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Jwork Home7.C.1 You take your backpack out of the car; hike to Ihe top of nearby mountain; and (5.00) retum with your backpack to your car at the bottom. Have you c...

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Jwork Home7.C.1 You take your backpack out of the car; hike to Ihe top of nearby mountain; and (5.00) retum with your backpack to your car at the bottom. Have you changed the amount of your backpack's mechanical energy?LogoutYesNo (0/1 submissions used) Save 7.C.1 Submit 7.C.1

Jwork Home 7.C.1 You take your backpack out of the car; hike to Ihe top of nearby mountain; and (5.00) retum with your backpack to your car at the bottom. Have you changed the amount of your backpack's mechanical energy? Logout Yes No (0/1 submissions used) Save 7.C.1 Submit 7.C.1



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You absentmindedly leave your book bag on the top of your car. Estimate the safe acceleration of the car needed for the bag to stay on the roof. Describe the assumptions that you made.

Okay, So question 53 you absent mindedly leave your book bag on top of your car. A estimating safe acceleration of the car needed for the back to sell. Describe the assumptions that you like and being estimate the safe speed describing the assumptions that you've made. Okay, so let's just assume that the top of the car is modeled on a horizontal surface. We can draw the book back is just some bloke I will have a normal force. Found the way to the book bag. Okay. And of course, if we've got I an acceleration, we're gonna have force of mass times. Acceleration is going to be pushing us backwards because we're moving forwards on by Newton's third Law and a causes us to move backwards on the force of friction Obviously prevents this from happening, which is why things don't instantly fall off surfaces. So for the acceleration side of things, for part a will just take a quick look here on will do some force balancing. So the normal reaction force has to be equal to the weight so n is equal to m g on dfo for the horizontal forces, M A must equal theme coefficient of friction multiplied by the normal reaction force, which is already worked out is mg. And here the masses cancel. So it doesn't actually matter how much the massive boat bag is. Okay? And now we have to make an assumption. So I'm gonna write our assumptions in red on. Our first assumption is that the coefficient of friction between the car and the book bag has got to be some value. And so you've gotta look something like this up. Really? In this sort of question, look for the idea of a fabric sliding against a metal that will give you some idea. Because, of course, the coefficient of friction is about what two things are signing against each other. A very rough estimate would place a coefficient of friction, say, at no 0.5. And so therefore a let some do that. I'm going to just write the estimations in red on everything else in another color. So acceleration is just going to be true to our core efficient of friction, which we've estimated most applied by my 0.8 is the value of G. And so we're going to give that to be you value a 4.9 meters per second squared. Okay, um, on now for the second part, which is estimated. So Speed describing this some things we've made. Ah, this is very interesting because really, for speed, we're assuming actually a forces acting due to a speed. But of course, if velocity is constant, there's no acceleration and therefore no net force. But this is an idealized version of the world in the actual reality. Of course, as you go fast that you do end up with a force and that's the force of drag. So the force of friction has to run up to the point where it can overcome the force of drag. And if the force of drag due to your velocity gets you great, freaking will be able to come on the book bag your slide off so well, the force of friction is just going to be equal to your coefficient of friction. Static friction in this case multiplied by M. G, and that's gonna be equal to your force of drag and looking up. The force of dragnet is equal to C D multiplied by the density of the medium that you're going through. So that it is the density. I was black by B squared most blood for the area of the object which is experiencing the drag and all of this and to so that entity of air is easy. Teoh calculate its just given value and the velocity is what we're trying to sell for. Uh, the area of the book bag is interesting. Gotto make an assumption when it comes to that on The assumption we're gonna make is that it's something like half a meter by half a meter, 50 centimeters by 50 centimetres. Facing it was very rough. Now let's 1/4 of us mater by 1/4 or a meter, so that's 25 by 25 centimeters. So just less than a square foot eso no 0.25 uh, meters squared. Stick this in brackets, which is going to be no point, not 6 to 5 meters squared. I am also through the massive out bag. Let's just stick this generous ward kilogram and finally, anything else. Well, CD here is very interesting. Cassie D is a coefficient constant, which depends on the shape of the object of how well it's going to resisted games drag on different shapes have different constants associated with them. But it's not unreasonable to say something very, very sort of on air dynamic, like a book bag would have a constant associative about one. So these the assumption values they were going to use here that sound guns in, plug in. I'm going to re arrange for squared Celeste. You got first B squared is going to be equal to Mu multiplied by M G. Let's not forget to most bye bye to cause and bring the two up from the bottom. Some new, most black by energy. I was employed by two on. Then we divide, of course, the whole thing by sea subscript de 10. Steve uh, Andi the area off the shape and we're going to substitute all of these things in. We know they don't, Steve. It's a given value. Let's just say it's 1.23 kilograms for me. It's a cute, and we do these substitution. Put them all into a calculator, and we determine that V squared is 128. So this means that are safest. Uh, maximum safe is velocity is equal to the square root of 128 which puts it at 11.3 meters per second. So in the first case we really were assuming that there was no air resistance. But in this case we've had to assume a fair bit about the shapes of the things theology acts that we've been looking at, as well as its mass in this area. And of course, we found to estimate the coefficient of friction as well. But the values were after Is this 4.9 reasons per second squared for acceleration, 11.3 meters per second for our velocity? Of course, these are very rough, their order of magnitude calculations, really, But they give you a good sense of what's going on on DSO these the answers to questions like questions.

