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 \(320 \mathrm{~N}\) weight of the upper torso is at the center of the spine. The \(160 \mathrm{~N}\) 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 \(12^{\circ}\) angle to the spine. Suppose the person in Figure P8.47 bends over to an angle of \(30^{\circ}\) from the horizontal.

a. What is the tension in the erector muscle?

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:

on FIGURE P8.47 -30 Pivot 12 Effective location of erector spinae muscles the Center of gravity of head and arms Center of gravity rilm 34 of upper torso