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

Question

When you bend over, a series of large muscles, the erector spinae, pull on your spine to hold you up. (Figure 1) 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 360 N weight of the upper torso is at the center of the spine. The 150 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 (Figure 1) bends over to an angle of 30 from the horizontal. If a person with the arm dimensions shown pushes down hard with a 90 N force, what force must the triceps muscle provide? Ignore the mass of the arm and hand in your calculation.

Part 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).

Explanation / Answer

A)

Torque summation around pivot:

150*L*cos30º +360*(½L)*cos30º - F*(L)*sin12º = 0

F*()*sin12º = [150 + 360*(½)]*cos30º

F = 330*cos30º/[()*sin12º] = 2.061*10^3 N

B)

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

360*sin30º + 150*sin30º + 2061*cos12º = 2.27*10^3 N

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