$(10$ points$)$ The masseter muscles on either side of the jaw are the primary muscles for biting. The jaw joint can be modeled as a hinge joint at point J$.$ Each muscle can generate a maximum force of $100$ N $.$

You are an engineer designing a new dental implant. To determine the appropriate material and geometry of the implant, you must know the force applied. What is the maximum force that can be applied by a piece of hard candy that is place between the teeth at the front of the mouth $($point A$)?$ Assume the force by the candy on the teeth acts in the vertical direction.

Figure $1$ Diagram of jaw and masseter muscle for lroblem $1.$

a$.$ Draw a FBD of the jaw bone $($mandible$),$ showing all forces and angles and an appropriate coordinate system. $(3$ points$)$

b$.$ Write equilibrium equations, including all relevant terms, directions and assumptions. $(3$ points$)$

c$.$ Calculate the force. $(4$ points$)$

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