SAMPLE LAB REPORT FOR MEASUREMENTS AND UNCERTAINTIES LAB
The following is a sample of what is expected in a lab report. This report would
get a high "A" (95% +).
There is no fixed form for reports--this is only an example. You need not imitate
this particular lab report. All that is required of your reports is that, like this
sample report, they be logically organized and exceedingly thorough.
Write your report as though the person reading it knows nothing about what you
have done in the lab, but does know something about physics in general. Try
reading your report aloud or have a classmate read it over. If something in it
doesn't seem clear, clarify it. Samples of calculations, notes explaining changes
in procedure or unusual results, neat uncrowded tables of data--all these things
contribute to a good lab report.
A GOOD LAB REPORT IS EASY TO READ, EASY TO FOLLOW, AND
DOESN'T LEAVE ANYTHING OUT.
The sample report starts on the next page.
A. G. Eckne--Principle Author
A.G. Eckne
H. A. Lorentz--Abstract, theory, & conclusion
M. Planc--Calculations
_ÉÜxÇàé
Max Planc
B. J. Ledbetter--Procedure, data verification,
assisted with calculations
PHYSICS 200 LAB--Lab #1
For Prof. Graney
August 13, 2004
B.J. Ledbetter
NOTE – You do not
have to divide up
duties the same way
these people did.
MEASUREMENT LABORATORY
ABSTRACT:
In this laboratory we measure simple physical quantities (for example,
distance and mass) and use the results of those measurements to
calculate other physical quantities (such as density and volume). We
also take note of the precision of our measurements via recording
experimental uncertainties and find that the uncertainties in our
measurements carry through or propagate into any quantity calculated
using those measurements.
THEORY:
Physics is a science based on observation--if a physical concept or
theory is to be considered a valid one it must agree with what is
observed to actually occur in the real world. For instance, any theory
that states that water flows up hill, no matter how brilliantly thought
out and argued, is invalid in physics, for observations show us that
water indeed flows down hill.
Physics is a science based on observation, so quantitative
observations, or measurements, are central to physics. Without knowing
how to make good measurements we cannot observe the universe in a
manner that tells us anything; we cannot test physical theories.
Physics says that the process of measurement is pretty much the same
for all common physical quantities. The measurement process is used in
many non-physics fields, from medicine to manufacturing, where
experimentation and observation are important.
As important as a measurement itself is a knowledge of the uncertainty
associated with the measurement (in trying to argue a speeding ticket
in court the ability to prove you were traveling at 64.0 mph +/- 0.5
mph would carry much more weight than the ability to prove you were
traveling at 64.0 mph +/- 10 mph). In our lab work it is important to
keep track of the uncertainties in our measurements and how those
uncertainties propagate though to other values calculated using our
measurement values. We think of this as "quality control" for our
data!
EQUIPMENT USED:
-meter stick
-metric dial caliper (Acme Scientific model #40891)
-micrometer (Sargent-Welch model #90918)
-graduated cylinder (Corning model #HHa456)
-samples of Lead, Tin, Zinc, Iron, and Uranium
-light string
PROCEDURE:
NOTE: Uncertainties were included in all measurements and propagated
through all calculations.
1) Measured length and width of table top in centimeters and in
meters. Calculated the area of the table top using these data.
2) Used caliper to measure height and diameter of cylindrical metal
samples. Samples not perfect cylinders, so this caused a larger
measurement uncertainty than would be expected using a precision device
like a caliper. Calculated volume of samples using these measurements.
3) Use micrometer to make the same measurements as in part 2 but only
on the smallest metal sample. Again, samples not perfect cylinders.
Volume calculated for smallest sample using micrometer measurements.
4) Used graduated cylinder and water to calculate volume of metal
samples by measuring water volume displaced by samples.
5)
Used balance to calculate mass of metal samples.
6)
Determined density of each sample using data from parts 4 and 5.
