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Physics 101
DIY : Make and Use a Barometer to Measure Air Pressure
Overview
Air pressure is the result of the weight of tiny particles of air (air molecules)
pushing down on an area. While invisible to the naked eye (i.e. microscopic),
they nevertheless take up space and have weight. For example, take a deep
breath while holding your hand on your ribs and observe what happens. Did
you feel your chest expand? Why did it expand?
Air pressure expands because the air molecules take up space in your lungs,
causing your chest to expand. Furthermore, air can be compressed to fit in a
smaller volume since there's a lot of empty space between the air
molecules. When compressed, air is placed under high pressure.
Meteorologists measure these changes in the air to forecast weather, and the
tool they use is a barometer. The common units of measurement that
barometers use are millibars (mb) or inches of mercury.
DIY Make a Barometer
A. Materials
o
B. Theory
How does this measure air pressure?
C. Procedure
1. Place the completed barometer and scale in a shaded location
free from temperature changes (i.e. not near a window as sunlight
will adversely affect the barometer's results).
2. In your notebook or the table below, record the current date, time,
the weather conditions, and air pressure (i.e. the level where the
end of the straw measures on the scale).
3. Continue checking the barometer twice a day (if possible) each
day over a four days period.
Date
Data Table
Weather
Air
Time
Conditions Pressure
Date
June 4,
2003
June 4,
2003
June 5,
2003
Sample Data Table
Weather
Air
Time
Conditions Pressure
Clear and
9:30 am
4
Sunny
2:30 pm
Cloudy
3
9:30 am
Rainy
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Barometer Analysis
Answer the following questions in complete sentences.
1. What problem were you trying to solve with your barometer?
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
2. Were there any changes in the weather during the week?
___________________________________________________________________________
___________________________________________________________________________
3. Did the barometer measurement change when the weather changed? How much?
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
4. Did the barometer measurement change without a change in weather? Why do you think that
happened?
___________________________________________________________________________
___________________________________________________________________________
5. How well did your barometer work?
___________________________________________________________________________
___________________________________________________________________________
6. What would you change if you could design the barometer again?
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
7. How do the barometer measurements help us understand the system of weather around us?
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
The Acceleration Due to Gravity
Prof. M.L.C. Murdock
version: Sept2015
Introduction
To sensibly describe the motion of objects in our universe, we need to understand
displacement, velocity and acceleration. This lab will emphasize the latter. When we use
the word “acceleration” we mean the rate at which the velocity of a moving object
changes with time. Accelerations are always caused by “forces.” (For those who missed
lecture, think of a force as a push or a pull.) This is the essence of Newton’s first law. In
today’s lab we will measure the acceleration due to the gravitational force exerted by the
earth on two different types of objects, a tennis ball and a ping-pong ball.
Theory
Newton's second law of force relates the amount of force on an object to its mass and
acceleration.
F = ma
(1)
The greater the force on an object, the larger is its acceleration. Beyond that, this equation
doesn’t say all that much until we know what to write on the left-hand side! Fortunately,
that is the case for today.
Probably the most apparent (and yet the weakest!) of the known forces in nature is the
gravitational force. Newton's Universal Law of Gravitation describes the mutual
attractive gravitational force (Fg) exerted on each other by two objects with masses m and
m’ that are separated by a distance r. The magnitude of this force is simply
Fg = G m(1) m(2)
d^2
(2)
The constant G is called the gravitational constant and, as its name implies, does not
depend on variables like mass or distance. This course will not explain where this
formula comes from or even the experimental tests done to verify it. Instead, we will
just use it.
To compute the magnitude of the gravitational force between the earth and an object, we
substitute the mass of the earth (ME) and the distance from the object to the center of the
earth (r). When the objects are on or near the earth's surface, this distance can be
approximated by the value for the radius of the earth (RE), so that Equation (2) becomes
Fg =
(3)
We see that the force on the object depends only on the mass of the object, because G,
ME, and RE are all constants and remain the same if we change our object. This force
(measured at the earth's surface) is called the weight of the object.
