How can i find breaking strength of steel, if it's possible at all?

[exibo177]

Homework Statement

For my project I need to calculate the maximum height that a Steel Rope could achieve while being hung between the Earth and the Moon.

Homework Equations

Tensile Strength of Steel is: 500*10^6
E of steel is: 200*10^9
distance from the Moon to he Earth is 406700

The Attempt at a Solution

i tried a lot of stuff like used the equation F/A=E*strain (where i got strain 2.5*10^15) but nothing goes right so help me if you can!

 

[Pkruse]

Are we assuming a constant gravity, or are we doing the math to figure out what it really is, knowing that for part of the way the moon's gravity will be stronger.

Also, with a wire rope the calculations are entirely different than for a steel rod. E means nothing in a rope because its stretching mechanism is much more complicated. So you need to decide which rope you are using, because each rope you can buy will be different. But if you look up the numbers in the rope manufacture's technical manual, the calculations will turn out to be much easier than you at first would think.

 

[exibo177]

we chose to do just math, i guess i would prefer to have a steel rod AND wire rope (i'm sorry for not mentioning it in the question). But i still don't understand how to calculate the critical point at which this rope/rod would break, so any type of help would be wonderful please. (with explanations)

 

[truesearch]

If you want to start somewhere make use of the ultimate tensile strength you have been given.
500 x 10^6 means that a force of 500 x 10^6 N on a steel bar of area of 1m^2 will 'break' the steel.
The problem now is...how long a rod of steel of cross section area 1m^2 needs to be to produce a weight of 500 x 10^6N.
You need to know the density of steel.
This is all assuming that the force of gravity does not change as height increases...it does of course...but see what length you get and decide whether the decreasing force of gravity will make much difference.

 

[Pkruse]

So much so good for a rod. For the rope, let's select a very common rope used in the rigging industry. 6 x 37 IWRC XIPS, one inch diameter. It has a very convenient generic breaking strength of 100,000 pounds and a weight of 1.85 pounds per foot.

So how long does it have to be to weigh 100,000 pounds and break its connection at the top? Divide it out and you get a length of 54,000 feet. Figure that you used a common swaged flemish eye as an end connection, with an efficiency of 85%. So now you are down to only 46,000 feet. That is a length short enough to make your uniform gravitational field assumption reasonable, and far short of the moon.

If you used a dyform rope with XXIPS steel, the best and strongest available, you might be able to find a rope with a 30% higher strength. But it won't change the results. You are still not even going to get out of the atmosphere, let along anywhere close to the moon.

 

[exibo177]

If you want to start somewhere make use of the ultimate tensile strength you have been given.
500 x 10^6 means that a force of 500 x 10^6 N on a steel bar of area of 1m^2 will 'break' the steel.
The problem now is...how long a rod of steel of cross section area 1m^2 needs to be to produce a weight of 500 x 10^6N.
You need to know the density of steel.
This is all assuming that the force of gravity does not change as height increases...it does of course...but see what length you get and decide whether the decreasing force of gravity will make much difference.

The density of steel is 8.03 (Stainless Steel). Please help, how could i calculate it?

 

[exibo177]

So much so good for a rod. For the rope, let's select a very common rope used in the rigging industry. 6 x 37 IWRC XIPS, one inch diameter. It has a very convenient generic breaking strength of 100,000 pounds and a weight of 1.85 pounds per foot.

So how long does it have to be to weigh 100,000 pounds and break its connection at the top? Divide it out and you get a length of 54,000 feet. Figure that you used a common swaged flemish eye as an end connection, with an efficiency of 85%. So now you are down to only 46,000 feet. That is a length short enough to make your uniform gravitational field assumption reasonable, and far short of the moon.

If you used a dyform rope with XXIPS steel, the best and strongest available, you might be able to find a rope with a 30% higher strength. But it won't change the results. You are still not even going to get out of the atmosphere, let along anywhere close to the moon.

Does it have any connection with density, volume, tensile strength of steel or anything else? or did you just use the number given out by the company that produces those ropes?