A steel wire has the following properties: Length = 5.00 m Cross-sectional area

Question

A steel wire has the following properties:
Length = 5.00 m
Cross-sectional area = 0.040 cm^2
Young's modulus = 2.0 x 10^11 Pa
Shear modulus = 0.84 x 10^11 Pa
Proportional limit = 3.60 x 10^8 Pa
Breaking stress = 11.0 x 10^8 Pa
The wire is fastened at its upper end and hangs vertically.

Part A
How great a weight can be hung from the wire without exceeding the proportional limit? w= ? N

Part B
How much does the wire stretch under this load? change in L = ? mm

Part C
What is the maximum weight that can be supported? max weight = ? N

Explanation / Answer

A) W = Proportional limit * cross section = 3.60x108 x0.040x10-4 = 1.44*103 N

B) Young's modulus

E = FL/AL

L = FL/AE = 1.44x103 x5.00 / (0.040x10-4 x2.0x1011 ) = 0.009 m. that is 9mm

C) max weight = Breaking stress * cross section = 11x108 x 0.040x10-4 = 4.4*103 N

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