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$\bullet$$\bullet$ Muscles and tendons. The gastrocnemius muscle, in theback of the leg, has two portions, known as the medial and lateralheads. Assume that they attach to the Achilles tendon as shownin Figure $5.40 .$ The cross-sectional area of each of these twomuscles is typically 30 $\mathrm{cm}^{2}$ for manyadults. What is the maximum ten-sion they can produce in the Achillestendon? (See the previous problemfor some useful information.)

1662.9 $\mathrm{N}$

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

University of Michigan - Ann Arbor

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.

02:04

The largest tendon in the …

02:18

Two muscles in the back of…

09:09

01:40

07:13

02:19

Two muscles in the b…

02:03

Muscles are attached to bo…

01:48

03:58

Tendons are, essentially, …

01:28

The Achilles tendon connec…

01:27

01:11

The large quadriceps muscl…

03:29

$\bullet$ Achilles tendon.…

07:05

01:45

Okay, so we have Ah, yeah. Two. We have two mussels that are holing up better that are exerting an upward for sad, a 45 degree angle. It's poorly drawn. Your apologies for that. Ah, and and and? And then a downward force is exerted by attention from the attendance. Okay, so this is the free body diagram in this case, and you want to find the f the maximum force or the maximum tension of the muscles exert. Calling this after Max on dso note that this 45 degree angle this is so this is 45 degrees and it is equally divided. Meaning each Each half is the same, 22.5 degrees. Okay, so the remaining should be 90 minus 22.5. That is 67.5 degrees on DSO. That's great. That's a big step, because this can help us find no f Max and the extraction. Or why direction, Whichever we choose. Um ah, and big by simply doing ah assigned data. Okay. We could have used this 45 of those 22.5 to bees to just use co side instead of signing my kiss. So anyway, we we want to use the second law. We want to resolve forces in the white direction and it's an equilibrium. So we need that zero known at force. So what this means is that let's look at the Y direction. You have the two F Max forces acting upwards to the white components of those would be I have F. Max sign 67.5, right, except they're the same the same force. So it would be two times halfback science of 67.5. Liner's attention from the tendon he called zero. So where you have is that t equals to ask Max Sign 67.5. Okay, what is F. Max? And to answer this question, we're going to have to refer Teo to problem. So Problem seven sees a different color here, which says that if Max be equal to Sigma Times, Ayerza cross sectional area and sigma is a constant. That's given to me three times 10 to the five ah, and Esai units that you don't have to worry about It's units. He's giving us the the right units for force. Please, Snow, that's enough. Okay. And then area we have, uh, in this case, 30 centimeters squared. And so that is not quite just dividing by 100. It's dividing by 100 and another 100 because one sentiment 100 centimetres is one meter. So 30 centimeters squared Would be s 01 centimeters 100 centimeter are rather one meter square will be 100 squared centimeters. So that's why we have these two factors of 100. They're, uh and so that gives us three times 10 to the negative three square meters for area. Okay. Therefore, if Max is just, uh, three times 10 to the five times three times 10 of the negative Negative. Um, well and so you have 900 Newtons for maximum force. And so finally your tension will be two times 900 times side. 67.5. That gets you of seven, seventeen 1,700 millions for them. Attention

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