# 10m Steel Wire Length/ +20 Degrees C

• Kaleb
In summary, a 10m steel wire is supporting a pendulum bob and the problem asks how many millimeters longer the wire will be when the temperature increases by 20 degrees Celsius. The equation for this is (delta)L = L * a * (delta)T, where L is the original length, a is the linear expansion coefficient for steel, and (delta)T is the change in temperature. Estimating the answer first, we can see that the change in length will be roughly 2mm. Plugging in the values, we get the correct answer of 2.2mm. The key is to have a "ball park" estimate before using the numbers in a calculator.
Kaleb
[SOLVED] 10m Steel Wire Length/ +20 Degrees C

## Homework Statement

10.00-m long steel wire supports a pendulum bob at its end. How many millimeters longer is the wire when the temperature increase by 20.0 C

## Homework Equations

(Delta)L = La(Delta)T
or
Change in Length = Length * linear expansion * change in temperature

Linear Expansion for Steel

a = 11x10^-6/C

## The Attempt at a Solution

The problem asks for: How many millimeters longer is the steel wire when the temp increases by 20 Celcius.

Variables:

L = 10M
a = 11x10^-6/C
(delta)T = (x+20)
x = original temp

equation: (delta)L = 10m * (11*10^-6/(x+20)) * (x+20)

Attempt at Solving:

110m * 10^-5 (the x+20 cancel out?)

And then I get confused as what to do. Any help is appreciated, tips are always welcome.

It is the change in temperature so you don't care about the original temperature
You had it exactly correct with
Change in Length = Length * linear expansion * change in temperature

Remember with these small numbers it is easy to make a calculator slip so estimate first.
10 ppm * 20 deg = 200ppm = 0.2 parts/thousand = 0.2mm/m so roughly 2mm

Thanks much. Ill go through again and see if I can come up with the same answer. I am sure yours is correct don't get me wrong, I just need to learn it myself too. You help is unbelievably appreciated.

My answer isn't correct (the answer is 2.2mm) I was just making the point that you need to have a 'ball park' estiamte of the answer before you start putting numbers into the caclualtor or you won't know if you made a typo.

You had exactly the correct method.

I was just getting back to posting with my answer being around 3mm :) I still need to work on my step by step process though obviously. Thanks again! You rock in my book of various stones. <--that was a joke, bad one, but still a joke!

## 1. How does the length of steel wire affect its properties?

The length of a steel wire can affect its properties, such as its strength and elasticity. Generally, a longer wire will have a higher tensile strength and be more flexible compared to a shorter wire.

## 2. What is the significance of a 10m steel wire length?

A 10m length is a common standard length for steel wires and is often used in various applications, such as construction, engineering, and manufacturing. It is a practical and manageable length for many purposes.

## 3. How does temperature impact the properties of steel wire?

Temperature can significantly affect the properties of steel wire. At higher temperatures, the wire may become more flexible and easier to bend, while at lower temperatures, it may become stiffer and more brittle.

## 4. What is the ideal temperature for using a 10m steel wire?

The ideal temperature for using a 10m steel wire would depend on the specific application and the type of steel used. Generally, room temperature (around 20 degrees Celsius) is considered an optimal temperature for most steel wires.

## 5. Is a 10m steel wire suitable for outdoor use?

Yes, a 10m steel wire can be suitable for outdoor use, depending on the type of steel and the environmental conditions. Some types of steel are more resistant to corrosion and rust, making them suitable for outdoor use. However, it is always essential to consider the specific environmental factors and choose the appropriate type of steel wire accordingly.

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