Question

Question: Unlike most of the other muscles in our bodies, the masseter muscle in the jaw, as illustrated inFigure 9.44, is attached relatively far from the joint, enabling large forces to be exerted by the back teeth. (a) Using the information in the figure, calculate the force exerted by the lower teeth on the bullet. (b) Calculate the force on the joint.

Short answer

(a) The total force exerted by the lower teeth is 116N.

(b) The force on the joint is 84N.

Step-by-step solution

Define the force

A force is an external factor that can change the rest or motion of a body. It has a size and a general direction.

Free-body diagram

The diagram for the leg muscles is shown below:

The net upward force is ${\text{F}}_{\text{m}}$, ${\text{F}}_{\text{reaction}}$ is the force exerted on the bullet by the lower teeth and${\text{F}}_{\text{J}}$ is the force on the joint.

Calculation of the force due to the lower teeth

(a)

Applying the equilibrium under the torque, we get,

$\begin{array}{rcl}{F}_M\times 2.90& =& F_{reaction}\times 5\\ F_{reaction}& =& \frac{F_M\times 2.90}{5}\\ & =& \frac{200\text{N}\times 2.90}{5}\\ & =& 116\text{N}\end{array}$

Hence, the force is 116N.

Calculation of the force on the joint

(b)

Applying the condition of equilibrium under forces, we get,

$\begin{array}{rcl}{F}_J& =& F_M+F_{reaction}\\ & =& 200-116\\ & =& 84\text{N}\end{array}$

Hence, the force is 84N.