QUESTION:

BIO Leg Raises. In a simplified 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 (Fig. P11.57). 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 approximately horizontal, so the angle 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 \(80-\mathrm{kg}\) 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.) (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?

Equation Transcription:

°  

Text Transcription:

55^{\circ}  

10 cm

80-kg

90 cm

15 kg

44 cm

605^{\circ}