A certain orthodontist uses a wire brace to align a patient\'s crooked tooth as

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 20.92 N. Find the magnitude of the net force exerted by the wire on the crooked tooth.
     N

left cable           N right cable           N bottom cable           N 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 20.92 N. Find the magnitude of the net force exerted by the wire on the crooked tooth

Explanation / Answer

net force = 2Tsin14 = 2*20.92sin14 = 10.12 N

bottom cable tension = weight of bird cage = 130 N

let left cable tension be Tl and right cable tension be Tr

horizontal components should cancel out

Tlcos60 = Trcos30

Tl = 1.732Tr

vertical components = 130

Tlsin60 + trsin30 = 130

putting Tl = 1.732Tr

1.732Trsin60+ trsin30 = 130

hence

Tr = 65 N

Tl = 1.732*65 = 112.58 N

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