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A 275 $\mathrm{N}$ bucket is lifted with an acceleration of 2.50 $\mathrm{m} / \mathrm{s}^{2}$ by a 125 $\mathrm{N}$ uniform vertical chain. Start each of the following parts with a free-body diagram. Find the tension in (a) the top link of the chain, (b) the bottom link of the chain, and (c) the middle link of the chain.

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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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okay, this probably years to find the tension of the top bottom in middle of this blue chain. Um, given the chain 145 he was uniformly. The bucket is to 25 Newtons and it's exciting it through the air. 2.5 meters per second squared. Yes, Let's go through these to all right. It's his two top the top to to So remember the tension is the magnitude of forces at a point. Those my top link when I had this top link I have a downward force of the weight of everything beneath it, which is 125 with 275 or 340 news going that direction. Um, but it's also being lifted at 2.5 meters per second squared. Okay, so it's also going up at a rate, which is if I take the total weight right. I don't think that's right. 200 does wonders. 304 100 I says, should be so. I mean top 400 Newtons. I am dividing them by the gravitational constant to obtain the mass of my chain, and I'm taking that mass and I am accelerating it times a new acceleration rate of 2.5 we years per second squared. So I end up with a upward force of 400 divided by 9.8 times 2.5 700 to B round 100 Newtons. And then, since from the tension is the magnitude of the forces. So the tension of top or I should say top attention is equal to 500 to Newtons. All right, that's the top. We'll check them, right? All right, now we're going to middle. Very similar idea idea. All right. The weight of the middle is the bucket plus half of this chain. So half of 125 is 62.5. So 60.5 plus 2 75 to go to 337.5 and the weight on the top is equal to again. We take this force and we're going to you divided by 9.8, but then multiplied tens, 2.5, I guess Meters per second squared meters per second squared. And that's going to be my upward force. So divided by 9.8 times 2.5 86.1. Hopefully I get the right answer for that. So I saw you six. Newton's okay, Studio right, um keeps going down to my prior scratch work, which of doing right so that so meditation is that some of these forces so attention is equal to 3.6 news in a long last last one. Bottom bottom again, the bottom weight of the bucket. It's 275 Newtons, and then that means that the upward is 275 divided by 9.8 meters per second. Squared times 2.5 meters per second squared, which is 70.2 Nunes, which means that attention is equal to 275 Newtons plus 70.2. Nunes is equal to 345 point to Newton's on a double check. My answers right with my prior work. Yes, so our tensions are 343 or 45 point tunes for the bottom 43.6 for the middle and five and two for the top. We're done

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