Thermal Expansion Lab ProjectThe data listed in Table 1 be

Thermal Expansion Lab Project
The data listed in Table 1 below shows the results of a set of
experiments performed on
a very remarkable material1. A one-meter length bar of this
material is heated to different
temperatures and the resultant length at that temperature was
measured. Your project is to
analyze and discuss this material, and present your findings in a
journal-quality writeup.
First, you should identify the material. Determine the
coefficient of linear expansion
(graphs are always nice!), and use that to figure out what the
material is - pay extra close
attention to the graph! Once you know what the material is,
research it a bit - why is it
so remarkable? How might the coefficient of expansion have
been measured, in the actual
experiment? Hopefully, you’ll notice something interesting
about the coefficient of expansion
- what is the explanation people have for this effect?
The point of this project isn’t to determine the coefficient
(that’s too easy!) - but rather
to get you used to doing a little research on something, and
learning to write it up in a
professional way. You’ll be graded on the effort that you put
into the writeup, and the
quality of the writeup, itself (I assume that you actually get the
correct coefficient and
material!). Some of the things that I am looking for:

• Did you follow the correct format for the formal lab write up?
Are all the group
members listed (alphabetically)? Did you write in complete
sentences, with good
grammar? Did you write things in paragraphs, instead of making
lists, and so on?
In other words, does the write up look professional - would it be
something that you
would proudly submit for publication in a real journal?
• Did you only write things that you can understand, and write
at a level at which any
classmate could understand? It’s tempting to include scary-
looking equations in your
paper because they look impressive - and you can! However, if
you’re including these
scary equations, be sure that you understand them, and can
explain them!
• When including equations and formulae, did you define your
variables? Don’t display
equations without telling the reader what the variables are!
Also, are the important
equations numbered? Do the equations look nice on the page (as
they would look in
a textbook, or when you’re writing them down), or are they
messily just stuck there
(i.e., do you write 1
2
at2, or 1/2 at∧ 2 - see how much better one looks than the
other?)?
• Did you cite your sources, and list them in the references
section? Were you sure to not

simply copy and paste stuff from the internet (that’s plagiarism,
and gets you kicked
out of science!)?
• Did you actually discuss things, instead of just showing a page
of calculations? Imagine
that you’re giving a lecture on this stuff, and type that up! Look
at real papers, and
how much writing there is, compared to the amount of math!
1Actually, these are calculated results based on different
experiments!
1
This list of stuff isn’t just for this write-up, of course - it
applies to all the labs that
we’re performing, as well as to your research paper! The whole
point of all this is to learn to
write technical documents, which is much more important to
your future careers than any
particular lab that we’re going to do!
2
Table 1: Length of Material at Various Temperatures
Temperature in Kelvins Length in meters
90 1
95 0.99998125
100 0.9999625

105 0.99994375
110 0.999925
115 0.99990625
120 0.9998875
125 0.99986875
130 0.99985
135 0.99983125
140 0.9998125
145 0.99979375
150 0.999775
155 0.99975625
160 0.9997375
165 0.99971875
170 0.9997
175 0.99968125
180 0.9996625
185 0.99964375
190 0.999625
195 0.99960625
200 0.9995875
205 0.99956875
210 0.99955
215 0.99953125
220 0.9995125
225 0.99949375
230 0.999475
235 0.99945625
240 0.9994375
245 0.99941875
250 0.9994
255 0.99938125
260 0.9993625
265 0.99934375
270 0.999325
275 0.99930625
280 0.9992875

