How To Find The Thickness Of Aluminum Foil....The Easy Way!!

If you were asked to determine the thickness of aluminum foil and you tried measuring it with a ruler...well, it's safe to say that would be extremely hard. In class we learned a much simpler and easier way of determining measurements through the use of different formulas.

1. We first started by measuring the mass of our aluminum foil in grams (g).
2. Next, we measured the side lengths of the piece of aluminum foil--length (l) & width (w)
3. We then used to different formulas- D = M/V (density = mass/volume) & V = l x w x h (volume = length x width x height)
4. We were given the estimated density of foil, which is 2.70 g/cm
5. Now all that's left to do is plug in your numbers! **listing your knowns and unknowns would be a good idea. It's an excellent way to see the problem clearly**

Ex.  D = 2.70 g/cm³
       M = 0.88 g
       V = ?
        l = 15.59 cm
       w = 17.00 cm
       h = ?

First step is to solve for V

D = M/V

2.70 g/cm³ = 0.88 g/V        <---- divide both sides by 0.88 g

0.326 cm ³ = V

Next solve for height (thickness)

V = l x w x h

0.326 cm³ = 15.59 cm x 17.00 cm x h         

0.326 cm³ = 265.03 cm² x h         <---- divide both sides by 265.03 cm²

h = 0.00123 cm       <---- write this number in the correct number of sig figs (in this case, 2)

h = 0.0012 cm        <---- write it in scientific notation

h = 1.2 x 10^-3cm   

So through these easy steps, you'll be well on your way to determining a close estimate to the thickness of a piece of aluminum foil! Hoorah!

Graphing

We went to the computer lab to do the graphing. First we entered the numbers and created a graph.We made three graphs. They are  temperature vs. the volume of gas, temperature vs. density, and mass vs. volume.

 In the first graph, temperature vs. the volume of gas, shows that the volume of gas raises when the temperature is high. 

In the second graph temperature vs. density shows that the density before 4 degrees is increasing, when the temperature reaches 4 degrees, density reaches the highest point,1. Then it begins to drop as the temperature keeps on increasing. 

In the third graph mass vs. volume, the volume increases while the mass gets higher.

 

From the formula of the line, you get easily get the slope by looking at the constant before the x.  Slope is equal to rise/run, or in this case, volume/mass.  So to get density, find the reciprical of the slope. 

 

Here's a helpful little video to show you how to make one.

http://www.youtube.com/watch?v=oZAZj7NIkic

Density

Density is anything that has both mass and volume.  The formula for it is D = m/v. 
Density is measured in many different ways.  Some common ways to measure it include g/cm^3, g/mL, an kg/L. 

Useful Info:     1 mL of water = 1cm^3 of water
                      density of water = 1000g/L
                      1 mL= 1cm^3= 1g/mL

Objects will float on liquids if they are less dense and sink if they are more dense. 
E.g. - during an oil spill, oil will float on the surface because it is less dense than the surrounding water. 

This is one of Bahama's blue holes.  They are underwater caves where dense salt water sinks and less dense fresh water(rainwater) moves above it.  The two layers do not mix.

Here's a cool video about the density of diet vs. normal pop. 
http://www.youtube.com/watch?v=MzsORE0ae10&feature=related

This clip shows sulphur hexafluoride, a gas 6 times denser than air
http://www.youtube.com/user/coolphysicsvideos#p/search/0/xQo-v_F1P9U

1 Question Uncertainty Quiz

     1)     Students on a fieldtrip to the forest are asked to measure the height of a certain sapling.  Here are their measurements.

Student	Measurement
1	2.893 m
2	2.866 m
3	2.885 m
4	289.0 cm
5	2.794 m

     a)     Calculate the absolute uncertainty using method 1.

     b)     If the students were given a metre stick with cm as the smallest increment, what is the absolute uncertainty?

     c)     Calculate the relative uncertainty from you answer 1a).

