Question

A certain orthodontist uses a wire brace to align a patient's crooked tooth as in the figure below. The tension in the wire is adjusted to have a magnitude of 18.9 N. Find the magnitude of the net force exerted by the wire on the crooked tooth.

Answer 1

The magnitude of the net force exerted by the wire on the crooked tooth is 37.8 N.

Step-by-step explanation:

The magnitude of the net force exerted by the wire on the crooked tooth can be found by considering the vertical component of the tension in the wire.

Since the wire is not perfectly horizontal, it is bent under the weight of the tooth. This means that the tension in the wire has an upward component that can support the weight of the tooth.

Using trigonometry, we can find the vertical component of the tension:

Fapp = 2Tsinθ

Fapp = 2(18.9 N)sin(90°)

Fapp = 2(18.9 N)sin(90°)

Fapp = 2(18.9 N)(1)

Fapp = 37.8 N

Therefore, the magnitude of the net force exerted by the wire on the crooked tooth is 37.8 N.