Looking at Equation (1) and equating F to the gravitational force (Fg), we see that:
ma = = mg ,
(4)
where
a= .
This quantity g is a special acceleration and is itself a constant because it depends on
quantities that do not change with time. We call this special acceleration the
gravitational acceleration and is, for example, the same acceleration a book
experiences when you drop it.
Allegedly, Galileo first demonstrated this result when he dropped cannonballs of different
masses (weights) from the Leaning Tower of Pisa to show that although they had
different masses, when dropped together, they landed together. This happened in this
manner because they both experienced the same acceleration. A similar experiment can
be done by dropping a coin and a feather. When dropped in air, the coin always lands
first, but when they are dropped in a vacuum, an environment where there is no air, they
land together! In the coin and feather case, the different velocities are due to the presence
of a force, the frictional force on the coin and the feather due to the presence of air. Our
Equation (4) equates the total force to the gravitational force and therefore neglects the
effects of air friction.
Let’s now try to discover a quantitative method for determining the gravitational
acceleration, g. We first look at the equation for displacement x in a one dimensional
universe:
x(t) = vo t + (1/2) at 2
(5)
Here, the quantities vo and a are, respectively, the initial velocity and the acceleration. In
this experiment, like Galileo, we will be dropping an object from rest, so that vo will be
zero. We will assume that the only acceleration present is due to the force of gravity so
that we can set a = g. We then obtain the relation that describes the distance the object
falls as a function of time
x(t) = (1/2) gt2 .
(6)
Equation (6) provides a means to measure g. All we need to do is to drop an object
through a known distance x and then measure the time t it takes to fall. If we know both x
and t, we can solve equation (6) for g,
g =
(7)
Hence, by measuring the travel distance and the travel time for an object falling from
rest, we can measure the gravitational acceleration.
Procedure
Data
Use the given lab form to record all data and extended data (t 2 ). You should also record
m, the mass of the ball. Remember to report all data with units. For the last column of all
four tables, the value of g to be used in computing |gave – g| is your value of g found from
that particular drop.
Calculations
1. Using the measured values for x and the calculated values for t 2, insert these values
into Equation (7) to get the measured values for g. Show all calculations and remember
to label the appropriate quantities with their respective units.
2. Find the average of the five measurements of g and record this in the table below.
3. As a measure of precision, we will be using the average deviation from the mean for
the measured value of the gravitational acceleration. Reread the lab write-up for
Measurement and Measurement Error to remind yourself on how to do this type of error
analysis. Your final result for the gravitational acceleration should be reported as:
g = gave ±
As a measure of accuracy, use the given accepted value for g (9.8 m/s2) and your
measured average value of g to compute the percentage error. Again, reread the
Measurement and Measurement Error write-up to refresh your memory on how to do
this.
Conclusion
1.
How did the gravitational acceleration vary with the different heights? Did it become
smaller, larger or remain roughly constant? Why do you think this is?
2.
What did you discover in this experiment?
Error Analysis
1. How well do you think you can measure distance in this lab? Explain.
2. How well do you think you can measure drop time in this lab? Is this a matter of
accuracy, precision or both? Explain.
3. Examine equation (7). Do you think it is more important to measure accurately the
drop time or the fall distance of the ball to determine g with the greatest possible
accuracy? Explain.
4. Compare your value of g with the accepted value of 9.8 m/s2. Is your value lower or
higher than this value? Why do you think this is? Try to identify the experimental
conditions or errors that may cause this discrepancy.
Ball type: ______________________
trial
1
X
t
t2
g
|gave-g |
2
3
4
Ball mass
Average measured value for g= _______________
Accepted value for g= _______
% error: _______
Calculations
Conclusions
1.
2.
3.
Error Analysis
1.
2.
3.
Morgan Extra Pages
Graphing with Excel (revised 6/10/13)
to be carried out in a computer lab, 3rd floor Calloway Hall or elsewhere
Name Box
Figure 1. Parts of an Excel spreadsheet.