285 0.99926875
290 0.99925
295 0.99923125
300 0.9992125
3
1
Data Analysis Assignment: Pendulum
You will measure the period of a pendulum and value of
gravity, switching out pieces of the setup
for new data runs (e.g., swap a metal ball). Record your data,
compute means and errors for
each data set, and compare your results to the theory for each
setup you test.
Equipment’s:
1. Pendulum PHET Simulation:
http://phet.colorado.edu/sims/html/pendulum-
lab/latest/pendulum-lab_en.html
2. Meter Stick: within the Simulation
3. Stopwatch: Cell phone
4. Protractor: within the Simulation
5. Mass: within the Simulation
Theory: A simple pendulum consists of a mass m suspended on

a massless string of length L.
The string is connected to a fixed point above the mass. The
only forces on the mass are gravity
and the string tension. The period of this simple pendulum for
small oscillations is
(1)
In real pendula, the string always has a mass, but as long as the
mass of the string is much
smaller than the mass hanging, it will be very close to the
idealistic case of the simple pendulum
model.
Setup: Pendulum for 2 different masses and at two angles (100
and 450 ).
Procedure and Data Collection
1. Record the instruments. Before doing anything else, record
the precision errors of your
measurement instruments:
TOOL PRECISION ERROR
METER STICK
DIGITAL
STOPWATCH
PROTRACTOR
2. Weigh objects: A single measurement for each will do.
OBJECT MASS ± PRECISION ERROR

MASS 1
MASS 2
Precision error here will be the 0.1 kg(from the simulation)
3. Experimental procedure:
a) Let the string come to rest. This is the equilibrium position.
b) Lift the mass to the appropriate angle (10° or 45°) from
equilibrium, then release.
2
c) Start timing with your stopwatch. Keep timing for the
required number of periods,
then stop your stopwatch at the end of the last period.
4. Measure pendulum length. Measure and record the length of
the pendulum from the pivot to
the center of the mass.
Pendulum Length Data and Results
(String, Mass 1)
Trial
#
Pendulum Length,

(units: ______)
1
2
3
4
5
Mean of length =
Standard deviation =
Standard error of length =
(random error)
Result with standard error:
5. Measure and record single and multiple periods. For this part
of only, you’ll first
investigate whether measuring a single pendulum period
multiple times or multiple periods
fewer times produces the best results.
Individual periods (Mass 1, 10° Amplitude)
Trial
#
Single
Period Time

(units: ____)
1
2
3
4
5
Mean of single period time =
Standard error of single period time =
(random error)
Now use the stopwatch to record the time it takes the pendulum
to swing 10 full periods
once. Calculate the time it takes for a single period of
oscillation, dividing the results by 10
(value and error) as appropriate to obtain your measured value
for a single period.
3
10 full periods (Mass 1, 10° Amplitude)

Trial #
Ten Period
Times
(units: _____)
1
10- period time result with error:
Single period time result with standard error:
Comparing the different ways you’ve just measured 10 periods,
answer which one:
• is the most time efficient?
• gives the best sample population statistics?
6. Analysis. For each 10 full swing trial in the table, divide the
results by 10 to obtain your
measured value for a single period. Be careful to calculate the
proper error on these single
periods, remembering that the total number of significant
figures stays the same.
(Remember you increase the precision in your period
measurement when use multiple
periods. You have the same total number of significant figures.
So if the time recorded for
10 swings of a trial is 7.84s, then the period for a single swing

will be 0.784s).
Pendulum Period: Case 1 (Mass 1, 10° Amplitude)
Tri
al
#
10-Period Time
(units: ______)
Single Period Time (T)
(units: ______)
1
2
3
4
5
T=

Compare results to theory. Use the measured pendulum length
and m/s2 to calculate
the theoretically expected pendulum period, then compare to
your experimental results. Ignore
any error in the theoretical expectation at this point.
Theoretical Expectation ( ) =
Experimental Result: Case 1 (with Error)=
Do they agree?
4
Analyze sources of error:
Tri
al
#
10-Period Time
(units: ______)
(units: ______)
1
2
3

4
5
T=
Do they agree?
Measure Length: (Use the ruler in the simulation to measure the
length of the pendulum)

