Problem

$\bullet$$\bullet$ Prevention of hip injuries. Pe…

06:28

Problem 62 Hard Difficulty

$\bullet$$\bullet$ In the previous problem, what would the answers in both
cases be if there were friction and the coefficient of kinetic
friction between the sled and the ice were 0.200 ?

Answer

a) 30.1 $\mathrm{cm}$
b) 34.752 $\mathrm{cm}$

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Physics 101 Mechanics

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Video Transcript

All right. So this problem, we have to refer to problem the preceding problem problem 61 on DSO Party A and party B are slightly different scenarios. Here's a free body diagram for apart. If you have normal for sacking upwards, gravity acted downwards and you have a stretching for us if acting to the right and an opposing fictional force to the left. Okay, so we use Newton's second law, obviously. And we was all forces and the Y direction first. And there's no net force their meaning that normal force is equal to force of gravity. Uh, and then in the extraction, um, you actually do have acceleration on DH. So here you have that f minus. The fictional force stretching forthe one's frictional forces M times except on that acceleration. And so, uh, and so f is cakes shushing force from hook slop. Ah Fook is coefficient of kinetic friction. Ah times normal force is equal to em ex And so that's just k X minus music a times and she the max therefore X is just em, eh? Plus, Mr K turns mg the ex over care and we have so we can take mass common. That's 9.5 kilograms. Time's a two meters per second squared that acceleration plus mu times CI, which is 0.2 times 9.8 meters per second. Squared on all of that is divided by care. Just 1 25 mutants per meter. Peter's so ex worked that out. You get that X is 0.301 meters and ah, 100 centimetres is one meter. So this is just 30.1 centimeters. All right? And this is part B. This is the free body diagrams. And as you can see, the only change here is that the stretching force is directed at an angle 30 degrees from the horizontal. And so the ex component of the stretching force F um is ah Kay Axe Co signed 30. The white component is CAC's signed. OK, so again, in the white direction you have known that force so and still mg. But in the ex direction you have you again have that force. So you have the ex component of Africa's K ex co sign 30 minus again the fictional force music, K times and so and an SMG that's equal to M tons acceleration in the X direction. Um, take the, um and so and and so you take ex Common. So this little it's just read the stand in terms of and, um and something that I but I didn't do right is that enemy Angie Aren't the only white component forces here? There is an inn, There is mg, but there's more to that. So m g is equal to n plus the white component of, uh of X. Okay, so that's cape of 1/2 side. So that's K X signed 30. So what we get here is K ex co sign 30 minus music care times and times and equals M a X So n here is just mg minus kxan 30. Right? So we can write that down here the place and with mg minus k x sign 30. And that's equal to m a X. So So you do some algebra here and you take the K ex term common. So okay, ex co signed 30 minus rather plus because the minuses cancel plus music. Eh? Uh, oops. There will be a music care Now I'll just be a sign. Actually, there will be a musical lips use of care sign 30. Ah, and that equals M a X plus Musa. Uh, New times, meesa okay, times. And he and so you you write. We read that you make an X the subject, and you have m times a setbacks plus Ms of care g the same same numerator we had there, divided by a co signed 30 plus music care sign 30 times care and again, em is so the numerator is the same and his 9.5 ayes to music case point too. And she's 9.8 and K is 1 25 So you work. You plant those present and you get 0.321 meters, which is 32.1 centimeters in this case.

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