The masseter muscle, the principal muscle for chewing, is one of the strongest m

Question

The masseter muscle, the principal muscle for chewing, is one of the strongest muscles for its size in the human body. It originates on the lower edge of the zygomatic arch (cheekbone) and inserts in the angle of the mandible.

Where d = 7.70 cm and D = 11.00 cm , find the magnitude of the torque produced about the axis of rotation by the masseter muscle. The force exerted by the masseter muscle is FM = 425 N . Assume that the mandible is in static equilibrium.

Find the magnitude of the biting force, FB, exerted on the mandible by the upper teeth.

Find the horizontal component of the force FJ exerted on the mandible at the joint where it attaches to the skull.

Find the the vertical component of the force FJ exerted on the mandible at the joint where it attaches to the skull. Assume that upward is the positive vertical direction.

Explanation / Answer

Let, the angle of the manidble 26 deg,

Torque,T = FM*cos(26deg)*(D-d)

T = 425N*cos(26deg)*(11-7.7)m/100 = 12.60N.m

FB= T / D = 12.60 N·m / 0.11 m = 114. 54 N

FJx = FM * sin(26deg) = 425N * sin(26deg) = 186.30 N

FJy = FB - FM * cos(26deg) = 114.54 - 425*cos(26deg)

= -267.45N

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