A stainless-steel orthodontic wire is a to a tooth, as in the figure below. The

Question

A stainless-steel orthodontic wire is a to a tooth, as in the figure below. The wire has an unstretched length of 2.80 cm and a radius of 0.14 mm. If the wire is stretched 0.13 mm, find the magnitude and direction of the force on the tooth. Disregard the width of the tooth and assume Young's modulus for stainless steel is 18 times 10^10 Pa. magnitude _____ N direction Assume that if the shear stress in steel exceeds about 4.00 times 10^8 N/m^2, the steel ruptures. (a) Determine the shearing force necessary to shear a steel bolt 1.20 cm in diameter. (b) Determine the shearing force necessary to punch a 1.75-cm-diameter hole in a steel plate 0.700 cm thick. _____ N

Explanation / Answer

3 ans

given that

length L=2.8 cm

streached length e=0.13 mm

youngs modulus Y=18*10^10 pa

radius r=0.14 mm

now we find the force

force F=YA*e/L=18*10^10*3.14*(0.14*10^-3)^2*0.13*10^-3/2.8*10^-2=0.051.4 N

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(a) In this case you are shearing the area of a circle (piD^2 /4)
Area = x 0.012^2 /4 = 1.1304*10^-4
Stress = force / Area
Force = stress x area
= 4 x10^8 x 1.1304 x 10^ -4
= 4.5216 x 10^4 N

(b) In this case you are shearing a cylinder of diam 1.75 cm and height 0.7 cm
Surface area of cylinder = 2x x R x h
= 2 x x 0.00875 x 0.007 = 3.8465*10^-4 m^2
Force = stress x area
= 4 x 10^8 x 3.8465 x 10^-4
= 15.386 x 10^4 N

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