Problem

Professional Application A $30,000-\mathrm{kg}$ …

03:08

Problem 35 Hard Difficulty

Professional Application
Two manned satellites approaching one another, at a relative speed of 0.250 $\mathrm{m} / \mathrm{s}$ , intending to dock. The first has a mass of $4.00 \times 10^{3} \mathrm{kg},$ and the second a mass of $7.50 \times 10^{3} \mathrm{kg}$ . (a) Calculate the final velocity (after docking) by using the frame of reference in which the first satellite was originally at rest. (b) What is the loss of kinetic energy in this inelastic collision? (c) Repeat both parts by using the frame of reference in which the second satellite was originally at rest. Explain why the change in velocity is different in the two frames, whereas the change in kinetic energy is the same in both.

Answer

(a) $v _ { \mathrm { f } } = - 0.163 \mathrm { ms } ^ { - 1 }$
(b) $\Delta K E = 0.082 \mathrm { J }$
(c)
(i) $v = 0.087 \mathrm { ms } ^ { - 1 }$
(ii) $\Delta K E = 0.082 \mathrm { J }$

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Physics 101 Mechanics

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Chapter 8

Linear Momentum and Collisions

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Video Transcript

Okay, so here we have a two man, two satellites. Right? So they're Mace's 81,500 cases. You just read that as someone easy quote 4000 kizzie on dhe. Em too. He's called to seven 1005 100 kizzie. Right? So the initial velocity off the 1st 7 night is zero. While the final velocity of the sorry the University of Seconds at night should be Jill 0.25 meters per second Because because the relative besties given after 1 to 5 and we're considering in question number one as the first settlers is in rest. Right? So we're getting the final velocity three Dr. Docking. Okay, so final Velocity v again by using the controversy enough. The moment, um, they should be equal to m one you want plus and to you, too. A bone want us into not black in the values off. So this first time goes to zero because a few one on if you can believe this distance of to be general 0.163 me just for a second. Okay, in that dressing up YouTube because this is not supposed to write. So what were to happen. It is to get to compare the loss of Canada in Jersey, right. So, to cover the loss of kinetic energy, what we need is the initial and final final energies. So this first got appear to the ancient energy. He I is equal to half m one. You want to swear? That is obviously, you know, because you wanted, you know. Yes, Half em. Dude, that is certainly 500. And you, too, Squire. That is 0.25 Esquire. So if you calculate Kristen's up to be, you want to close to 234.38 Tools similarly find energy he f is equal to now. They are together. So half want us into ordered their fine adversity. The right savi. It's called. We have developed a deep and one and entered. This place is in here. This gives us one year 52.77 jewels. All right, So the loss in energy loss in energy loss in Canada, energy is 1/4. You're 24.3 in shit. My its final there is 1 52.7 Sarah. So the loss is equal to 81 point by Jews here. You okay? This is the loss. So now for biopsy of the question, we need to repeat. Okay, Deputy Andy, in this case, we considered that the first second said that is a crest. So this case you want to remind their 0.25 so that the rich diversity is still I don't want to fight on you. Took brain is knowledge era. OK, now, in this case, now be prime would be called to everyone. You want a friend last him to you to prime home. And one person too. No, you to private zero. So plugging the values of M 11 time and one and two, these gents are to be minus zero point, you know, eight saved one just for a second. What? Right now we have to also calculate the loss in energy. Right? So in this case, the incident candidate energy would be Now how much? Just you two is there. So when do you want brain so half em one? You want Frank. That was out to be under enter into five jewels. Similarly, the final candidate energy he finally e f is equal to half off again. The same instead. Off V. We have reprints 11 Dantley recalculation here. Right, So you can sit up in this expression. We just did this be with B brown hair and a 0.87 negative. So this just out to the hold 43 borned. 478 Jules. So what did the loss? So loss is equal to Wondered if I was the initial minus 43 point. Well, it that turns out to be home. Well, you're the 1.5 almost right. So seems like the loss off Canada energy insane in both the cases. Well, yeah, this and this This seems to be the same loves The question now is asking us. Explain why the city is different in the two friends. Well, if you see the velocity, the velocity in the first frame is there a 20.163? I mean, the second frame The city is zero point digital age seven million per second. The honesty is different, right? Even the drinks that is different Then why is not the loss in Canada goner z different? Well, for this you have to understand that. Okay, right. This here here there is no. Any external force, right? They were close. So that your comes time Mississippi. There is no any extreme course. So since there is no enemy force for this two body problem, the center off maths is off his face. Publicity! Oh, center off, muss. It's constant. No force, no force winds, no acceleration, no accident, Simmons. Constant velocity off. What off the center of mass, considering both. Thus subject to be a singer system. Right? So for the single stem, the velocity is constant. Right now, this publicity is given by 0.163 and the appointment of ex seven. Well, now, if they it diversity is constant. So what should happen? What must happen is if we see this constant velocity from different friends, then obviously the dismal citizen. Different crime. So let's read your different frames. Offer friends from friends up your prints give different results far. What a city! All right, so we have explained why diversity the measurement is because this Felicity is constant and for a constant value. If we look from different prints, we will obviously see different Paris. That's it. Right? Okay. Now why is there is the change in Canada attended the same. Well, this is internal, right? The system is acting intimately. So the loss off Canada energy lost in Canada. Energy is not because off extra systems, right loss it carry dignity is same in both trips because cannon is lost. Not so. I'm going to Jersey. I do, too. Internal forces. It's same regardless. Oh, the frame. All right, so we are done with this question.

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