The Excel spreadsheet consists of vertical columns and horizontal rows; a column and row intersect
at a cell. A cell can contain data for use in calculations of all sorts. The Name Box shows the currently selected cell (Fig. 1).
In the Excel 2007 and 2010 versions the drop-down menus familiar in most software screens have
been replaced by tabs with horizontally-arranged command buttons of various categories (Fig. 2)
Figure 2. Tabs.
___________________________________________________________________
Open Excel, click on the Microsoft circle, upper left, and Save As your surname.xlsx on the desktop. Before leaving
the lab e-mail the file to yourself and/or save
to a flash drive. Also e-mail it to your instructor.
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EXERCISE 1: BASIC OPERATIONS
Click Save often as you work.
1. Type the heading “Edge Length” in Cell
A1 and double click the crack between
the A and B column heading for automatic widening of column A. Similarly,
write headings for columns B and C and
enter numbers in Cells A2 and A3 as in
Fig. 3. Highlight Cells A2 and A3 by
dragging the cursor (chunky plus-shape)
over the two of them and letting go.
2. Note that there are three types of cursor
crosses: chunky for selecting, barbed for
moving entries or blocks of entries from
cell to cell, and tiny (appearing only at
the little square in the lower-right corner
of a cell). Obtain a tiny arrow for Cell
A3 and perform a plus-drag down Column A until the cells are filled up to 40
(in Cell A8). Note that the two highlighted cells set both the starting value of
the fill and the intervals.
Figure 4. A formula.
5. Highlight Cells B2 and C2; plus-drag
down to Row 8 (Fig. 5). Do the numbers look correct?
Click on some cells in the newly filled
area and notice how Excel steps the row
designations as it moves down the column (it can do it for vertical plus-drags
along rows also). This is the major programming development that has led to
the popularity of spreadsheets.
Figure 3. Entries.
3. Click on Cell B2 and enter a formula for
face area of a cube as follows: type =,
click on Cell A2, type ^2, and press Enter (note the formula bar in Fig. 4).
4. Enter the formula for cube volume in
Cell C2 (same procedure, but “=, click
on A2, ^3, Enter”).
Figure 5. Plus-dragging formulas.
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Figure 6. Creating a scatter graph.
6. Now let’s graph the Face Area versus
Edge Length: select Cells A1 through
B8, choose the Insert tab, and click the
Scatter drop-down menu and select
“Scatter with only Markers” (Fig. 6).
7. Move the graph (Excel calls it a “chart”)
that appears up alongside your number
table and dress it up as follows:
a. Note that some Chart Layouts have
appeared above. Click Layout 1 and
alter each title to read Face Area for
the vertical axis, Edge Length for the
horizontal and Face Area vs. Edge
Length for the Graph Title.
b. Activate the Excel Least squares
routine, called “fitting a trendline” in
the program: right click any of the
data markers and click Add Trendline. Choose Power and also check
“Display equation on chart” and
“Display R-squared value on chart.”
Fig. 7 shows what the graph will
look like at this point.
c. The titles are explicit, so the legend
is unnecessary. Click on it and press
the delete button to remove it.
Figure 7. A graph with a fitted curve.
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8. Now let’s overlay the Volume vs. Edge Length curve onto the same graph (optional for
203L/205L): Make a copy of your graph by clicking on the outer white area, clicking ctrl-c
(or right click, copy), and pasting the copy somewhere else (ctrl-v). If you wish, delete the
trendline as in Fig. 8.
a. Right click on the outer white space, choose Select Data and click the Add button.
b. You can type in the cell ranges by hand in the dialog box that comes up, but it is easier to
click the red, white, and blue button on the right of each space and highlight what you
want to go in. Click the red, white, and blue of the bar that has appeared, and you will
bounce back to the Add dialog box. Use the Edge Length column for the x’s and Volume
for the y’s.
c. Right-click on any volume data point and choose Format Data Series. Clicking Secondary Axis will place its scale on the right of the graph as in Fig. 8.
d. Dress up your graph with two axis titles (Layout-Labels-Axis Titles), etc.
