The drawing shows a wire tooth brace used by orthodontists. The top-most 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 19.4 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 need to determine the vector sum of the two forces acting on it. The forces have the same magnitude of 19.4 N, but they are not in the same direction. We can use vector addition to find the net force.
1. Draw the two forces as vectors:
- Draw the first force, F1, with an arrow pointing in one direction.
- Draw the second force, F2, with an arrow pointing in the opposite direction.
Note: When adding vectors, you can move one vector so that its tail is at the head of the other vector. This allows you to join the tail of the first vector to the head of the second vector.
2. Add the two vectors:
- Join the tail of the first vector to the head of the second vector.
- The vector from the tail of the first vector to the head of the second vector represents the net force.
3. Measure the magnitude of the net force:
- Use a ruler or a scale on the diagram to determine the length of the net force vector.
- This length represents the magnitude of the net force in the same units as the individual forces (N).
Based on the diagram and calculations, you should be able to determine the magnitude of the net force exerted on the tooth by these two forces.