# Calculating Elastic Modulus Using Steel Wire Stretching Data

• GiovanniG
In summary, the conversation revolved around a homework problem involving a steel wire with a diameter of 2.9mm and an elastic modulus of 2.0×10^11N/m^2. The question was to find the mass of an object suspended from the wire given its small amount of stretch (0.038%). The conversation also considered the possibility of the stretch being a mistake and actually being 0.038 mm. After clarification, the problem was solved by using the equation for Young's modulus for elasticity.
GiovanniG

## Homework Statement

A steel wire 2.9mm in diameter stretches by 0.038{\rm \\%} when a mass is suspended from it. The elastic modulus for steel is 2.0×1011N/m2

*that {\rm \\%} value is in my homework, I assumed it was a mistake and was meant to be mm

## Homework Equations

young's module for elasticity F/A=E(Δl/l)

## The Attempt at a Solution

So to answer this I think I need to find F because that equals mg, so I'll just divide F by 9.8.

However I'm not given l so inserting the numbers into the equation I get
F/ [(.5*.0029)^2*π]=2.0*10^11{[(l+.00038)-l]/l}
There are two unknowns and I don't know about other equations to answer this problem, usually original length is given so I'm very confused.

GiovanniG said:

## Homework Statement

A steel wire 2.9mm in diameter stretches by 0.038{\rm \\%} when a mass is suspended from it. The elastic modulus for steel is 2.0×1011N/m2

*that {\rm \\%} value is in my homework, I assumed it was a mistake and was meant to be mm

## Homework Equations

young's module for elasticity F/A=E(Δl/l)

## The Attempt at a Solution

So to answer this I think I need to find F because that equals mg, so I'll just divide F by 9.8.

However I'm not given l so inserting the numbers into the equation I get
F/ [(.5*.0029)^2*π]=2.0*10^11{[(l+.00038)-l]/l}
There are two unknowns and I don't know about other equations to answer this problem, usually original length is given so I'm very confused.
It's not clear what you are supposed to find here, F or the length of the wire.

The exact question is "How large is the mass?"

GiovanniG said:
The exact question is "How large is the mass?"
What if instead of the wire stretching by 0.038 mm, it stretched by 0.038% of its original length?

SteamKing said:
What if instead of the wire stretching by 0.038 mm, it stretched by 0.038% of its original length?

That makes so much more sense and I was able to solve it, thank you so much I was working on this problem forever :)

## 1. What is the purpose of stretching a steel wire?

The purpose of stretching a steel wire is to increase its length and decrease its cross-sectional area in order to increase its strength and durability. This process is commonly used in the production of steel cables and ropes.

## 2. How does stretching affect the properties of a steel wire?

Stretching a steel wire causes the atoms and molecules in the wire to align in a more orderly manner, increasing the wire's strength and stiffness. It also decreases the wire's ductility, or ability to deform under stress, making it less likely to break or snap.

## 3. What factors determine the amount of stretching a steel wire can withstand?

The amount of stretching a steel wire can withstand depends on its material properties, such as its composition, purity, and grain structure. It also depends on external factors such as temperature, pressure, and rate of stretching.

## 4. How does the cross-sectional area of a steel wire change during stretching?

As a steel wire is stretched, its cross-sectional area decreases due to the elongation of the wire. This results in an increase in the wire's strength and stiffness, making it capable of withstanding greater forces.

## 5. Are there any limitations to the amount of stretching a steel wire can undergo?

Yes, there are limitations to the amount of stretching a steel wire can undergo. If the stretching exceeds the wire's elastic limit, it will permanently deform or even break. Additionally, factors such as temperature and rate of stretching can also affect the wire's ability to withstand stretching.

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