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$\bullet$ $\bullet$ Artificial tendons. The largest Young's modulus measured for any biological material is 30 GPa, for the S-layer of cell walls. Suppose that in the future we are able to use this material to construct an artificial Achilles tendon (see previous problem) for an athlete who has damaged his. The artificial Achilles tendon should be just as long as the original one so that it can connect at the proper places. (a) If the artificial tendon has a circular cross section, what should be its diameter be so that it will have the same force constant as the natural Achilles tendon? (b) How does this diameter compare with that of a natural Achilles tendon?

a) 2.2 $\mathrm{mm}$b) smaller

Physics 101 Mechanics

Chapter 11

Elasticity and Periodic Motion

Equilibrium and Elasticity

Periodic Motion

Cornell University

Rutgers, The State University of New Jersey

University of Sheffield

University of Winnipeg

Lectures

04:12

In physics, potential energy is the energy possessed by a body by virtue of its position relative to others, stresses within itself, electric charge, and other factors. The unit for energy in the International System of Units is the joule (J). One joule can be defined as the work required to produce one newton of force, or one newton times one metre. Potential energy is the energy of an object. It is the energy by virtue of an object's position relative to other objects. Potential energy is associated with restoring forces such as a spring or the force of gravity. The action of stretching the spring or lifting the mass is performed by a force which works against the force field of the potential. The potential energy of an object is the energy it possesses due to its position relative to other objects. It is said to be stored in the field. For example, a book lying on a table has a large amount of potential energy (it is said to be at a high potential energy) relative to the ground, which has a much lower potential energy. The book will gain potential energy if it is lifted off the table and held above the ground. The same book has less potential energy when on the ground than it did while on the table. If the book is dropped from a height, it gains kinetic energy, but loses a larger amount of potential energy, as it is now at a lower potential energy than before it was dropped.

02:18

In physics, an oscillation is the repetitive variation, typically in time, of some measure about a central value or between two or more different states. The oscillation may be periodic or aperiodic.

03:29

$\bullet$ Achilles tendon.…

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The Achilles tendon, which…

02:50

BIO Tendon-Stretching Exer…

04:33

$\bullet$ $\bullet$ Tendon…

03:18

Tendon-stretching exercise…

02:03

Muscles are attached to bo…

04:51

Biomechanical engineers de…

04:16

$\bullet$ Tendons. Tendons…

04:45

BIO Tendons. Tendons are s…

05:31

$\bullet$$\bullet$ A stude…

I guess so. Full question A. We need to deter me the diameter off the artificial tendons. Okay, so while first in order to determine that I am your the artificial tendons when true, figure out the force constant from the regular are contenders. Okay, Because that you were saying that their unofficial tendon has the same force constant as the RTD tender. So we know. OK, which is the force? Constant secret or forced? Um, by changing this is oh, is also is equal to White House eight tons divide by lto. Why is the yes ma jealous and the young man you have fought for the R key 10 days 14 74 m par which is 14 74 times 10 to apartment six part a sa area off the arcade attendance which is about 78.1 millimeters square which is equal to 78.1 times 10 to Apollon, a six meter square and al zero Here is the the land of RP attendance, which is 25 centimeters, which is 250.25 meters. Okay, so now we have all valid to figure out the force constants. So this pocket of values we get 14 74 times 10 to the power of six, huh? Times 78 going one times tend to a power legs six meters square over 0.25 meter. We get that. The fourth constant is equal to 459,880 A. Newtok. Her meter. So that's the fourth constant body, our contender and artificial tender. Okay, so now we're looking forward to find out the diameter off the artificial tendon. But first, we need to figure out the radius of a artificial tended okay? And how cool. If you got the Regis, I agree. You can know the just the area off the official tender, we can gather radius. And remember Forest Constant. What's the equal to why times a over ground zero. Okay. Which means that a kim equal to que times al zero over. Why so well, in this case, we're looking for to find out the area off the artificial tended. So let's use a prime to stand for the artificial tends of the area of artificial tender and the why here, Let's market is white. Prime was just, uh, yes. Marches, marches for the unofficial tended. And you were saying that the lands off the artificial tendons to saying as the Arcadia tended. So it's just still a little here, so we don't need you, Mark as l prime. Okay, So just leave. Life is for and remember why Prime, which is the Youngs? Barges of it off the artificial tended was given as 30 g p A. If we convert to P A, you'll give us 30 times tend to evolve in. I, uh Okay, so, no, it's plug in the values. Okay, so we'll get okay, which is wander and 59 in 880 A no Tom per meters times 0.2 of I meter, divided by 30 kinds. Tension about tonight. Uh, and we got three point a 3 to 4 times power. Tend to a power in 86 meter square. Remember, the era is just simply equal to pi R square. Okay, so the power square, where you go to three point a 3 to 4 turns potential problem in 86 meter square. Okay, which means that are we could do square roots off three point a 3 to 4 times tens of about 186 meter square over pie. Okay. And this will give us the radius is equals. Who? 1.1 times tend to probably 93 meter. Okay, which is 1.1 man in here. So the diameter or you go to two times radius. I would give us 1.1 millimeter times two, which is equal to 2.2 meter. So let's of the anger, boy. Unofficial attended for question be went into detail when you compare the diameter off the artificial tendon and the diameter of the our Achilles tendon. Well, remember, that area for the Arcadia tendon is 78.1 millimeters square. Okay, so which means that the pie are square. Let's use pi. RCO here. Good par zero square is you go to 78 when? One millimeters square. Okay, So are zero square is equal to 78. We want millimeters square. Do you have a pie? So are zero. So are zero is equal to cook square root. Oh, you know what? Every move. What we're doing S o. R. Zero is equal to square of 78 0.1 millimeters square. Do you away high And they would give us about. Fine. Really? Mitter for the radius off the Arcuri tendon. So the diameter of the article architect no equal to two times are zero, and they will give us two times find millimeter, which is 10 man here. And as you can tell, the damned er from the artificial attendant is smaller. Then the diameter off Arcady tendon. Okay? And thank you.

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