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.