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You walk into an elevator, step onto a scale, and push the "up" button. You also recall that your normal weight is 625 $\mathrm{N}$ . Start each of the following parts with a free-body diagram. (a) If the elevator has an acceleration of magnitude $2.50 \mathrm{m} / \mathrm{s}^{2},$ what does the scale read? (b) If you start holding a 3.85 kg package by a light vertical string, what will be the tension in this string once the elevator begins accelerating?

784 $\mathrm{N}$47.4 $\mathrm{N}$

Physics 101 Mechanics

Chapter 4

Newton's Laws of Motion

Physics Basics

Motion Along a Straight Line

Motion in 2d or 3d

Rutgers, The State University of New Jersey

Simon Fraser University

McMaster University

Lectures

03:28

Newton's Laws of Motion are three physical laws that, laid the foundation for classical mechanics. They describe the relationship between a body and the forces acting upon it, and its motion in response to those forces. These three laws have been expressed in several ways, over nearly three centuries, and can be summarised as follows: In his 1687 "Philosophiæ Naturalis Principia Mathematica" ("Mathematical Principles of Natural Philosophy"), Isaac Newton set out three laws of motion. The first law defines the force F, the second law defines the mass m, and the third law defines the acceleration a. The first law states that if the net force acting upon a body is zero, its velocity will not change; the second law states that the acceleration of a body is proportional to the net force acting upon it, and the third law states that for every action there is an equal and opposite reaction.

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In mathematics, a proof is a sequence of statements given to explain how a conclusion is derived from premises known or assumed to be true. The proof attempts to demonstrate that the conclusion is a logical consequence of the premises, and is one of the most important goals of mathematics.

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All right, so in this problem, we have an elevator and a man or a whole person in this elevator standing on some type of scale. Hey, it's button that makes the elevator go up. He's accelerating up 2.5 years per second squared, and his is Ah, normal. Wait. 625 Newtons. Yeah. Doo doo doo doo doo doo. OK, so that's our problem. We want to know with accelerating what this scale reads. Well, first we need to know is we need understand the mass of this person because I want to calculate the force of this vertical acceleration. And so I'm gonna do 6 25 Newtons and divide that by 9.8 meters per second squared. That will get me, um, tell me the wait in the mass in kilograms, and then I'm gonna take that mass, and I'm gonna multiply it. Times 2.5. You're saying squared to convert it back into Newman's, but a new Newton measurement. And I'm gonna cheat. Use my scratch work because I read this in a calculator earlier, and I got a, uh, did do ignore my notes your second. I'm sorry. A 1 59.4 right. Okay, go to it. One nine point for So I don't know the weight on that scale. Well, let's draw. This drawing will bigger. Here's my scale in a down direction. I had the persons of weight 625 news. But in the what do you do in the upward direction did you do? How do you say that's the scales moving upward at, um 100 wound 59 right, For we don't know the massive scale How to say this dress better. Mm. Okay, here we go. This person is being the person on scale is being accelerated at 159 0.4. So not only but so that means that not only is their weight millions of persons wait being sent back onto the scale, but we also have If the scale if this person being pushed upward at this force was my force, then it's going to send a equal and opposite force back into the scale. So there's also this is gonna send a equivalent equal opposite back into the scale. That means that our but you dio means that air scale has to has a downward force being put on it. Down. Enforcement put on our scale is equal to the weight plus the normal force of the persons. Yeah, no one prospers. Exploration of scale because this whole elevators pushing this person up 100 59.4 Nunes, that means there's a normal response backwards. Was that responsive? Push against the scale. So we add the two symptoms equal to 6 25 Nunes plus 1 59.4 Nunes physical to 700 and 770 than 14. 780 4.4 Newtons. Okay, I'm giving give or take surrounding air. I think I didn't use any rounding error. Thank you. Did that. Okay, but, um give or take grounding air. It says part A and then did it too. The B I guess to be We have a string being held in a person's hand hand. The string is holding a weight. That is, uh, 3.5 kilograms. And we are supposed to ask, um what the tension on the string is, I believe. And so if we had this set up here, what I know is I have I think about this link right here connecting the weight to the string. I have some tension going this way. Gonna have some thing going this way. This is gonna be the Rio, the weight force of gravity on the mass for the wait, which is gonna be equal to 3.85 times 9.8, which is I don't know if my head never down 37.7. All right. And then we know that this object, because of what the object is gonna be accelerating with the person we know that this object is accelerating at 2.5 meters per second squared. So we know and for our formulas. We know that this means that 37.7 mutants plus rev attention is it's the equal. The mass times acceleration of the objects of 37.7 Newtons. The tension needs to equal but do 3.85 times, two point by which is 9.6. And I think I messed this up sort were to mess up. Oh, technically, this would be a negative if I'm writing this equation out because the downward force and the tension is an upward force which would mean that this is negative, which would then make that tea is equal to 37 plus nine is 46.7, 47 0.3. Nunes. That's attention in our string and thats party, and we're done.

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