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

When you bend over, a series of large muscles, the erector spinae, pull on your spine to hold you up. Figure P8.47 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 in Figure P8.47 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).