Classical Dynamics of Particles and Systems
5th Edition
ISBN:9780534408961
Author:Stephen T. Thornton, Jerry B. Marion
Publisher:Stephen T. Thornton, Jerry B. Marion
Chapter9: Dynamics Of A System Of Particles
Section: Chapter Questions
Problem 9.5P
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Question
When you bend over, a series of large muscles, the erector spinae, pull on your spine to hold you up. Figure shows a simplified model of the spine as a rod of length L that pivots at its lower end. In this model, the center of gravity of the 320 N weight of the upper torso is at the center of the spine. The 160 N weight of the head and arms acts at the top of the spine. The erector spinae muscles are modeled as a single muscle that acts at an 12° angle to the spine. Suppose the person shown bends over to an angle of 30° from the horizontal.
a. What is the tension in the erector muscle? Hint: Align your x-axis with the axis of the spine.
b. A force from the pelvic girdle acts on the base of the spine. What is the component of this force in the direction of the spine? (This large force is the cause of many back injuries).
Transcribed Image Text:Effective location
30°
of erector spinae
muscles
Center of gravity
of head and arms
12°
Center of gravity
of upper torso
Pivot
FIGURE P8.68
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