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 vector T and vector T ' on this tooth in order to bring it back into alignment. If the forces have the same magnitude of 24.0 N, what is the magnitude of the net force exerted on the tooth by these forces?
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To find the magnitude of the net force exerted on the tooth, we need to combine the two vectors T and T'.
Since the forces have the same magnitude and are in opposite directions (T is likely directed to the right, while T' is directed to the left), we can subtract them to find the net force.
To subtract vectors, we can add the negative of vector T' to vector T.
Negative of vector T' can be denoted as -T'.
So, the net force (F_net) can be calculated as:
F_net = T + (-T')
Since the magnitudes of T and T' are both 24.0 N, we can substitute the values:
F_net = 24.0 N + (-24.0 N)
Subtracting 24.0 N from 24.0 N will give us:
F_net = 0 N
Therefore, the magnitude of the net force exerted on the tooth is 0 N.
To find the magnitude of the net force exerted on the tooth by the two forces, we can use vector addition. Since the two forces have the same magnitude, we can treat them as two equal vectors.
To add two vectors of equal magnitude, we need to find their resultant vector or the vector sum. In this case, the two vectors are T and T', both having a magnitude of 24.0 N. Since the vectors are pointing in the same direction (as indicated by the wire tooth brace), we add their magnitudes to find the net force.
The magnitude of the net force is given by:
Net force = |T| + |T'|
Net force = 24.0 N + 24.0 N
Net force = 48.0 N
Therefore, the magnitude of the net force exerted on the tooth by these forces is 48.0 N.