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$\bullet$$\bullet$ A student attaches a series of weights to a tendon andmeasures the total length of the tendon for each weight. Hethen uses the data he has gathered to construct the graphshown in Figure 5.65 , giving the weight as a function of thelength of the tendon. (a) Does this tendon obey Hooke's law?How do you know? (b) What is the force constant $($ in $N / m)$ forthe tendon? (c) What weight should you hang from the tendonto make it stretch by 8.0 $\mathrm{cm}$ from its unstretched length?

a) Yes. From the graph given in the problem, we can see that the weight (and also force) is directlyproportional to the length of the tendon since the graph is a straight line.b) 50 $\mathrm{N} / \mathrm{m}$c) 4 $\mathrm{N}$

Physics 101 Mechanics

Chapter 5

Applications of Newton's Law

Motion Along a Straight Line

Motion in 2d or 3d

Newton's Laws of Motion

Applying Newton's Laws

Simon Fraser University

Hope College

University of Sheffield

McMaster University

Lectures

04:01

2D kinematics is the study of the movement of an object in two dimensions, usually in a Cartesian coordinate system. The study of the movement of an object in only one dimension is called 1D kinematics. The study of the movement of an object in three dimensions is called 3D kinematics.

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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question 73 states that a student catches a series of weights to attend in and measures the total length of the tendon for each weight. He then uses the data he has gathered to construct the graph. Shown what I've represented here, given the way as a function of the length of the tendon. Eight. Does this tendon obey Hook's Law? How do you know be or is a force constant of the tendon and see what wait. Would you hang from the tendon to make it stretch by eight centimetres from its stretched like So here's the data. I I indicated to fairly known data points here given by the the rounded points. Um, but the question asks Is this does his OBE Hook's law and it's your hand, sir, to this question is yes, you know, the Hook's law is given by the relationship of, um, this Force Constant K, both played by the Stretch Distance X, which is, of course, a linear relationship. So in the were planning weight versus L, which I should probably l hear from my variable just be consistent. The graph closes, say it's the force equals K Times L. They were planning weight versus the length. So if the scenarios were hanging a spring from some object to measure that force or measure, I mean, we're measuring the weight based on this compression l So this new the net force acting in this direction if I called my positive Y direction to be up the net force acting, why has to be zero? Because we hang the weight and after a while, the spring and Matt system stops moving, meaning that our force, our spring force, pulling up on the mass because it wants to the spring itself wants to return back with equal a good position. Since there's bits of restoring for us, it's balanced with the weight here, so that means they're forces s has to be counteracted by the weight. So that, of course, is ko and the weight. So this is a linear leadership. Although it doesn't start at the origin, that doesn't matter. Just be doing that linear relationship. So, yes, this spring does observed observed Hook's law in this domain. What is the force constant? Well, based on what we found from the scenario here, we can say that our weight in the scenario is equivalent to K times l And so by looking at this scenario what we're planning here, we have religious to solve for K replying the change in the weight over the change for length Is it simply looking at a graph? This would be a cool into the slope of a graph rate are y term? Here are rise is our weight and our run Our distance is l is the expert turn. So are changing way between these two data points which it runs through on our, um graph here. So we go from 15 mutants on top, so 15 minus, you know, for our rise and then I'll run, you know, 50 centimeters down to 20 centimeters. So I mean to cover that the meters. So that's 50 centimeters is 500.5 meters minus 0.2 meters for 20 centimeters. And my cackling this we would find at our rise over run or slope for this craft. This of the 50.0 Newtons per meter. Great. And so the last part of the question is, what weight would you hang from the tendon to make it stretch by eight centimeters? So we concert from our relationship very started party. The weight equals K l. The way our see just based on Arsene roses Mass times G. So if we know this in the scenario l equals eight centimeters. That's equivalent to 0.8 meters. Then we can solve this year for the mass to bkl over G. But this is simply state. Wait, So is it necessary? Mean mass? So I could have just honestly could have left it as w That's me. I mis read this near here. Apologies for that. So I just rewrote Matt Way equals Kate himself three times still appointees for that. But we can sit biggest multiply 50 times Point. Oh, wait. We find that the weight required is simply a 4.0 mutants. There you go.

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