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Question

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Answers

Superman must stop a $120-\mathrm{km} / \mathrm{h}$ train in $150 \mathrm{~m}$ to keep it from hitting a stalled car on the tracks. If the train's mass $3.6 \times 10^{5} \mathrm{~kg}$, how much force must he exert? Compare to the weight of the train (give as \%). How much force does the train exert on Superman?

So the train is coming to a stop. We know that if the initial would be equal to 120 killem kilometers per hour, let's convert one meter per second for every 3.6 kilometers per hour and this is giving us 33.33 meters per second. Of course the train is coming to a stop, so the final would be zero meters per second and we need to calculate average velocity. This would be equal to the final squared minus V initial squared, divided by two times Delta acts. We know the final square to zero, so eliminate that term and this is equaling negative 33.33 meters per second. Quantity squared, divided by two times Ah, the distance of 150 meters. Now at this point Ah, this would equal the average acceleration And the force that is, um that Superman is, um, exerting on the train would be in the opposite direction of the initial velocity off the train because again, this train is coming to a stop so we can say that to the average force would be equal to the mass of the train times the average our average deceleration in this case, so it would be 3.6 times 10 to the fifth kilograms multiplied by negative 33.33 meters per second. Quantity squared, divided by two times, 150 meters. And this is giving us negative 1.33 times 10 to sixth Nunes now. Ah, this would be the force that Superman needs to exert on the train. In order for the train to stop comparing this to the actual weight of the train, we could say force average divided by the mass of the train times acceleration due to gravity, this would equal 100 was a 1.33 times 10 to the sixth. Newton's divided by 3.6 times 10 to the fifth kilograms multiplied by 9.8 meters per second squared. This is going to give us approximately point three 89 or we can say 38.9% of the trains wait. And after this they're asking us what is the force that the train exerts on Superman. Well, in this case, due to Newton's third Law, every force has an equal every reaction has an equal and opposite reaction. Therefore, we can say that train exerts a 1.33 times 10 to the sixth Newton Force on Superman inthe e direction of the initial velocity. That is the end of the solution. Thank you for watching.

Mhm. So in this question, luis is moving down world with a constant acceleration G An initial speed of the Louis zero. And the superman who is moving upward with an acceleration is and As initial speed is also zero and that presents initial response between work up them. Yes, let's see. Right, so the acceleration of acceleration of louis with respect to Superman is the acceleration of Superman. Okay, minus the acceleration of louis. And the acceleration of Louis to Superman is the acceleration of Superman is uh 15.0 m four seconds. We are taking upward as positive minus The Exhibition of Lewis's -9.8. We just for a second split. So the net acceleration of loose with Superman is 24.8 m/s squared. Now the height the right way is equal to the exploration of fluid. Lewis with respect to Superman into P square upon to or we can write the time when the both of them meet each other is a cost to the initial white wine into the acceleration of this with this and from this we find the time tears two and 2 300 m Upon 24.8 m/s squared. At the time When they meet each other is 4.9- six. No party. The height of fall after louis. When she meets with the Superman is half of judy square or the height of follies, 0.9.8 meters four seconds square into 4.92 seconds squared at the height of fall for the loses 118 1 6 m. Okay, no party The time when they both meet each other. We have a limited idea that is 4.92 seconds now. Part C. Well, the A spirit of louis is equal to the exhibition of clues into the time team Of the school of loose. When she meets with Superman is 9.8 m four seconds square into the time, that is 4.92 seconds. Our spiritual loses 48.2 leaders possible. And they speeded, the superman is the acceleration of the superman into the time. T and from this uh Spirit Superman is right, 15 m four seconds square into 4.92 seconds. Our speed of the superman's 73.8 m or so. Right and along a corporation. Yeah, no party. So when luis and the superman meet each other, the speed of Lewis's 48.2 meters per second and speed up the superman V. S is 73.8 m positive and both of them are moving in the opposite direction. So because of such a large speed, the impact. The core is an impact. Okay, right. The collision impact. Oh yeah. Impact will be very large, yeah, yeah. And yes, she can be heard hard by superman. Oh,

