object-1-moves-with-an-initial-speed-of-v_0-toward-object-2-which-has-a-mass-half-that-of-object-1-i

Question

Object 1 moves with an initial speed of $v_{0}$ toward Object $2,$ which has a mass half that of Object 1. If the final speed of both objects after colliding is o, what must have been the initial speed of Object 2 (assuming no external forces)?
(A) $v_{\mathrm{o}}$
(B) 2$v_{\mathrm{o}}$
(C) $\frac{1}{2} v_{0}$
(D) 4$v_{0}$

Vishal Gupta · Accepted Answer

Hi. Suppose the mass off the first object is m one is able to em so the mass off second object will be half so that off the first object means it will be m by two initially speed initial means before collision Initially speed off. The first objectives we won is going to be not an initially speed off. The second object is missing. Actually we have to find it and finally speed off both of the objects. Whether it is first object or it is second object, both the objects comes to rest after collision because they&#x27;re finally speedy has been given as zero. So using conservation off linear momentum as no external force is acting the objects hands their initial momentum before the collision should remain the momentum after the collision. So we can say linear momentum before the collision is equal toe that after the collision No, For the first object, Lena momentum will be given by the product off its mass with its velocity for the second object. This is M two into veto and as finally, both the objects are coming to rest. Hence their final momentum will be zero now for em. When this is M for we even this is we not plus for em to This is M by two. And we two This is missing. We have to find it. Hence this M in Toby two by two comes out to be minus m minus. Mm Into the note. Now canceling this am here. This veto comes out to be equal to minus toe. Be not so if we ignore the negative sign speed off the second object before religion waas wise off, we not. Hence here we can see it. Option her options, See? Sorry. Hair option B is correct. Hope I answer your question, vice. Thank you.

Ze-Han Lee · Answer

So in this problem, we have two objects of Jake a one object to so the mass of the object of wise Ah ah is half a star. It&#x27;s a twice off object to and initial velocity all for the optical wise we notes. So we have turned that Ah mo mentum of object of wines and one times mean off. Right? And the moment, um, off the supposed the velocity will be to be Ah, are. Anyway, this is this. Suppose this is everyone. Okay, So this is the one So supposed toe. Ah, velocity of the two as me too. So em one times V one, which is the mo mentum of object one miners. And to be to equal zero. All right, so we come to that be to equal and once even I am too Times we won. All right. And em One deal I am too is too according to this equation. So there&#x27;s equal to be one. So the velocity everyone According to the problem, it&#x27;s the not so this sequel to be not all right

Kristela Garcia · Answer

in the situation. You have one maps moving at a velocity of the knot and you have a second mass, which is two times the mass of the first mess, moving at a separate velocity in the same direction. And these two objects are going to stick together, are going to collide and sticks together and then move off with same final velocity. And the final velocity is given as half the initial velocity of mass one. So this a conservation of moments and problem meaning that are mo mentum at the beginning total is going to be equal to our mo mentum at the end. So I can say that the first object has momentum. So I&#x27;m gonna call that m one v nut. That moment was just mass times velocity. So it&#x27;s woman is mass, one times initial velocity plus, and then the second object has two times the mass of mass one. And it has its own velocity, which we&#x27;re trying to solve for because we don&#x27;t know it and they stick together. So they&#x27;re going to have the same final velocity 0.5. Be not, and because it sticks together, they&#x27;re going to have their masses ad so too em one so we can simplify a couple of these things. This gives us three and one and I can write the right hand side as three m one v. Not all over to since 10.5 is 1/2 and then the left side looks like just em. One v not plus two m one v. And again, our goal here is this all for that final velocity. So I can subtract and one be not from both sides and find a common denominator and we get 3/2 minus two halves. Gives me 1/2 our mess. One&#x27;s cancel. And this too comes down to the bottom, giving me a final velocity equal to 1/4 the initial velocity or 0.25 times the initial velocity.

Ze-Han Lee · Answer

So in this problem, we have two objects. Subject one has mass m an object to has missed two. So object the winds moving toward object to with velocity. And after the Clyde together, the ah, they combined together. And ah, we want to know what fraction of the energy of the collision is, is it? Ah, compared to the original connector Kinetic energy of the object one. So, uh so before the collision, we know that never meant him off. The system is that only comes from the object. What that is and puffy. And after the clich is the mo mentum comes from both and it becomes m times V prime plus two m times every Friday. Right? So this is a three impound three. Prime obtained that Toby Prime equal 1/3 will be right so we can compare the energy, the kinetic energy before and after the cliche. So before the collision, the Connecticut the kinetic energy is Ikea, which is half em be squid, right? And after the closure of the kind of energy is Ikea Prime, which is half and sorry. 3 a.m. Times of the prime squared, which is 1/3 time&#x27;s okay says we can see that

Ze-Han Lee · Answer

So in this problem, we have elastic. Ah, collision problem. So we have a massive and one and ah, we know that a clot was some all no mess. So let&#x27;s say this is a news. Them too. All right. But we do know notable. Also, you&#x27;ll be off someone. So let&#x27;s suppose the velocity off the M one it would be before the collision, okay? And after the collision. So let&#x27;s suppose their velocity becomes so there&#x27;s m one. This is them to becomes. I see. It&#x27;s ah, b one and B two. Okay. So Ah, we can, because this is elastic collision rate. So we can, at least to the conservation of momentum and the conservation of energy. So the conservation of the moment, um, gives that gives us and one times e equal. So this is the moment before the collision. It quote the moment, um, after the collision, which is m one v one plus and two times me too. All right. And then the conservation of energy gives us half and one times three squid. So we choose the kind of energy before the collision. They call it a kinetic energy, often creation. So has expression half and we&#x27;ll be one squared plus half em to me. To squid. Right. So we have two equation now, but we check out this two equations we see that we have full on the perimeters. We do not know the V. We do not know and to We do not know V one on the way to not to be too. All right, so we have full on the perimeters. But we only have two questions. So that means we are missing two information&#x27;s two pieces of information. All right, so come back to the problem. Saves that. Ah ah. So we have three choices. Choice A says that the final speed of object one. So that is the one and Choice B says that Ah, the initial speed opted of one. So that is we. So there&#x27;s a be C c c. Is that the initial sorry the final speed of object to so that it&#x27;s free too. So, as I mentioned previously, we need two pieces off information to be able to result this equation. All right, so Ah, we will need any off this to any other than these three information and and I mean I need two of these three. Information&#x27;s too Resolve this resolve, these two equations. So either we know V and we won either. We know. Ah, Rie and me too, or we know we want me to. So, uh, if we know I dealt them, we can resolve this two questions. All right, so the correct choice for this problem is the all right.

Abhishek Jana · Answer

so we can use the following question post all defining velocity Where the F is defined velocity V is the initial velocity is the exploration and exits the distance traveled? Now since, uh, here the masses initially stationery the eye will be zero. So the question simplifies to year equals two square root off place off e time six. Now we have to figure out what will be the velocity when ax elation is doubled. So if ax elation is doubles, then we have two times twice off a times X and ah, that means we have to multiply squared off, too, on the left so that we eventually get back this equation. And so we see that the acts when the ax elation is doubled the velocity the final velocity increases by a factor off square root off too. So that means option B will be the correct choice. Thank you.

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