Please post detailed mathematical explanations. Also if you could post quick way

Question

Please post detailed mathematical explanations. Also if you could post quick ways to round and solve this problem without a calculator as it is an MCAT problem, thanks!

The human skull resting on top of the spinal column can be modeled as a lever in rotational equilibrium. In this model of a lever, the joint between the skull and spinal column is acting as the fulcrum, the weight of the head is producing a downward force on one side of the fulcrum, and the trapezius muscle is producing a downward force on the other side of the fulcrum. The torque due to the weight of the head is (4.8kg)(9.8m/s2) (0.018m). In order to maintain rotational equilibrium this torque needs to be balanced by (F)(0.011m) where F is the force applied by the trapezius muscle. Solving for F gives 77 N, which matches with choice (C). Note that this can also be estimated fairly accurately by making the following approximations:

Explanation / Answer

From rotational equilibrium,

Torque due to weight of head = torque due to force on trapezius muscle

mg*r = F*d

4.8*9.8*0.018 = F*0.011

0.8467 = F*0.011

F = (0.8467) / (0.011)

F = 76.97

in round figure, F = 77 N

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