In a circus balancing act, a woman performs a headstand on top of a standing performer's head, as Figure 4.15a illustrates. The woman weighs 490 N, and the standing performer's head and neck weigh 50 N. It is primarily the seventh cervical vertebra in the spine that supports all the weight above the shoulders. What is the normal force that this vertebra exerts on the neck and head of the standing performer (a) before the act and (b) during the act?

a, SUPRI/Reuters/Landov LLC Figure 4.15    (a) A young woman keeps her balance during a performance by China's Sincuan Acrobatic group. A free-body diagram is shown (above the shoulders) for the standing performer (b) before the act and (c) during the act. For convenience, the scales used for the vectors in parts b and c are different.

Solution  

The physics of the human skeleton.

(a)   Figure 4.15b shows the free-body diagram for the standing performer's head and neck before the act. The only forces acting are the normal force and the 50-N weight. These two forces must balance for the standing performer's head and neck to remain at rest. Therefore, the seventh cervical vertebra exerts a normal force of . (b)   Figure 4.15c shows the free-body diagram that applies during the act. Now, the total downward force exerted on the standing performer's head and neck is 50 N + 490 N = 540 N, which must be balanced by the upward normal force, so that .