So for the first question, the changing potential energy can be go to gravity test each any heights. Gravity's with M G. M is the mass of the hiker, which is 55 kilograms, and G. He's the acceleration of gravity which go to ah, 9.8 meters per second squared. Any changing high is you go to 3300 meter minus 1600 meter and this is equal to a 1700 meter. So now it's blocking about is back into the equation to determine the changing potential energy which is you go to If I your program, what about by nine point a meter per second square and then times 1700 meter. And this is you go to nine point to times 10 to the power of If I do so for part B. According to energy conservation, all the minimal work down should be go to the changing potential energy in this case, which is equal to 9.2 times 10 to the power Viju. So for Parsi? Well, yes, the actual work down should be morning This because, for example, in a real case, when we climb a mountain, I went to overcome the friction. So you you require more work down, uh, to be done in order to kind of monster in these i d. Answers for this question.

This problem covers the concept of the work and attitude. Um, and they worked on by the average person, We assume first mass of a average person is 75 Kg. Okay, so the weight of the person is MG. And the Washington by the person is equivalent to MG into hide of the person elevated. Okay, so we can die. The work done by the person is 75 into 30, Kg. Into 9.8 Needles for 2nd square into The height and the height is 1.5 km. We need to convert kilometer into meter. Therefore we need to multiply but 1000 m or kilometers. So the work done by the person against the gravity is 1.1 enter, Then there's six jewels. And from the work magisterium, the work done equals to energy. So the minimum energy required, We know of energy is the work done that is 1.1 and two And the six tooth. So this is the minimum energy required by the person. Two Climb up a mountain of 1.5 km of altitude.

Okay, So the first part of this problem asks for the change in gravitation potential and she was just given by Delta U equals mass times acceleration due to gravity times, change in height and so mass. Here is 56.5 kilograms. Ah g, of course is 9.8 meters per second squared and a change in height is 26 60. Sosa's final hide, minus initial heights or 26. 60 meters minus 12. 70 meters. And so this gives you 7.7 times 10 to the five jewels or a 7 70,000 jewels. It's not Hey 7 70,000 You'll increase in potential energy in part B. We want the minimum work down, some minimum work done. We'll just be equal to the changing gravitational potential energy. This is assuming no dissipated forces such as fiction. Which brings us to part C. Can the actual work done be greater than, ah can actual work down w B credit than w men? Answer is yes, it absolutely can. This is because of you other forces that that the climber had to overcome which required work to be done and so w. So the minimum work is for the perfect case where there's no fracture, no off air friction, no ground fiction. And of course, no fiction do to Bo do toe joints and other body parts, rum and various end of resistance and stuff like, Well, I guess that is our affection on DSO, right? Lots of dissipated forces that you have to kind of give tract against two to make that God t that goes into the work done. So obviously W could be greater than W main infact it almost certainly will be.


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