# force supplied by vertebrae, minimal strain, center of grav

#### nmyers77

Please note that the solution to this problem is not being submitted for any credit.

A person working at a drafting board may hold her head as shown in figure 5.45 requiring muscle action to support the head. The 3 major forces acting are shown. Calculate the direction and magnitude of the force supplied by the 5th vertebrae to hold the head stationary assuming it acts along a line through the center of mass as do the weight and muscle force. Is the direction of the 5th vertebrae likely to produce minimal strain in the upper vertebrae?

Really confused here. Perhaps use trig to determine the forces highlighted in red. Then use arctan to determine theta?

Thank you very much.

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#### Unknown008

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Well, I assume that F_v is the force that the 5th vertebrae exerts...

You can resolve the forces or use Lami's Theorem. But I'll go with resolving the forces first and if you want to know about the Lami's Theorem, I'll post upon your request.

Components acting along the vertical:

50 + 60 sin(33) = F sin(\theta)

Components acting along the horizontal:

60 cos(33) = F cos(\theta)

Two equations, two unknowns. It should be easy to solve for F and theta.

As for the minimal strain, I'm afraid that it goes into biology, more specifically into bones and locomotive system which I'm not familar with.

nmyers77