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 340 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 1) bends
over to an angle of 30∘ from the horizontal.
[Part A]
What is the tension in the erector muscle? Hint:
Align your x-axis with the axis of the spine.
[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).
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