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Question

I have no idea how to do this problem. Please help me! I will give out 10 points for the best answer.

A stainless-steell orthodontic wire is applied to a tooth (as in the figure I linked). The wire has an unstretched length of 2.8 cm and a diameter of 0.25 mm. If the wire is stretched 0.08 mm, find the magnitude of the force on the tooth. Disregard the width of the tooth and assume that Young's modulus for stainless steel is 18 x 10 to the 10th power Pa.

http://www.webassign.net/sf5/p9_66.gif

Answer 1

Convert all this to MKS units and find the cross-section of that wire.

E (stainless-steel) is given to be 18 x 10^10 N/m^2.
Cross-section is from pi(r^2). This must be in m^2, not mm^2.
3.14159(0.125*10^-3 m)^2 = 4.909 x 10^-8 m^2 cross-section.

Young's modulus (E) is given as,

E = (delta F / cross-section) / (delta length / original length)

Delta F is the tension in the wire, thats the first part of solving this problem. So rearrange the equation for delta F, renaming delta F as "tension" and substitute the value given in place of E:

Tension = (18 x 10^10 N/m^2) * (8 x 10^-5 m / 0.028 m) * (4.909 x 10^-8 m^2)

Tension in the wire is therefore 25 N.

The magnitude of force on the tooth is 25 sin 30 deg or 12.5 N

Warning!: While the reasoning is sound, double-check all of my math. Also, note that I rounded the intermediate answer 25 N.

Answer 2

You're going to have to look up the formula.

I believe Young's modulus is the stress divided by the strain per unit length.

You are given the diameter and the inital length and the amount of stretch (strain).

Pacals are a force per unit area unit.

should be something like Y = stress/strain

strain = stretch/length

stress = force/ area area is the pi x diameter of the wire^2/ 4

Better check your text on the Young's Modulus definition my memory is falible.