Figure 8. Adding a second curve and
y-axis to the graph
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EXERCISE 2: INTERPRETING A LINEAR GRAPH
Introduction: Many experiments are repeated a number of times with one of the
parameters involved varied from run to run.
Often the goal is to measure the rate of
change of a dependent variable, rather than a
particular value. If the dependent variable
can be expressed as a linear function of the
independent parameter, then the slope and yintercept of an appropriate graph will give
the rate of change and a particular value,
respectively.
An example of such an experiment in
PHYS.203L/205L is the first part of Lab 20,
in which weights are added to the bottom of
a suspended spring (Figure 9).
ing weights in newtons of 0.49, 0.98, etc.
The weight pan was used as the pointer for
reading y and had a mass of 50 g, so yo could
not be directly measured. For convenient
graphing Equation 1 can be rewritten:
-(Mg) = - ky + kyo
Or
(Mg) = ky - kyo
(Eq. 1′)
Procedure
1. On your spreadsheet note the tabs at the
bottom left and double-click Sheet1.
Type in “Basics,” and then click the
Sheet2 tab to bring up a fresh worksheet.
Change the sheet name to “Linear Fit”
and fill in data as in this table.
Hooke’s Law
Experiment
y (m)
-Fs = Mg (N)
0.337
0.49
0.388
0.98
0.446
1.47
0.498
1.96
0.550
2.45
2. Highlight the cells with the numbers,
and graph (Mg) versus y as in Steps 6
and 7 of the Basics section. Your Trendline this time will be Linear of course.
Figure 9. A spring with a weight
stretching it
This experiment shows that a spring exerts a
force Fs proportional to the distance
stretched y = (y-yo), a relationship known
as Hooke’s Law:
Fs = - k(y – yo)
(Eq. 1)
where k is called the Hooke’s Law constant.
The minus sign shows that the spring opposes any push or pull on it. In Lab 20 Fs is
equal to (- Mg) and y is given by the reading
on a meter stick. Masses were added to the
bottom of the spring in 50-g increments giv-
If you are having trouble remembering
what’s versus what, "y" looks like "v",
so what comes before the "v" of "versus"
goes on the y (vertical) axis. Yes, this
graph is confusing: the horizontal (“x”)
axis is distance y, and the “y” axis is
something else.
3. Click on the Equation/R2 box on the
graph and highlight just the slope, that
is, only the number that comes before the
“x.” Copy it (control-c is a fast way to
do it) and paste it (control-v) into an
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empty cell. Do likewise for the intercept
(including the minus sign).
SAVE
YOUR FILE!
5. The next steps use the standard procedure for obtaining information from linear data. Write the general equation for
a straight line immediately below a
hand-written copy of Equation 1′ then
circle matching items:
(Mg) = k y + (- k yo)
y
= mx+ b
(Eq. 1′)
6. Solve Equation 2 for k, that is, rewrite
left to right. Then substitute the value
for slope m from your graph, and you
have an experimental value for the
Hooke’s Law constant k. Next solve
Equation 3 for yo, substitute the value for
intercept b from your graph and the
value of k that you just found, and calculate yo.
7. Examine your linear graph for clues to
finding the units of the slope and the yintercept. Use these units to find the
units of k and yo.
Note the parentheses around the intercept term of Equation 1′ to emphasize
that the minus sign is part of it.
8. Present your values of k and yo with their
units neatly at the bottom of your
spreadsheet.
Equating above and below, you can create two useful new equations:
9. R2 in Excel, like r in our lab manual and
Corr. in the LoggerPro software, is a
measure of how well the calculated line
matches the data points. 1.00 would indicate a perfect match. State how good a
match you think was made in this case?
slope m = k
(Eq. 2)
y-intercept b = -kyo
(Eq. 3)
10. Do the Homework, Further Exercises on
Interpreting Linear Graphs.
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Name . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Section . . . . . . . . . . . . . . . .