So we have the initial velocity of the train one hundred and twenty kilometers per hour. We're going to convert this so one thousand meters for every kilometer and then for every one hour there are thirty six hundred seconds and we're getting thirty three thirty three point three three three meters per second. So for sixty exploration, we can say that velocity final squared minus velocity initial squared, divided by two times the change in distance. We know that Superman is trying to bring this train to arrest. So final velocities zero and we can say that there's going to be equal to negative on thirty three point three three three squared, divided by two times the change in distance. Here it's going to be one, one hundred and fifty and we can't keep this like this fishing for now and say that the force average there's going to be equal to the mass times the acceleration. So we can simply said, this is going to be equal to whatever we have here times the mass of the train. So it'LL be negative. Three point six times ten to the fifth times thirty three point three three three squared divided by two times one fifty. And we have that the average force exerted by the train on Superbad and exerted by the Superman on this train ah is going to be equal. Teo negative one point three three, three times ten to the sixth Mittens. So this would be essentially the force of Superman on the trade because the force here is negative, which means that the train is going to be slowing down. However, due to Newton's third Law of Motion, the train is going to be exerting an equal but opposite force on Superman. And Superman just has to take the force. Um, Cinnamon has to take the force. Ah, and essentially just be resilient in order to stop the trade. However, I just want just ah, he's exerting. Ijust wanted Teo note that he s he's exerting a force ah of this magnitude on the train. However, the train is exerting the same amount of force on Superman again. This is our final answer. That's the end of the solution. Thank you for water

Mhm. So this question, we are going to review the relationship between falls and momentum. So it is given that louis is falling from a building and we are given the mess of louis as 50 kg. Also, the terminal velocity with which she is falling is 60 meters per second. At this point the superhero comes and catches her and brings her to a stop in a time of 0.100 seconds. And Mhm what we are asked to calculate is how much force does the superman superman exert on her? So the relationship between force and momentum looks something like this F equals delta P. Or delta T. So force would be called to the rate of change of momentum. Mhm. And since the momentum is a vector quantity, they will have to decide beforehand whether we want to take which direction is positive and which direction is negative. So for this question, I'm going to take us anything going down as negative and anything going up has positive. So I said earlier that force is rate of change of momentum. And so this would be the final momentum of louis lane minus the initial momentum divided by the time taken for this whole thing, which is given to us as 0.1 seconds. The final momentum over here would be zero because eventually She comes to a stop and hence the final speed is zero and hence the final moment of missile, the initial momentum. So just writing it down again, This will be 0-. The initial momentum would be of the mass is given to us as 50 And the velocity as 60. But once again this number will be negative because the sign convention that I've chosen is such that anything going down, I'll take us negative. So this number would actually be with a negative sign. So this negative and negative will become past and they were this But the total time, which is zero point. And if you do this calculation, you'll find that the total force that the superman exerts on her would be 30,000 noodles. And this number is positive, which means that Supermoon Superman is exerting a force in upward direction as denoted by our side convention, which is what we would normally expect. So that's the answer to the first part. How much force the superman exerts? A loosely For the 2nd part. It is said that the maximum acceleration that Lewis land can withstand is seven G. Which implies that the maximum force that she can withstand would be mass times, acceleration, Her masses 50 kg. And the maximum accelerations you can withstand is 70, Which means that the maximum force that she can withstand is 350 cheap. And once again we will use the same relation A factor equals DELTA B. Or delta T. And uh So force, maximum force that she can withstand is 350G. It's on the left hand side. I'm going to write three 50 G. Her final momentum is again zero because she's coming to a stop. The initial momentum would once again be negative 50 times 60. This negative sign is because the same convention that I'm choosing is such that anything going down I'm taking as a negative divide by delta T. It is this delta T. That we are asked to calculate. Mhm. And so if you go on and do this calculation, you'll find that delta T. Would be eight point. I'm sorry. If you do this calculation, you'll find that delta T. Would be equal to 8.57 divided by G. Plugging in the value of GS 9.8 m/s square. This Delta T Would come out to be 0.875 seconds, so this is the answer, The 2nd part of the question.


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