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6-6 and 6-7 Conservation of Mechanical Energy 31. (I) A novice skier, starting from rest, slides down an icy fric- tionless 8.09 incline whose vertical height is 10...

Question

6-6 and 6-7 Conservation of Mechanical Energy 31. (I) A novice skier, starting from rest, slides down an icy fric- tionless 8.09 incline whose vertical height is 105 m. How fast is she going when she reaches the bottom?

6-6 and 6-7 Conservation of Mechanical Energy 31. (I) A novice skier, starting from rest, slides down an icy fric- tionless 8.09 incline whose vertical height is 105 m. How fast is she going when she reaches the bottom?



Answers

(I) A novice skier, starting from rest, slides down a frictionless $35.0^{\circ}$ incline whose vertical height is 185 $\mathrm{m}$ . How fast is she going when she reaches the bottom?

Okay, So the question was asking us how fast issue going when she reaches the bottom, which is asking us what is the final speak for her. Okay, so we know the energy, the energy from divisional, which is the initial potential energy MGH I plus initial kinetic energy won't have envy. I square is equal to the final potential energy. Plus, the final kinetic energy was one have nb finals were and we found is the long we're looking for two. So, Jay, So we know that, um since he said you start arrest so which means that be initial the initial speed is zero. So why have m v I square is thorough This we got MGH. I is equal to energy Asia plus 1/2 uh, m V Final Square, as you have is the final high. We know their final highs is on the ground. So the highest zero. So the final high school Joel was you give us just MGH I is equal to 1/2 m B Final square. Okay, here am I am Can you guys all So we'll get g h. I is equal to what have you find us work So we've I know square is equal to to G h I. So we finally can be equal to square root to a G A shop. Okay, Jesu, acceleration of gravity and h I is in the higher, which is one point. I'm sorry. 105 meter. Okay, we're plugging. We'll get square or two times 9.8 meters per second. Squared times initial. How? We just wanted a five meter. This will give us the final speed is about 45 point 37 meters per second. Okay. And this is the answer for the question. Thank you.

So we have a skier who is starting from rest and slide stone, a frictionless incline. So we have a skier here and it's a CZ. The angle here, let's assume to be theater here, which is 13 and the secure sliding down, it says. How fast is the skier going? Then she reaches the bottom. Here starts from rest here. Now this problem can be solved by the Newtonian mechanics, but we'll use the energy approach solving this problem. The forces acting on the skier at this point are the normal force. The force of gravity are the only two forces, which is mg, and there is no friction. It's a it's a frictionless incline. Now I will write out the generalized work energy principle for using the conservation of energy. Now, whenever we approach a problem of conservation of energy, the first thing we need to do is we need to select this system so I'll draw a boundary around the system. And our system is consisting off the person and as well as the earth here and in this zone somewhere we have the external effects, if any. So right now, since we have resumed Earth as a part of our system. So the F external or external forces are doing no work on our system. The normal force is perpendicular to the direction off motion of the object. As you can see that the angle between the normal force and displacement is 90 and the work done is F D course I, Aunt ADA and since cause 90 0 therefore the work done by normal forces zero. It's in fact, the external forces a zero on the system and the we learned your gravity as such Here, uh, to do work on a system because the gravity we have taken in the part of our system. So I'll write down the generalize work energy principle which states that the some off the initial energies of the system. So we have the initial interview, a system we like kinetic energy, glass, the gravitational potential energy bless the external work done on the system is equals to the final kinetic energy place. The final gravitational potential energy bless some internal energy, which I'll call you. I n t Now in this scenario, the work done by the External forces and Zito and there is no internal energy deflection because it's friction on the surface. So we have a simple equation Unity, energy, initial place, gravitational potential, energy equals gonna take energy, final place, gravitation, potential energy. So we just court the values of kinetic energy here. So we get half and even squared. Bless mg. Why one assuming that this distance is why one and the velocity here is vey even. And the velocity here is we too. This is my one is equals 2/2 em Vito squired place M g right too. So we have This is you know So we have zero place mg by one his equals to have him Vito squared. And as the object reaches the bottom of the incline, her height become zero here. So therefore the potential energy zero. So if you saw this equation simply get V two is equals the square root off to G. Why one? And by plugging in the values in the question, we get square root off two times 9.8 times 1 25 meters as it has given the problem. It's the initial height. So if you saw that you will get 49 meters per second, which is a cable into around 110 Maya's, but are

