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. Leg raises. In a simpli- fied version of the musculature action in leg raises, the abdominal muscles pull on the femur (thigh bone) to raise the leg by pivoting it about one end, as shown in Figure $10.64 .$ When you are lying horizontally, these muscles make an angle of approximately $5^{\circ}$ with the femur, and if you raise your legs, the muscles remain approx- imately horizontal, so the angle $\theta$ increases. We shall assume for simplicity that these muscles attach to the femur in only one place, 10 $\mathrm{cm}$ from the hip joint (although, in reality, the situation is more complicated). For a certain 80 kg person having a leg 90 $\mathrm{cm}$ long, the mass of the leg is 15 $\mathrm{kg}$ and its center of mass is 44 $\mathrm{cm}$ from his hip joint as measured along the leg. If the person raises his leg to $60^{\circ}$ above the horizontal, the angle between the abdominal muscles and his femur would also be about $60^{\circ} .$ (a) With his leg raised to $60^{\circ},$ find the tension in the abdominal muscle on each leg. As usual, begin your solution with a free-body diagram. (b) When is the tension in this muscle greater, when the leg is raised to $60^{\circ}$ or when the person just starts to raise it off the ground? Why? (Try this yourself to check your answer. $(\mathrm{c})$ If the abdominal muscles attached to the femur were perfectly horizontal when a person was lying down, could the person raise his leg? Why or why not?

a) 3731 $\mathrm{J}$b) when the person just stars to raise it off the ground.c) No

Physics 101 Mechanics

Chapter 10

Dynamics of Rotational Motion

Newton's Laws of Motion

Rotation of Rigid Bodies

Equilibrium and Elasticity

Cornell University

Hope College

University of Sheffield

McMaster University

Lectures

02:34

In physics, a rigid body is an object that is not deformed by the stress of external forces. The term "rigid body" is used in the context of classical mechanics, where it refers to a body that has no degrees of freedom and is completely described by its position and the forces applied to it. A rigid body is a special case of a solid body, and is one type of spatial body. The term "rigid body" is also used in the context of continuum mechanics, where it refers to a solid body that is deformed by external forces, but does not change in volume. In continuum mechanics, a rigid body is a continuous body that has no internal degrees of freedom. The term "rigid body" is also used in the context of quantum mechanics, where it refers to a body that cannot be squeezed into a smaller volume without changing its shape.

02:21

In physics, rotational dynamics is the study of the kinematics and kinetics of rotational motion, the motion of rigid bodies, and the about axes of the body. It can be divided into the study of torque and the study of angular velocity.

02:46

BIO Leg Raises. In a simpl…

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In a simplified version of…

06:03

02:22

During concentric oading o…

05:10

During a concentric loadin…

06:12

"Problem 5.6 Consider…

01:22

If you stand on one foot w…

03:57

A person is doing leg lift…

03:44

Forearm. In the human arm,…

03:48

Leg lift You are doing one…

05:24

In the human arm, the fore…

01:55

BIO Forearm. In the human …

03:22

The large quadriceps muscl…

01:15

07:05

02:12

The femur of a human leg …

So let's draw what's happening. We have this angle here theta, um, you have directly in the middle of the weight. Um, this right here would be considered the pivot. We have attention force going here, and we know that this distance is 10 centimeters and we know that this distance is 34 centimeters. Um, we're going to choose counterclockwise to be positive. So for party, when they want the tension, you can say Sigma Town equal zero. The scent of the net torque equals zero because this is not rotating, and this will be detention force times 10 centimeters time sign of theta minus the weight. The times 44 centimeters Times Co sign of data. And so tea is going to be equal to four point for W, divided by 10 of Seita. And this is going to equal for 0.4 times 15 kilograms times 9.8 divided by tangent of angle 60 degrees. And so the tension force is going to be 370 Newtons. So it will be your answer for party and then for part B. It's asking us, um, when is the tension greater in part A or when he just starts to lift his leg. So when he just starts to lift this leg, Fada is very small. So we can say that if fate is very small according to this. So this formula again T hose 4.4 w divided by tangent If ADA and as they did become smaller tangent if they become smaller, which means that the tension will be much greater when he first starts to let us when it when he first starts to lift his leg because again, if right when he first starts to lift his leg, the angle is going to be very small, which means that the tension is going to be much greater. And for part c, we can say that as, uh, the angle approaches zero degrees. Tension is going to be equal is going to approach rather infinity. So essentially, if this if he was horizontal to the floor, the person would not be able to raise his leg because he wouldn't provide torque to move the leg. There was no torque there. There would be no torque. So we can say as person, we can say the the athletes cannot lift his leg because he would not be able to provide the torque to do so. Here. The torque is out. I say the torque is being provided by his hip so his hip wouldn't be ableto prevent the torque. That is the end of the solution. Thank you for watching.

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