Solution to Exercise 1, as Seen on Facebook.

Problem:

The simple force is applied to the crown of the incisor with an angulation alpha of 30 degrees.

The magnitude is 100 gr.

The distance from the center of resistance to the X-axis is  9mm.

The distance from the point of application of the force to Cr is 14mm.

Calculate the equivalent force system at Cr.

Solution:

Calculation of the force system applied to the crown of the tooth.

1. Force determination in X and Y axis:

F= 100 gr

Fx = F x  cos alpha = 86.60

Fy = F x sin alpha =  50 gr

2. Calculation of Moments:

First we determine the length of d2 (missing distance on the X axis).

d₂ = 10.72 mm

M of Fx =  86.60x 9 = 770.42 gr mmCCW

M of Fy=  50 x 10.72 = 536.20 grmm CW

Moment = 770.42 – 536.20 = 243 gr mm CCW