10m Steel Wire Length/ +20 Degrees C

[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.

 

[mgb_phys]

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

 

[Kaleb]

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.

 

[mgb_phys]

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.

 

[Kaleb]

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!