Pendulum Length Data and Results
(Mass 2)
Trial
#
Pendulum Length,
L2
(units: ______)
1
2
3
4
5
Mean of length =
Standard error of length =
(random error)
L2 =
5
Pendulum Period: Case 3 (String, Mass 2, 10° Amplitude)
Tri
al

#
10-Period Time
(units: ______)
(units: ______)
1
2
3
4
5
T=

Do they agree?
Tri
al
#
10-Period Time
(units: ______)
(units: ______)
1
2
3
4
5

T=
6
Do they agree?
7. Analysis: Find g?
Considering the period of a simple pendulum for small
oscillations:
Uncertainty in g is given by:

Where is error in L and is error in T
Compute g with error
Case 1 Case 2 Case 3 Case 4
Mass1
Amplitude:
10°
Mass1
Amplitude:
45°
Mass 2
Amplitude:
10°
Mass 2
Amplitude:
45°
Measured Length (m)
Measured Period (s)
Experimental (m/s2)
Experimental (m/s2)
Result:
(m/s2)

Compare experimental quantity to accepted value:
“Agreement Test” Two values and , which are expected to be
equal, are said to
reasonably “agree” if
Accepted value, m/s2.
7
Do and agree? (Yes/No)
Case 1:
Case 2:
Case 3:
Case 4:
8. Determine what factors the frequency of oscillation depend
on.
The cyclic frequency is found with the formula f = N/t, where f
is the cyclic frequency, N is the
number of oscillations, and t is the time interval. Given a
measured number-of-oscillations-with-
error N ± δN (where δN is the counting error that will be ) and
a fixed time-interval t, using

relative frequency , find the error in the cyclic frequency δf.
1) Fill in the table below (keep the length and amplitude fixed).
Trial 1 2 3 4
Time Interval (s) (t)
2 10 20 30
Number of
Oscillations
(N)
Cyclic Frequency
(Hz)
(f = N/t)
Relative Error
Error in Cyclic
Frequency (δf) (Hz)
From the table what do you think, which time interval gives you
better results and why?

8
Dependence of Frequency on Amplitude
b) Fill in the data table below (keep the length and mass fixed).
Desired
Amplitude
(degrees)
Error
(degrees)
Number of
Oscillations
(N)
Time
Interval
(s) (t)

Cyclic Frequency
(Hz)
(f = N/t)
c) Based on your data, try to describe how frequency depends
on amplitude.
Dependence of Frequency on Mass
a) Fill in the data table below (keep the length and amplitude
fixed).
Mass (m)
(kg)
Error
(δm)(kg)

Number of
Oscillations
(N)
Time
Interval (s)
(t)
Cyclic
Frequency
(Hz)( f =
N/t)
9

b) Based on your data, try to describe how frequency depends
on mass.
Dependence of Frequency on Length
Finally, we investigate how the frequency depends on the length
of the string.
Desired
String
Length
(l)
(m)
Error (δl)
(m)
Number of
Oscillations
(N)
Time
Interval
(s) (t)
Cyclic
Frequency

(Hz)
( f = N/t)
gexp
(g=
4π2lf2)
c) Based on your data, try to describe how frequency depends
on length.
9. Find g using F
Frequency is inverse of Time period therefore frequency can
be written as:

Find:
a) The average value of g from table above:
b) Standard deviation in average g:
c) Standard error in average g:
10
Result g ± Standard error in g:
Compare experimental quantity to accepted value ( m/s2):
Use agreement test ( )
Procedure and Data Collection

Thermal Expansion Lab ProjectThe data listed in Table 1 be

Recommended

Recommended

More Related Content

Similar to Thermal Expansion Lab ProjectThe data listed in Table 1 be

Similar to Thermal Expansion Lab ProjectThe data listed in Table 1 be (20)

More from GrazynaBroyles24

More from GrazynaBroyles24 (20)

Recently uploaded

Recently uploaded (20)

Thermal Expansion Lab ProjectThe data listed in Table 1 be