A 35mm diameter steel cable carries a mine skip to a depth of 625m. The mass of the skip is equal to the mass of the 625m length cable. The unit mass of the steel cable is 7.85 x 10^3 kg/m^3 . The cable unwinds from the surface. Calculate the extension in:
a) The full length of the cable
b) When the cable is extended for half itslength, (present your answers in mm).
Assume E for the steel cable = 210000N/mm^2 and use g = 10m/s^2
When I try to do this :
7.85 * 10^3 = 7850
1kg = 9.81N
7850 * 9.81 = 77008.5 N
Stress = Force/Area
Area = π * (35)^2/4 = 962.1127502
77008.5/962.1127502 = 80.04103468
E = Stress/Strain
Strain = Stress/E
80.04103468/210000 = 3.811477842^-04 or 0.0003811477842
625 * 1000 = 625000
Strain = Change in Length/Length = 0.0003811477842 * 625000 = 238.2173651
The answer is 292mm but, I keep getting 238mm. I do not knowwhere I am going wrong. Also, I have no idea how to answer part B. The answer to this is 109mm. Please can anyone help?
a) The full length of the cable
b) When the cable is extended for half itslength, (present your answers in mm).
Assume E for the steel cable = 210000N/mm^2 and use g = 10m/s^2
When I try to do this :
7.85 * 10^3 = 7850
1kg = 9.81N
7850 * 9.81 = 77008.5 N
Stress = Force/Area
Area = π * (35)^2/4 = 962.1127502
77008.5/962.1127502 = 80.04103468
E = Stress/Strain
Strain = Stress/E
80.04103468/210000 = 3.811477842^-04 or 0.0003811477842
625 * 1000 = 625000
Strain = Change in Length/Length = 0.0003811477842 * 625000 = 238.2173651
The answer is 292mm but, I keep getting 238mm. I do not knowwhere I am going wrong. Also, I have no idea how to answer part B. The answer to this is 109mm. Please can anyone help?
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