Yeah. Hi, everybody. So we're gonna be looking a question about a skier. So a skier is 66 kilograms, and they start from the rest at the top of a mountain for a trail on They dropped to 30 from top to bottom as they go down. And they have a velocity of love and meters per second. So first of all, what we're gonna dio is put em the mass. And that's gonna be the skier. It's always important to stop to start with what we know first, and we also skin draw a little picture of that helps. And maybe guys I know some people kind of like it. I am not gonna be the best drawer, so I apologize. Um, so the Boston here is at rest in this part. We're actually not gonna care that much about because what we want is the work to go down here. And that's gonna be our velocity 11.9 years per second. And another fact that we always gonna make sure is is gravity involved is gravity involved. That is gonna be, um, 9.8 meters per second squares luminously race that here we go is gonna be 9.8 meters first, I can't square and then we know that our height here is gonna be to 30 meters. And the velocity here is they said was 11 point meters per second and we want how much know how much energy was dissipated by friction. Okay, so we're gonna be meeting this equation, which is Here we go. We got potential energy minus kinetic energy and ologists have that here to have a potential if I can spell potential father drives but my spelling potential and we got to know it now, before you and I totally still it entered the wrong because that is being adults. So before I kind of start with this, I want you guys to think of What am I about to write? What equation? And my about to write with these? Because these to the potential And the Connecticut, even this worker actually very vital for physics. So what am I about to? Right, So this is gonna be a genetic. It's 1/2 Tynes mass velocity squared. This is very important for you guys to remember. And then we have mass times, gravity times this stands or hype here on. And that is also a highly important physics problem. For most of physics classes, these are gonna be the most vital. So let's began with the potential energy here. Yes, You okay? And we see the mass. And we know our mass is 66 kilograms. Always make sure you have the units here, because sometimes you may not actually have do your math right in the units or some of the best ways to gauge what you did wrong. And this is Gravity's. Oh, that's meters for seconds. Where'd times are heights, which waas to 30 years? Okay, so let's multiply this and I'm gonna do this. Show you a MRI number for you. So we're gonna dio doing this to horse, okay? And that our units are K g m. That's where Okay. And work finds, you know, but 2:30 a.m. And this little dot Here is my multiplication right there. You can use this if that the x multiplication That helps I for the dot Other people prefer brackets. Just because it's easier. The higher up you go, the more dots since exes meet other things. Okay, so here we're gonna multiply again. and I'm not going to simplify it is quite yet, because I'm trying to let you guys see. And so we got this. 148,915 0.8 kilograms, meter squared and some gets word. Okay, beautiful. So now we're gonna do the kinetic energy. Hey, e equals Got 1/2. You can represent this by 0.5 as well, if you like. We have 66 kg and 11 meter second square. Yeah. So we're gonna do the 1/2 burst, and that's just gonna be 33 grounds times. What is 11 kinds? It's So you want anyone? Make sure you square those units. Here we go. And then one of them multiply that together. So get three 99 32,099 3 Such a beautiful number. I think so. Um, beautiful. Now, what is gonna add Pete, Me and Katie, and we're gonna plug in shower here? Yeah, get more here, but simple signs. You know what? What is imperfections. Okay, so we have 14 eight 91 five 0.8, minus 93 and I'm accidents gonna put units on the outside. I think they're both the same. We don't need you writing it every 10 seconds. Okay, so this part you should be able to deal. This is basic math. On we get one 144,000 922 and then get our units now work on 1/2. A simplified Because physicists like to simplify things. So I take this little dot and we're gonna try get it about here. So you get one to three. Four. So that means this is gonna be one. Here is found. I did my five places, and this is time, as you know, because you see how where we're at and this is you go by tens. 5 10 15 point. We're counting, and we're gonna have to around, so get four here. Some professors air fine with just this, but you do see this nine here. That is important. So we're gonna put 51.45 times 10 to the fifth and this next to be simplified. And that's gonna be Newtons. So your answer is this. So the porn lessons from here is Remember to simplify your information use. This is not gonna be this. Wait here is not your final solution. You need to simplify it and always remembered grabby. And this so thank you guys. And I hope that help you with.


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