Steel | |
Young's Modulus (Y) | 20 X 1010 N/m2 |
Shear Modulus (S) | 8.1 X 1010 N/m2 |
Bulk Modulus (B) | 16 X 1010 N/m2 |
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.
1)What is the diameter of the wire?
d1 =__________ cm
3)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?
d2 =______________ cm
1) let the diameter of the wire be 'd' m
now, stress = force/cross-sectional area = 300/(pi*d2/4) = 1200/(pi*d2)
now, as per Hooke's Law,
stress = young's moldulus*strain
strain = change in length/original length = 0.12/440 = 2.73*10-4
thus, 1200/(pi*d2) = (20 X 1010)*(2.73*10-4) = 2.45*107
or, d2 = 7*10-6 m
or, d = 2.646*10-3 m
or, diameter = 0.2646 cm
2) strain = 0.06/440 = 1.364*10-4
thus, 1200/(pi*d2) = (20 X 1010)*(1.364*10-4) = 2.73*107
or, d2 = 1.4*10-5 m
or, d = 3.74*10-3 m
or diameter = 0.374 cm
Steel Young's Modulus (Y) 20 X 1010 N/m2 Shear Modulus (S) 8.1 X 1010 N/m2 Bulk...
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