Determining smallest possible diameter of a cable

  • Thread starter Thread starter kaffekjele
  • Start date Start date
  • Tags Tags
    Cable Diameter
AI Thread Summary
To determine the smallest possible diameter of a steel cable under a force of 8.2 kN and an ultimate strength of 400 MPa, the formula δ = N/A (where A is the area) is applied. The area of the cable is calculated using the formula A = πr^2, leading to the rearranged equation r^2 = N/(δπ). After substituting the values, an initial radius of 0.0255 meters was found, which was later corrected to indicate that this value represented the radius, not the diameter. Thus, the correct diameter is 2 * r, resulting in a diameter of 0.051 meters, or 5.1 cm. The discussion emphasizes the importance of unit consistency and careful decimal placement in calculations.
kaffekjele
Messages
20
Reaction score
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)
 
Physics news on Phys.org
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 ?
 
Also check the location of the decimal point in the answer.
 
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)
 
Have you checked the location of the decimal point, as suggested by TSny ?
 

Thread 'Errors and significant figures'

I multiplied the values first without the error limit. Got 19.38. rounded it off to 2 significant figures since the given data has 2 significant figures. So = 19. For error I used the above formula. It comes out about 1.48. Now my question is. Should I write the answer as 19±1.5 (rounding 1.48 to 2 significant figures) OR should I write it as 19±1. So in short, should the error have same number of significant figures as the mean value or should it have the same number of decimal places as...
View full post »
Thread 'A cylinder connected to a hanging mass'

Thread 'A cylinder connected to a hanging mass'

Let's declare that for the cylinder, mass = M = 10 kg Radius = R = 4 m For the wall and the floor, Friction coeff = ##\mu## = 0.5 For the hanging mass, mass = m = 11 kg First, we divide the force according to their respective plane (x and y thing, correct me if I'm wrong) and according to which, cylinder or the hanging mass, they're working on. Force on the hanging mass $$mg - T = ma$$ Force(Cylinder) on y $$N_f + f_w - Mg = 0$$ Force(Cylinder) on x $$T + f_f - N_w = Ma$$ There's also...
View full post »

Similar threads

What Is the Stretch of a Cable Under Load?
Replies
2
Views
5K
Problem involving space elevators
Replies
19
Views
2K
Fluids: Concept about Fluid Pressure in a relation with Force and Area
Replies
6
Views
3K
Find the tension in the cable and reactive forces at ground
Replies
4
Views
5K
Magnetic energy density, and pressure due to magnetic force
Replies
23
Views
4K
Total internal reflection inside a fiber optic cable
Replies
3
Views
2K
How Much Power Can a Coaxial Cable Transmit Before Breakdown?
Replies
1
Views
2K
Find the maximum safe depth of a submarine
Replies
2
Views
4K
Calculate the forces and the work
Replies
2
Views
2K
Centripetal acceleration problem
Replies
22
Views
3K

Hot Threads

Recent Insights

Back
Top