# Homework Help: Thermal expansion of steel tape

1. Nov 18, 2005

### donjt81

A steel tape measure gives the length of a brass rod 102cm when both are at 12 degree C. What would the tape measure read (d) when the temperature increases to 45 degree C?
coeff of linear expansion of steel = 1.9 * 10 power -5
coeff of linear expansion of brass = 1.1 * 10 power -5
so this is my approach
deformation = coeff * change in temp * length

for the steel tape I get
deformation = 1.9 * 10 power -5 * (45-12) * 102
=.063954

for the brass rod i get
deformation = 1.1 * 10 power -5 * (45-12) * 102
=.037026

So now my question is
What would the tape measure read (d) when the temperature increases to 45 degree C?
the tape measure would read 102 + .063954 = 102.063954 (is this correct?)

then why would they give coess for brass rod. seems like i could have gotten this answer without that also.

please help

thanks in advance

2. Nov 18, 2005

### NateTG

The answer should definitely be less than 102cm.

Let's imagine for a moment that we have two rods that are both length 102 cm at 12 degrees - one steel, the other brass. If we heat both to 45 degrees, which will be longer, and what will the difference in their lengths be?

3. Nov 18, 2005

### donjt81

okay lets take a step back

I am confused about what they are asking for here.

the question says "What would the tape measure read (d) when the temperature increases to 45 degree C?"

are they asking
1. What is the final length of the steel tape at 45 degrees
OR
2. What is the final lenth of the brass rod at 45 degrees
OR
3. What is the difference between the final length of the steel tape and the final length of the brass rod.

From your comment it sounds like they are asking #3. is this correct.

4. Nov 18, 2005

### NateTG

Actually, what they're asking for is slightly different -- the problem is tricky because the length of the scale is changing.
Let's also assume (for now) that the steel scale reads true at 12 degrees C.
Then the number you have calculated is the length that a reading of 102 corresponds to on the scale at 45 degrees C. So the steel scale is no longer reading true at 45 degrees C. The question is asking what the brass rod will measure at on this un-true scale at 45 degrees C.
What I was trying to point out is that since the brass rod is expanding more slowly than the steel scale, the length of the brass rod will be less than the length of the scale at the 102 mark at 45 degrees.

5. Nov 18, 2005

### donjt81

whoa that was a tricky one. I am still not sure if i got it right but this is what i have...

in the case of the steel tape
old 102 = new 102.063954
this means that 1cm on the un-true scale will be equal to 102/102.063954 = .999373 on the true scale

in the case of the brass rod
102.037026 will now be = 102.037026 * .999373 = 101.9730888

so the length of the brass rod on the un-tru scale is 101.9730888

does that look right?

6. Nov 18, 2005

### NateTG

Well, the number shoud be right.

The words are a bit confusing because you can't really assume that either of the scales is true in a problem like this, and it would be much easier to read if you had: "1cm on the true scale will be equal to .999373 on the un-true scale" rather than what you have.

7. Nov 18, 2005

### donjt81

thats true
that is a better way to put it.

thanks nate

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