The drawing shows a wire tooth brace used by orthodontists. The topmost tooth is protruding slightly, and the tension in the wire exerts two forces and ' on this tooth in order to bring it back into alignment. If the forces have the same magnitude of 17.0 N, what is the magnitude of the net force exerted on the tooth by these forces? (the angle is 16.0 degrees)
what angle? You have to figure the force normal to the tooth.
To find the magnitude of the net force exerted on the tooth, we can use vector addition. The net force is the sum of the two forces acting on the tooth.
1. Start by drawing a diagram of the situation. Draw two vectors representing the forces acting on the tooth. The angle of one force is given as 16.0 degrees.
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| 17.0 N
|
|
|
| 17.0 N
------------>
2. Break down each force into its x-component and y-component. The x-component can be found using the formula: Fx = F * cos(angle), and the y-component using Fy = F * sin(angle).
For the force on the left:
Fx₁ = 17.0 N * cos(16.0 degrees)
Fy₁ = 17.0 N * sin(16.0 degrees)
For the force on the right:
Fx₂ = 17.0 N * cos(180 degrees - 16.0 degrees)
Fy₂ = 17.0 N * sin(180 degrees - 16.0 degrees)
Note: The angle for the second force is 180 degrees minus the given angle, as it is acting in the opposite direction.
3. Calculate the x-component of the net force by adding the x-components of the two forces:
Fx_net = Fx₁ + Fx₂
4. Calculate the y-component of the net force by adding the y-components of the two forces:
Fy_net = Fy₁ + Fy₂
5. Use the Pythagorean theorem to find the magnitude of the net force:
F_net = √(Fx_net^2 + Fy_net^2)
Now, plug in the values and calculate the magnitude of the net force.