Question 3. 122 pts] Your team is developing a new centar implant that can be surgically implanted into the jawbone to restore a person's ability to chew. The dental implant system

consists of the crown, abutment, and implant body. The implant body is a hollow tube which has an outer radius of 4 mm and inner radius of 3.5 mm. The radius of the crown and abutment can be described by the function: -0.625 2² + 4.5mm mm As a biomechanical engineer, you were asked to perform an initial analysis regarding a reactive torque throughout the implant body and possible angle of twist when the abutment is installed. You searched research articles and publicly available data and found tightening the abutment into the implant body will apply an external torque of 'T = 80 N cm to the implant body. This external torque T will cause a reactive torque on the implant body, which can be expressed by the equation of t = (kz2) N mm/mm, where z is in mm. Crown Abutment TAB== Implant Body T = 80 N-cm 2=0 Z 2 mm Jawbone N-mm mm 0000 -z² + 4.5mm B t = kz² 8 mm racy = 3.5mm BCo = 4mm (+) -0.625 TAB== 7:1771 A. [5 pts] In this scenario, determine the constant k. B. [6 pts] Determine the internal torque in each section of the implant. C. [5 pts] Determine the polar moment of inertia for each section of the implant. D. [6 pts] Set up (BUT DO NOT SOLVE) an integral to compute the total twist in the implant.