# Thread: Mechanics and Materials Change in Length and Stress/Strain

1. ## Mechanics and Materials Change in Length and Stress/Strain

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?

Instead of using 1kg = 9.81 N. I used 10 as it does state use g = 10m/s^2 But, I still got 242 instead of 292.

2. ## Re: Mechanics and Materials Change in Length and Stress/Strain

Please, can somebody help me?

3. ## Re: Mechanics and Materials Change in Length and Stress/Strain

The problem said "use g = 10m/s^2" but you used 9.81. For part (b) do exactly the same thing but use 625/2 for the length.

4. ## Re: Mechanics and Materials Change in Length and Stress/Strain

The problem is right here: Originally Posted by JimCrown
7.85 * 10^3 = 7850

1kg = 9.81N

7850 * 9.81 = 77008.5 N
You should ALWAYS include units in your calculations, as it would clearly show your error. I'll do it for you:

7.85 x 10^3 Kg/m^3 x 9.81 m/s^2 = 77008.5 Kg/m^2-s^2.

This is NOT units of force. You need to multiply the density of the steel cable by its volume in order to get its mass in Kg, then you can multiply by 'g' to get its weight in newtons. But remember that the cable has a uniform density, which means that the stress it experiences due to the weight of the cable goes from 0 at the bottom end to a maximum at the top end, and has an average value equal to half of that max value. Finally, don't forget the mass of the skip.