before, it's still moving at VHi after. OK? Now, this is never strictly true, right? But in the case where you can ignore the mass of the bug, that's the limit that you would approach. Good. Questions about that one?
>> Hello class. Professor Anderson here. Let's try our hawk versus bug problem, right? We're big fans of hawks these days. Hopefully that hawk will get out of the classroom that it was locked in earlier. So let's take a look at this picture. And the idea is the following. We're going to have a hawk that's flying to the right. I don't know how to draw a bird, but we'll see what it looks like. That's not right. OK. There's my hawk. It's a fish bird. [ Laughter ] OK and it's moving to the right at V hawk initial. And then there is a bug here that is flying along. I guess if it's flying it's got to have some wings on it, right? It's flying along at V bug initial. OK? There's a mass of the hawk. There is a mass of the bug. And what's going to happen is the hawk's going to eat the bug. So this is the before picture. And in the after picture, the hawk is going to eat the bug. Let's see if I can draw the hawk almost the same. Alright. Got a little fatter, I guess. [Laughter] Now the bug's in the hawk's belly. Not so happy about it, OK? And the whole thing is moving in this direction with some V final, which we don't know yet. But we want to find out what that is. So, this is what type of collision? Is it elastic or inelastic? What do you guys think? [Inaudible student replies] Inelastic, right? Any time two things stick together, that is inelastic. When you hear that word inelastic, think like clay. Right? Clay is kind of sticky. Any time things stick together, that's inelastic. Elastic is like a super ball, right? If things bounce off each other, that's an elastic collision. And in this case, if the bug had bounced off the bird's beak, that would be elastic. Alright. Let's take a look at conservation momentum -- all one dimension, so we're only worried about X. So what do we have initially? Initially we have the mass of the hawk times the speed of the hawk going to the right. We have the mass of the bug times the speed of the bug going to the left. That is our P initial. P final in the X direction is the mass of the hawk plus whatever is in its belly, the mass of the bug, times V final of the whole system. OK? They're stuck together and so we can combine the two masses because they're both moving at the same speed. And now we can just set them equal to each other And now we can just set them equal to each other and we can solve for Vf. What do we get? Vf is equal to m of the hawk V of the hawk minus m of the bug V of the bug all divided by mass of the hawk plus the mass of the bug. OK? That's what your solution looks like with all the variables still intact. And again, it's nice to hang onto the variables just to make sure it makes sense. So a second ago when we talked about the collision between two cars and we wanted the final velocity to be equal to zero, we had the mass of one was equal to the mass of the other. And their speeds were equal. If that was the case here, then mass of the hawk would equal the mass of the bug. Speed of the hawk would equal the speed of the bug. Numerator goes to zero. Final velocity is zero. OK? So if this bug was not a bug but a hawk, and they were flying at each other and they hit each other and stuck together, they would come to rest and they would fall out of the sky. Right? If the hawk is much, much more massive than the bug, what do you think's going to happen to the speed of the hawk? Chris? Hand Chris the microphone. >> Can you repeat the question, please? >> Let's say the hawk is huge. >> Yes. >> Alright? There was a hawk flying around not only in our classroom, but over my house the other day. Hawks are really big. Like, they're much bigger than sort of normal blackbirds and blue jays that are flying around. They're huge, right? Let's say the hawk is gigantic. OK? It's a particularly big hawk. And this thing is not a ladybug or something like that. Let's say it's like a mosquito. Do you think the hawk's going to slow down at all as it swallows the mosquito? >> No, it's -- yeah. The mass of the bug would be negligible. >> Negligible. So let's take a look at that condition. If the mass of the bug is much smaller than the mass of the hawk, then how would our equation change here? Vf would equal what? Well, if mass of the bug is small, we can ignore it compared to the mass of the hawk. And so we get mH VHi divided by mH because we're going to ignore that term on the bottom and we're going to ignore this term on the top. The m's now cancel out and we get VHi. The hawk doesn't change its speed. If it's moving at VHi before, it's still moving at VHi after. OK? Now, this is never strictly true, right? But in the case where you can ignore the mass of the bug, that's the limit that you would approach. Good. Questions about that one?