The table to the above represents various properties of steel. You have steel wi

Question

The table to the above represents various properties of steel. You have steel wire 4.4 meters in length that stretches 0.12 cm when subjected to a force of 300 N. What is the diameter of the wire? d_1 = _____ cm If you wanted the wire to stretch a smaller distance when subjected to this same force, how would you change the diameter of the wire? 1 = make the diameter bigger 2 = make the diameter smaller 3 = you can't do this by only changing the diameter Type in the number that corresponds to the correct answer _____ What would the diameter of the wire be if you wanted the wire to stretch 0.06 cm less when subjected to this same force? d_2 = _____ cm

Explanation / Answer

Hooke's Law: F = k x

Stiffness of a rod (wire) in axial direction: k = A E/L

k = (pi x d2)/4 x (20 x 1010) / 4.4

Therefore, F = k x

300 N = [pi x d2/4 x (20 x 1010) / 4.4] x 0.0012

then, d1= 0.00265 m = 0.265 cm

(b) In part b the value of x will be 0.0006

F = k x

300 N = [pi x d2/4 x (20 x 1010) / 4.4] x 0.0006

then, d2 = 0.00378 m = 0.378 cm

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