Date . . . . . . . . . . . . . . . .
Lab Partners . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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L A B O R A T O R Y 1
Measurement of Length
LABORATORY REPORT
Data and Calculations Table 1 (nearest 0.0001 m, which is 0.1 mm)
Trial
X1 (m)
X2 (m)
Li L (m)
Li = X2 – X1 (m)
n
X
ðLi LÞ2 (m2 )
ðLi LÞ2 ¼
COPYRIGHT ª 2008 Thomson Brooks/Cole
1
L¼
sLn1 ¼
L sLn1 ¼
L þ sLn1 ¼
aL ¼
19
20
Physics Laboratory Manual n Loyd
Data and Calculations Table 2 (nearest 0.0001 m, which is 0.1 mm)
Trial
Y1 (m)
Y2 (m)
Wi W (m)
Wi = Y2 – Y1 (m)
n
X
ðWi WÞ2 (m2 )
ðWi WÞ2 ¼
1
W¼
sW
n1 ¼
W sW
n1 ¼
A¼LW ¼
SAMPLE CALCULATIONS
1. L1 ¼ X21 X11 ¼
2. W1 ¼ Y12 Y11 ¼
10
1 X
Li ¼
3. L ¼
10 1
10
1 X
4. W ¼
Wi ¼
10 1
5. L1 L ¼
6. ðL1 LÞ2 ¼
7. W1 W ¼
8. ðW1 WÞ2 ¼
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
n
1 X
ðLi LÞ2
9. sLn1 ¼
n1 1
10. L sLn1 ¼
11. L þ sLn1 ¼
W þ sW
n1 ¼
sA ¼
aW ¼
Laboratory 1 n Measurement of Length
12.
sW
n1
21
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
n
1 X
¼
ðWi WÞ2
n1 1
13. W sW
n1 ¼
14. W þ sW
n1 ¼
15. A ¼ L W ¼
16. sA =
QUESTIONS
1. According to statistical theory, 68% of your measurements of the length of the table should fall in
the range from L sLn1 to L þ sLn1 . About 7 of your 10 measurements should fall in this range. What
is the range of these values for your data? From __________m to __________m. How many of your 10
measurements of the length of the table fall in this range? __________? State clearly the extent to which
your data for the length agree with the theory. What is your evidence for your statement?
W
2. Answer the same question for the width. Range of W sW
n1 to W þ sn1 is from __________m to
__________m. The number of measurements that fall in that range is __________. Do your data for the
width of the table agree with the theory reasonably well? State your evidence for your opinion.
COPYRIGHT ª 2008 Thomson Brooks/Cole
3. According to statistical theory, if any measurement of a given quantity has a deviation greater than
3sn–1 from the mean of that quantity, it is very unlikely that it is statistical variation, but rather is more
likely to be a mistake. Calculate the value of 3sLn1 . Do any of your measurements of length have a
deviation from the mean greater than that value? If so, calculate how many times larger than sLn1 it is.
Do any of your measurements of the length appear to be a mistake, and, if so, which ones?
4. For the width measurements calculate 3sW
n1 . Do any of your measurements of width have a deviation from the mean greater than that value? If so, calculate how many times larger than sW
n1 it is.
Do any of your measurements of width appear to be a mistake, and, if so, which ones?
Name ________________________________________
Date __________________________
Period _________
The Conservation of Momentum
Find the Lab
In your web browser, go to www.gigaphysics.com, then go to Virtual Labs, and then click
Conservation of Momentum.
If someone else used the computer for this lab before you, click New Experiment. This will
ensure that you have your own unique cart data when you do the experiment.
Part I: Measure the Carts
To find the length of the purple cart, use your mouse to drag the cart over the caliper in the
upper left corner of the lab. Convert the length to the SI unit of meters, then record your result
in the table below. Repeat for the green cart.
Find the masses of the carts by dragging each one in turn over the electronic balance in the
upper right corner. The balance reads in grams, so convert each mass to the SI unit of
kilograms, then record your data.
