Chapter 8, Problem 55GP

(a)

To determine

The magnitude of the force applied by the neck muscle system which is acting in the downward direction to balance the torque caused by the force exerted by Earth on the head of a football player, if his head is considered as a lever with the vertebra acting as the fulcrum. The center of mass is $0.025\text{ m}$ in front of the axis of rotation, mass of the helmet is $8\text{ kg}$, and the muscle system includes trapezius, levator, etc. which are $0.057\text{ m}$ behind the axis of rotation, as shown in the given figure.

(b)

To determine

The muscle force applied by the neck muscles to keep the head in equilibrium, if an opposing player applies $180\text{ N}$ downward force in addition to the force exerted by the earth on the head, if his head is considered as a lever with the vertebra acting as the fulcrum. The center of mass is $0.025\text{ m}$ in front of the axis of rotation, the mass of the helmet is $8\text{ kg}$, and the muscle system includes trapezius, levator, etc. which are $0.057\text{ m}$ behind the axis of rotation, and the force applied on the facemask is at a distance of $0.14\text{ m}$ from the axis of rotation, as shown in the given figure.