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When you bend over, a series of large muscles, the erector spinae, pull on your

ID: 1513388 • Letter: W

Question

When you bend over, a series of large muscles, the erector spinae, pull on your spine to hold you up. The 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 380 N weight of the upper torso is at the center of the spine. The 170 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 in the figure bends over to an angle of 30? from the horizontal. (Figure 1)

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).

Effective location of erector spinae 30° muscles Center of gravity of head and arms 123 Center of gravity of upper torso L Pivot

Explanation / Answer

(a)

Torque summation around pivot:

170*L*cos30º 380*(½L)*cos30º - F*(L)*sin12º = 0

F*()*sin12º = [170 + 380*(½)]*cos30º

F = 360*cos30º/[()*sin12º] = 2249.29 N

(b)

The force along the length of the spine is the sum of force components along the spine from the three forces

380*sin30º + 170*sin30º + 2249.29*cos12º = 2455.13 N

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