Mass of purple cart
Length of purple cart
Mass of green cart
Length of green cart
These measurements will stay the same as long as you don’t refresh the screen or click the button to
start a new experiment. If you don’t complete the lab if one sitting and have to load the lab page again,
the lengths and masses will change. If this happens, you will need to measure them again and use the
new values for the remainder of the lab.
Part II: Determine the Carts’ Velocities
Select “same direction” from the Carts’ Direction menu and “inelastic” from the Collision
Behavior menu.
Click Start Carts to put the carts in motion. The red numbers you will soon see tell you how
many seconds it took each cart to pass through that photogate. If you lose track of which
photogate is measuring which cart, notice the purple and green arrows labelling each; a half
purple/half green arrow is used when both carts were stuck together as they passed through.
You can also click Start Carts if you want to watch the collision again.
Record your times in the data table at the top of the next page. Also copy the lengths from
part I. Be sure to add the lengths of the two carts when the carts are stuck together.
Calculate each cart’s velocity and enter it in the table as well.
1
Elapsed time
Length
Velocity
Purple cart before collision
Green cart before collision
Carts stuck together after collision
Part III: Calculating Momentum
Use the fact that momentum equals mass times velocity to calculate the momentum of each
cart. Remember to add the masses when the carts are stuck together.
Mass
Velocity (from part II)
Momentum
Purple cart before collision
Green cart before collision
Carts stuck together after collision
Calculate the total momentum of the two carts before and after the collision.
Purple cart’s momentum
Green cart’s momentum
--------------------
----------------------
Total momentum
Before collision
After collision
You should find that the total momentum before and after the collision is identical (at least to
within rounding errors.) If you don’t, you should find out what went wrong and correct it before
you complete the next part.
Part IV: The Elastic Collision
This time, set the Carts’ Direction to opposite and the Collision Behavior to elastic. Repeat the
same steps as in part II and III. (The data table is at the top of the next page.)
When you calculate the velocities and momenta, signs matter.
Make sure that carts that are moving to the left have negative
velocities. If you lose track of which direction the carts were
going for each photogate, you have the arrows to help you, and
you can click Start Carts to watch the collision again.
2
Elapsed time
Length
Velocity (with sign!)
Mass
Velocity
Momentum
Purple cart’s momentum
Green cart’s momentum
Total momentum
Purple cart before collision
Green cart before collision
Purple cart after collision
Purple cart before collision
Purple cart before collision
Green cart before collision
Purple cart after collision
Purple cart before collision
Before collision
After collision
Part V: One More Case
Repeat the experiment once more, this time with any combination of Carts’ Direction and
Collision Behavior you have not used already. Record which settings you use, then complete the
calculations as before.
Carts’ Direction ___________________________
Elapsed time
Collision Behavior _________________________
Length
Velocity (with sign!)
Purple cart before collision
Green cart before collision
Purple cart after collision
Purple cart before collision
3
Mass
Velocity
Momentum
Purple cart’s momentum
Green cart’s momentum
Total momentum
Purple cart before collision
Green cart before collision
Purple cart after collision
Purple cart before collision
Before collision
After collision
Part VI: Conclusions
What did you notice about the total momentum before the collision and the total momentum after
the collision in each of the above cases?
____________________________________________________________________________________________________________
____________________________________________________________________________________________________________
____________________________________________________________________________________________________________
The principle you should have noted in the previous question is called conservation of momentum.
What do you think it means to say something is conserved in the context of physics?
____________________________________________________________________________________________________________
____________________________________________________________________________________________________________
____________________________________________________________________________________________________________
Do you think there is any combination of conditions in this lab under which momentum would not
have been conserved? Explain your answer.
____________________________________________________________________________________________________________
____________________________________________________________________________________________________________
____________________________________________________________________________________________________________
Learning physics? Teaching physics? Check out www.gigaphysics.com.
© 2016, Donovan Harshbarger. All rights reserved. This activity guide may be reproduced for non-profit educational use.
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