The head of a football running back (see the figure below) can be considered as

Question

The head of a football running back (see the figure below) can be considered as a lever with the vertebra at the bottom of the skull as a fulcrum (the axis of rotation). The center of mass is about 0.025 m in front of the axis of rotation. The torque caused by the force that Earth exerts on the 8.0-kg head/helmet is balanced by the torque caused by the downward forces exerted by a complex muscle system in the neck. That muscle system includes the trapezius and levator scapulae muscles, among others (effectively 0.057 m from the axis of rotation).

Part A

Determine the magnitude of the force exerted by the neck muscle system pulling down to balance the torque caused by the force exerted by Earth on the head.

Part B

If an opposing player exerts a downward 180-N (40-lb ) force on the facemask, what muscle force would these neck muscles now need to exert to keep the head in equilibrium?

I am in AP Physics Algebra based plz help

Explanation / Answer

PART A

Balancing torque about axis y:

fmuscle*0.057 - fgravity*0.025 = 0

fmuscle = 8*9.81*0.025/0.057 = 34.42 N

PART B

Applying F = 180 N

The toeque about y

fmuscle*0.057 - fgravity*0.025 - F*(0.14+ 0.025) = 0

fmuscle = (8*9.81*0.025 + 180*0.165)/0.057 = 555.47 N

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