     

A Perfectionist's Worst Nightmare

Perfectionists would cringe if they heard this unfortunate fact: NO MEASUREMENT IS EXACT.  You can always divide a measurement into smaller pieces.  1m = 1000000000 nm.  So, the only thing that's exact are quantities which you can count. 


1 banana



2 apples



3 cupcakes

Absolute Uncertainty
The last digit of a measurement is just an estimate, and absolute uncertainty is about looking at the amount of error a measurement could have. 

Method 1:
Discard data that doesn't fit.  Calculate the average measurement. Then find the largest difference between the data and the average measurement. That (+) is the absolute uncertainty.

E.g.
5 students measure the length of a classroom with metre sticks.  Here is the data they collected.  Find the absolute uncertainty. 

Student	Measurement
1	10.236 m
2	10.280 m
3	10.201 m
4	10.102 m
5	10.258 m

1)     Cancel out student #4's measurement because it doesn't come close to the other students.
2)     Find the mean measurement. [10.236+ 10.280 + 10.201 + 10.258 = 40.975/4 = 10.243 m]
3)     Largest measurement - average = 0.037
4)     Smallest measurement - average = -0.042
5)     Absolute uncertainty = 10.243 + 0.042 m.

Method 2:
Every measuring instrument has some degree of uncertainty.  A ruler can only measure to mm.  Since we always use 0.1 of the smallest measurement, we would state the absolute uncertainty as +0.001 m.

Relative Uncertainty
Relative uncertainty is a ratio of the absolute uncertainty/estimated measurement.  It is stated in %. The greater the quantity and the less absolute uncertainty, the more precise a measurement is. 

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Rounding Numbers

Although you've probably been rounding for over half your life, this year we will be learning some new rules.

Just like in previous years - 5> number = round down
                                       - 5< number = round up
E.g.- 9.43 (2 s.f.) = 9.4
      - 5.867 (3 s.f.) = 5.87

Now it's time for some fun!
1)     If the rounding digit is = 5 and there are MORE numbers following it, round up.
            -6.32452 (4 s.f.) = 6.325
            -2.500001 (1 s.f.) = 3
2)     If the rounding digit is = 5 and there are NO more numbers following it, round to make the last digit even.
            -4.5 (1 s.f.) = 4
            -43.498735 (7 s.f.) = 43.39874

Adding and Subtracting
When adding or subtracting, calculate the equation first.  Then round to the least exact number (least decimal places)

          
Multiplying and Dividing
When multiplying or dividing, calculate the equation first. Then round to the least amount of significant figures.

Want some more practise?  Here's a good sight to give you a quick review.
http://www.lon-capa.org/~mmp/applist/sigfig/sig.htm

Significant Figures

Significant figures are the numbers in a measurement that make it more precise.  More s.f = more precise!
All the s.f. are exact except for the last digit because they have been measured. The last digit is uncertain because it is just a best estimate. 

Rules for determining the amount of s.f. in a number:
1)     All digits from 1-9 are significant.
            -2435 = four s.f.
2)     0s preceding the number(leading zeros) do not count.
            -0.24 = two s.f.
3)     0s following the number(whole numbers) do not count unless there is a decimal point.  They are just there as placeholders.
            -480 = two s.f.
            -480. = three s.f.
4)     0s after digits in decimal numbers count because they represent an exact value of zero.
            -9.8740 = five s.f.
            -0.03274000 = seven s.f.
5)     0s between two digits always count.
            -93.40200008 = ten s.f.

Exact Numbers have an infinite amount of zeros.  These include things that can be directly counted or conversion factors. 

 

How many penguins are there?   Think hard!

You can't say there are 4.0045 or 4.2 penguins because you can't have 0.0045 of a penguin.  There are only 4.

Accuracy vs. Precision

Accuracy: How close to the accepted or actual value the measurement comes.
Precision: The degree of exactness to which something can be measured.  E.g.- 30 cm ruler that can measure to 1 mm vs. a metre stick which can only measure to 5 mm,= 30 cm ruler is more precise.