Determining smallest possible diameter of a cable

[kaffekjele]

Homework Statement

You have a round steel cable with diameter d and a ultimate strenght of 400Mpa.
There is a force of 8,2KN working along the cable.
What is the smallest possible diameter the cable can have without breaking?

Homework Equations

δ= N/A
Area of a circle: πr^2

The Attempt at a Solution

δ= N/A = N/πr^2

Where N is the force working on the cable and δ is the ultimate strength of the cable.

Not sure about the placement of δ here:

r^2 = N/δπ

I tried working with the formula above by putting 8,2*10^3N/400*10^6Pa*π and taking the square root of the answer in order to find r. I ended up with an answer(for r) of 0,0255 and that seems too small to be correct.

I'm basically wondering about two things:

Am I on the correct path with regards to the formula?
Am I using the units correctly? (Pa vs N)

 

[SammyS]

Homework Statement

You have a round steel cable with diameter d and a ultimate strenght of 400Mpa.
There is a force of 8,2KN working along the cable.
What is the smallest possible diameter the cable can have without breaking?

Homework Equations

δ= N/A
Area of a circle: πr^2

The Attempt at a Solution

δ= N/A = N/πr^2

Where N is the force working on the cable and δ is the ultimate strength of the cable.

Not sure about the placement of δ here:

r^2 = N/δπ

I tried working with the formula above by putting 8,2*10^3N/(400*10^6Pa*π) and taking the square root of the answer in order to find r. I ended up with an answer(for r) of 0,0255 and that seems too small to be correct.

I'm basically wondering about two things:

Am I on the correct path with regards to the formula?
Am I using the units correctly? (Pa vs N)

(Use adequate parentheses.)

What are your units for the answer, 0.0255 ?

Is that a diameter or a radius ?

 

[TSny]

Also check the location of the decimal point in the answer.

 

[kaffekjele]

My bad, the answer would be for radius, r, so the diameter would be 2*r which would be 0,051.

As for units, if the answer above is correct, the only thing that makes sense is that it's in meters, thereby giving a diameter of 5,1cm. (But, units, exponents etc. is something i really have to work on)

 

[SammyS]

Have you checked the location of the decimal point, as suggested by TSny ?