Well, hard to imagine the picture, but by the description the wires each side are at 16 deg. back on each side of the tooth, i.e. each at 16 deg. to the face of the tooth. Each has 18N. tension.
(sin 16) x 18 = 4.9608N.
Double it (2 wires), = 9.9216N. back on the tooth.
2•T•sinφ=2•19.5•sin16º=10.75 N
From the given information, it appears that there are two wires on each side of a tooth, and each wire is at an angle of 16 degrees relative to the face of the tooth. The tension in each wire is 18N.
To calculate the force acting backward on the tooth from the wires, you need to find the component of tension in each wire that acts in the opposite direction. This can be done using trigonometry.
The formula to find the component of force in a given direction is:
Component of force = Force x sin(angle)
So, to find the component of tension acting backward on each wire, we can use:
Component of tension = 18N x sin(16 degrees)
Using a calculator, we find that the component of tension in each wire is approximately 4.9608N.
Since there are two wires on each side, the total force acting backward on the tooth from both wires would be the sum of the individual forces:
Total force = 2 x component of tension
Thus, the total force acting backward on the tooth from both wires is:
Total force = 2 x 4.9608N = 9.9216N