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$\bullet$ A 575 N woman climbs a staircase that rises at $53^{\circ}$ abovethe horizontal and is 4.75 long. Her speed is a constant45 $\mathrm{cm} / \mathrm{s} .$ (a) Is the given weight a reasonable one for an adultwoman? (b) How much has the gravitational potential energyincreased by her climbing the stairs? (c) How much work hasgravity done on her as she climbed the stairs?

a) Yes, 58 $\mathrm{kg}$ is a reasonable weight for an adult woman.b) 2181 Jc) -2181 J

Physics 101 Mechanics

Chapter 7

Work and Energ

Physics Basics

Applying Newton's Laws

Kinetic Energy

Potential Energy

Energy Conservation

Cornell University

Rutgers, The State University of New Jersey

Hope College

University of Winnipeg

Lectures

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Okay, so two Ah, look at the problem. We see that we have a stare, and then the woman is climbing on the stairs. Now, if we say that the woman starts from here and ends about the top point, then the potential energy or the work done, do you decline? Being will be simply am times G times eight were ages, the height on DA. That's the potential energy and we stored on her are that will be the form off worked on now, Initially, if we want to solve for part way, we need to figure out whether her weight is reasonable. We need to convert the weight two pounds, and if we do so, we see that weight is 5 75 mutants and we convert that two pounds and we get 1 29 pounds, which is pretty reasonable now for the second part where we need to figure out the gravitational are we need to find find out, detainee in potential energy. As we mentioned that they should be m times d times. Let's call it Y f minus y I where Why I is the initial point and why F is the final point now, Teo, to see how how we figure out why f minus why I as you mentioned, that this distance will be equal to why I being here toe, Why f being here, which is nothing but why f minus y I is equal to a judge. And the reason for that is because when we do the potential energy calculation and we consider only one access which is, let's say, wily access in our case, then we on. We're only concerned about how much height Ah, has bean traveled by the woman? So which is why f minus y eye. So we can actually ignore this one. And we can consider why being this here because we're only considering the wind direction Now if we try to figure out why f minus why, I will see that this will be nothing but the length off the staircase times sine data where they die is the angle between the stairs with the horizontal. So we know that the length from here too here is 4.75 meters. So why f minus y I will be 4.75 sign data and Dada is giving us 53 degree Celsius. Sorry. 53 degrees. So that's going to be 4.75 meters times signe 53 degrees, which will, um, let's do the calculation there. So that's that's why mine is way. And since we know md md is given as, um 5 75 mutants so we can use this piece of information and this one together to find out Team final, between your potential energy. So that's what we did here. So why F minus whyi is, as we mentioned this quantity and empties five points of 5 75 mutants. So if we combine all of them together Ah, recall that tells you, is mg times why f minus Why I So if we combine all of them together, we see that potential energy is a 2.18 times sent about three jewels. And also we should know that the work done by priority should be negative off the potential energy due to gravity. So whatever pretension as we got there, it should work should just be the negative of that. Sandwiches negative 2.1 intense into a tree on Jules s O to summarize whenever we have, we are dealing with a potential energies. We only consider how much height has been covered. So no matter how much slope we have, or in other words, no matter what angle today is, we always consider the height in Why direction and that high times master's gravity gives us the change in potential energy. So that's what we did. And to find out the height we needed the help off the length of the stairs, which was 4.75 meters and we took sign. Scientists are 4.75 which gave us the height. And using that height with mg, we've got the potential energy and from potential energy. As we mentioned that, it's Ah Walton is negative off the potential energy. So whatever principles we got, we just put in every sigh in front of that to get to work. Thank you.

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