An individual leans forwards to pick up a box of 100 N. The weight of his upper body has a magnitude of 450 N. The back is pivoting around the base of the vertebral column. Consider the back of the individual as a rigid bar that is controlled by a muscle with an angle of 12° (See picture, d = trunk-head distance = 1 m). a) Calculate the magnitude of muscle force required to lift the box. b) Calculate the magnitude of the force at the base of the vertebral column.
An individual leans forwards to pick up a box of 100 N. The weight of his upper body has a magnitude of 450 N. The back is pivoting around the base of the vertebral column. Consider the back of the individual as a rigid bar that is controlled by a muscle with an angle of 12° (See picture, d = trunk-head distance = 1 m).
a) Calculate the magnitude of muscle force required to lift the box.
b) Calculate the magnitude of the force at the base of the vertebral column.
Hints: For (a) solve the equilibrium of moments, i.e. what force is required in the muscle to balance out the moments acting around the base of the spine.
For (b), solve the equilibrium of forces acting on the spine, including the muscle force you’ve just calculated, in x and y separately. There are two extra forces not shown in the diagram: x and y contact forces acting at the base of the spine. These are whatever is needed to keep the total forces acting on the spine = 0 (so the spine isn’t accelerating off in some direction!). The y component of this force is about 100 N.
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