1. Back to your problem with the oral surgeon... Now you're focusing on the surgical post which must be screwed into the jaw bone. The post can be modeled as a tapered cylinder with length L, a minimum radius of R=0.5a and a maximum radius of Rmax = a. The shear modulus is G. For simplicity, we'll assume it's a solid frustum, not a hollow one. When the surgeon twists the top of the post with total torque Tapply, equilibrium is achieved. The contact between the sides post and the bone along L is modeled as a uniform resistive torque (all around the cylinder) to per unit surface area as shown. Derive a formula for the total angle of twist in terms of Tapply, L, a and G (make sure to solve for to). Feel free to use a calculator/Matlab/Wolfram as needed but please note what software you used. Because the algebra can get a little ugly, I provide for you the surface area at some arbitrary cut at location y as a sanity check. Please note, you must show how you go this equation (or an algebraic equivalent) for full credit. SA(y) = ay(y+2L)a + 4L 4L Note: the surface area of a partial cone (a frustum) is below. No, I do not expect you to know this without looking it up. Area (R+ (R 2+h 2 -r Volume=h(R+ +R) Note: the answer to this problem is op = 20LTA 9a4G Crown TApply RMAX Abutment Dental Implant "Tooth Root" "Surgical Post" [ to torque area