A wire tooth brace used by orthodontists. The top-most tooth is protruding slightly, and the tension in the wire exerts two forces at 16 º angle on this tooth in order to bring it back into alignment. If the forces have the same magnitude of 19.5 N, what is the magnitude of the net force exerted on the tooth by these forces?
2•T•sinφ=2•19.5•sin16º=10.75 N
The topmost tooth is protruding slightly, and the tension in the wire exerts two forces T and T’ on this tooth in order to bring it back into alignment. If the forces have the same magnitude of 21.0 N, what is the magnitude of the net force exerted on the tooth by these forces?
To find the magnitude of the net force exerted on the tooth, we can use the concept of vector addition.
First, let's resolve the forces into their horizontal and vertical components:
- Force 1 (F₁) Horizontal component = 19.5 N * cos(16º)
- Force 1 (F₁) Vertical component = 19.5 N * sin(16º)
- Force 2 (F₂) Horizontal component = 19.5 N * cos(16º)
- Force 2 (F₂) Vertical component = -19.5 N * sin(16º) [negative because it acts in the opposite direction]
Next, calculate the sum of the horizontal components:
F_net_horizontal = F₁ horizontal component + F₂ horizontal component
= 19.5 N * cos(16º) + 19.5 N * cos(16º)
Similarly, calculate the sum of the vertical components:
F_net_vertical = F₁ vertical component + F₂ vertical component
= 19.5 N * sin(16º) - 19.5 N * sin(16º)
Lastly, use the Pythagorean theorem to find the magnitude of the net force:
F_net = √(F_net_horizontal² + F_net_vertical²)
Plug in the values to calculate the magnitude of the net force.
To find the magnitude of the net force exerted on the tooth by these forces, we can use vector addition.
Given that the forces have the same magnitude of 19.5 N and are exerted at a 16 º angle on the tooth, we can represent each force as a vector. Let's call the two forces F1 and F2.
To calculate the net force, we need to find the sum of the forces. Since the forces are acting at an angle, we can use trigonometry to break them down into their horizontal and vertical components.
Let's first find the horizontal components of the forces. The horizontal component of each force can be calculated using the formula:
Fx = F * cos(θ)
where F is the magnitude of the force and θ is the angle it makes with the horizontal axis.
For F1:
Fx1 = 19.5 N * cos(16 º)
Similarly, for F2:
Fx2 = 19.5 N * cos(16 º)
Next, let's find the vertical components of the forces. The vertical component of each force can be calculated using the formula:
Fy = F * sin(θ)
For F1:
Fy1 = 19.5 N * sin(16 º)
Similarly, for F2:
Fy2 = 19.5 N * sin(16 º)
Now that we have the horizontal and vertical components of the forces, we can add them to find the net force.
To find the net horizontal component, add the horizontal components of the forces:
Net Fx = Fx1 + Fx2
To find the net vertical component, add the vertical components of the forces:
Net Fy = Fy1 + Fy2
Finally, we can find the magnitude of the net force using the Pythagorean theorem:
Magnitude of the net force (|F|) = sqrt((Net Fx)^2 + (Net Fy)^2)
By substituting the values we calculated into the equation above, we can find the magnitude of the net force exerted on the tooth by these forces.