Stress and Strain/ Hooke's Law Question

[swifel7]

Homework Statement

A 50 kg traffic light is suspended above an intersection by a continuous steel cable. The cable has a diameter of 1.0 cm, and the light is depressed 12 degrees below the horizontal. What is the percentage increase in the length of the cable due to the mass of the traffic light?

Homework Equations

Stress=Force/Area
Strain=Change in length/original length
Young's elastic modulus(E)=Stress/Strain
Area = (pi) x (r^2)

E for steel is 200 x 10^9

The Attempt at a Solution

Well I found the stress and strain, but now I am lost.

 

[Q_Goest]

Hi swifel Welcome to the board. Can you calculate the tension in the cables first? Can you then find the stress in the cable? Once you do that, do you know how stress, strain and modulus relate? Can you then determine the length change?

 

[mgb_phys]

are you given the value for steel or did you look it up?
I think you are overreading the question and it is simple a triangle geometry question

 

[swifel7]

I was given the E value for steel.

 

[ideasrule]

The question wants the percentage increase in the cable's length and you've found strain, which IS the percentage increase in length.

 

[Q_Goest]

hi ideas.

The question wants the percentage increase in the cable's length and you've found strain, which IS the percentage increase in length.

where above do you see strain being calculated?

 

[mgb_phys]

In that case you can easily find the stress (weight of light and area)
Then with E you can find strain, strain is the relative increase in length

 

[ideasrule]

hi ideas.

where above do you see strain being calculated?

The OP said he calculated the stress & strain. He probably had trouble calculating the absolute change in length of the cable, not realizing it wasn't necessary to calculate percentage change.

 

[Q_Goest]

The OP said he calculated the stress & strain. He probably had trouble calculating the absolute change in length of the cable, not realizing it wasn't necessary to calculate percentage change.

lol ... yep...

 

[swifel7]

Wow, I already had the answer? Now I feel dumb, oh well. Thanks for the help guys, I really appreciate it.