Length of wire with given yielding strength

In summary, the greatest length a steel wire can have without yielding if it yields at 40 ksi is 11,800 ft or m. However, the method for calculating this length is not provided and may involve computing the volume and weight of the wire. The diameter of the wire is not given, but it can be represented as 'd' in calculations. The wire's weight is equal to the buoyancy force of the balloon.
  • #1
megr_ftw
71
0

Homework Statement


A steel wire is being hung from a high altitude balloon. What is the greatest length is can have without yielding if the steel yields at 40 ksi??


Homework Equations


I know all the stress and strain equations but I have yet to find or be taught an equation for finding this. I feel like it's very simple but I just can't figure is out. Stress= force/area
Stress= (E-modulus)(strain)

The Attempt at a Solution


The answer is 11,800 ft or m, not sure which one. But I have no clue how to get to the answer. I did my homework and everything but this problem was "recommended" and I NEED to figure it out
 
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  • #2
megr_ftw: Hint: Wouldn't you want to compute the volume of the wire, and then the weight of the wire? Wouldn't the wire be carrying that weight?
 
  • #3
they don't give you the diameter so you can't calculate the volume
 
  • #4
Could you let the diameter be d?
 
  • #5
oh yea i guess that would be the easiest option. as long as it cancels in the end.

The force of the wire's weight equals the buoyancy force created by the balloon right?
 
  • #6
Yes, you could say that. Well said.
 

What is the significance of the length of wire in relation to its yielding strength?

The length of wire is an important factor in determining its yielding strength, as a longer wire will have a greater surface area and therefore be able to withstand more force before reaching its yield point. This means that longer wires will generally have a higher yielding strength compared to shorter wires.

How is the yielding strength of a wire affected by its material composition?

The material composition of a wire plays a major role in determining its yielding strength. Different materials have different atomic structures and bonding, which can affect their ability to resist deformation and yield under stress. For example, a steel wire will have a higher yielding strength compared to an aluminum wire of the same length due to its stronger bonds.

What other factors besides length and material composition can affect the yielding strength of a wire?

Apart from length and material composition, other factors that can affect the yielding strength of a wire include its diameter, temperature, and any external forces acting on it. A thicker wire will generally have a higher yielding strength compared to a thinner wire, and higher temperatures can reduce the strength of a wire. Additionally, external forces such as tension or compression can also impact the yielding strength of a wire.

How is the yielding strength of a wire measured and expressed?

The yielding strength of a wire is typically measured in units of force per unit area, such as pounds per square inch (psi) or newtons per square meter (N/m²). This is known as the stress at yield and is determined by dividing the force required to cause the wire to yield by its cross-sectional area. The resulting value is then compared to the yield strength of the material to determine the wire's yielding strength.

What is the difference between ultimate strength and yielding strength of a wire?

The ultimate strength of a wire refers to the maximum amount of stress it can withstand before breaking, while the yielding strength is the amount of stress it can withstand before permanently deforming or yielding. In other words, the ultimate strength is the breaking point of a wire, while the yielding strength is its limit before it begins to deform. The yielding strength is typically a lower value compared to the ultimate strength.

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