Determining smallest possible diameter of a cable

In summary, the discussion revolves around determining the smallest possible diameter for a round steel cable with an ultimate strength of 400Mpa and a force of 8,2KN working along it without breaking. The suggested formula for this is r^2 = N/δπ, where r represents the radius, N is the force, and δ is the ultimate strength. There is some confusion about the placement of δ and the units being used, but it is determined that the answer for the diameter should be 5.1 cm.
  • #1
kaffekjele
20
0

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)
 
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  • #2
kaffekjele said:

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 ?
 
  • #3
Also check the location of the decimal point in the answer.
 
  • #4
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)
 
  • #5
Have you checked the location of the decimal point, as suggested by TSny ?
 

FAQ: Determining smallest possible diameter of a cable

What is the purpose of determining the smallest possible diameter of a cable?

The purpose of this determination is to ensure that the cable can safely and efficiently carry the required amount of electrical current without overheating or breaking. It also helps to determine the appropriate size and type of cable to be used for a specific application.

What factors are considered when determining the smallest possible diameter of a cable?

The factors that are typically considered include the amount of electrical current that needs to be carried, the length of the cable, the type of insulation material, and the temperature and environment in which the cable will be used. Other considerations may include cost, voltage drop, and safety requirements.

How is the smallest possible diameter of a cable calculated?

The calculation involves using Ohm's Law, which relates current, voltage, and resistance. By knowing the current and the length of the cable, the resistance can be determined. Then, using the appropriate safety factor and insulation type, the minimum diameter can be calculated to ensure the cable can safely carry the required current without exceeding its temperature rating.

What are the consequences of using a cable with a diameter that is too small?

If a cable with a diameter that is too small is used, it can result in overheating, which can cause damage to the cable itself and any connected equipment. It can also increase the risk of fire or electrical hazards. Additionally, using a cable that is too small may not meet safety codes and regulations.

Can the smallest possible diameter of a cable change based on different circumstances?

Yes, the smallest possible diameter of a cable can change depending on various factors, such as the type of insulation, environmental conditions, and the amount of current being carried. It is important to carefully consider all of these factors when determining the appropriate diameter for a cable.

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