Problem 1131 Correcting Torsiversion Torsiversion is a medic

Problem 11.31: Correcting Torsiversion Torsiversion is a medical condition in which a tooth is rotated away from its normal position about the long axis of the root. For example, the first premolar in the figure is not only displaced slightly in the negative y direction, it is also rotated clockwise from its proper orientation. To correct this condition, an orthodontist might use an archwire and a bracket to apply both a force and a torque to the tooth. In the case shown, the forces F1 and F2 produce a net force in the positive y direction of 1.9 N and a torque about the center of the tooth (the origin of the coordinate system) of 0.0082 Nm .

Part A Find the magnitude of the two forces, given that the distances indicated in the figure are d = 3.5 mm and D = 4.4 mm .

Solution

Resutant of forces F₁ and F₂  is 1.9 N.

that is  F₂ - F₁ = 1.9 --------(1)

equating the torques about the center of the tooth,

F₁ x 3.5 x 10^-3+ F₂ x ( 4.4 - 3.5 ) x 10^-3 = 0.0082

3.5 F₁ + 0.9 F₂ = 8.2 -----(2)

using (1) and (2)

3.5 F₁ + 0.9 F₁ + 0.9 x 1.9 = 8.2

4.4 F₁ = 6.49

F₁ = 1.475 N

substituting the value of F₁ in (1)

F₂ = 3.375 N