DATA/DATA ANALYSIS/ERROR ANALYSIS:
PART 1:
Data--Table Top Measurements
Length
Width
Area
-----------------------------------------------------------1.62 +/- .04 m
0.54 +/- .02 m
0.875 +/- .054 m2
162 +/- 4 cm
54 +/- 2 m
8750 +/- 54 cm2
Sample data and error analysis calulations:
A = lw = 1.62 (.54) = 0.875
Area = 0.875 m2
Estimating uncertainty in area-Maximum possible area is (1.62 + .04 m) x (0.54 + .02 m)
1.66 m
x
0.56 m
0.930 m2
Minimum possible area is (1.62 - .04 m) x (0.54 - .02 m)
1.58 m
x
0.52 m
0.822 m2
So Area = 0.875 m2 but could range as high as 0.9296 m2
or as low as 0.8216 m2.
Therefore the uncertainty in the area is about 0.54 m2 because
0.875 + 0.054 = .930 (approx.)
0.875 - 0.054 = .822 (approx.)
Final Answer:
Area = 0.875 +/- 0.054 m2
Error analysis discussion:
Sources of error in part (1) consist primarily of our limitations in
reading the meter stick to the best precision. The edge of the table
was curved, so we had to "eyeball" its length with the meter stick.
Had the edge of the table not been curved, we could have measured it to
better than 1 mm accuracy.
PART 2:
Data--Metal Samples
Sample
Height (mm)
Diameter (mm)
Volume (mm3)
-----------------------------------------------------------------Aluminum
101.0 +/- .1
10.0 +/- .1
7933 +/- 166
Tin
50.0 +/- .1
9.9 +/- .1
3849 +/- 85
Copper
37.0 +/- .1
9.9 +/- .1
2848 +/- 65
*Lead
25.0 +/- .1
10.0 +/- .3
1963 +/- 126
Sample data and error analysis calculations:
π
V = - d2 h
4
π = 3.1415927 (approx.)
= (π/4) (10.0)2 101.0 = 7933
Volume = 7933 mm3
Estimating uncertainty in volume-Largest possible volume = (π/4) (10.1)2 101.1 = 8100 mm3
Smallest possible volume = (π/4) (9.9)2 100.9 = 7767 mm3
So volume is 7933 mm3 but could range as high as 8100 mm3
or as low as 7767 mm3.
Therefore volume has uncertainty of 167 mm3 because
7933 + 167 = 8100 (approx.)
7933 - 167 = 7767 (approx.)
Final Answer:
Volume = 7933 +/- 167 mm3.
Error analysis discussion:
Precision in part (2) is limited by our ability to read the caliper.
*However, the lead sample was so misshapen as to not really be
cylindrical. It was difficult to determine the cylinder's diameter,
hence the higher error in its diameter. Note that this error carries
through into a relatively high error in the volume.
PART 3:
Data--Metal Samples
Sample
Height (mm)
Diameter (mm)
Volume (mm3)
-----------------------------------------------------------------Lead
25.02 +/- .01
10.0 +/- .25
1965 +/- 99
Calculations same as for part (2).
Error analysis discussion:
The micrometer allowed a much more precise measurement of the lead
sample's height, but because the lead sample was such a mess it was no
easier to get a better measurement of the sample's diameter.
PART 4:
Data--Metal Samples
NOTE: We recorded the water level in the graduated cylinder both
before and after we lowered the metal sample into it. The difference
is the volume of the sample.
Final
Initial
Water level
Water Level
Volume
(all measurements in cm3)
---------------------------------------------------------------Aluminum
60.0 +/- .5
52.5 +/- .5
7.5 +/- 1
Tin
53.5 +/- .5
50.0 +/- .5
3.5 +/- 1
Copper
53.0 +/- .5
50.0 +/- .5
3.0 +/- 1
Lead
32.0 +/- .5
30.0 +/- .5
2.0 +/- 1
Sample
Sample data and error analysis calculations:
V = final - initial
V = 60.0 - 52.5 = 7.5
Volume = 7.5 cm3
We used a shortcut formula this time:
∆V = ∆(final) + ∆(initial) = .5 + .5 = 1.0
Uncertainty in volume = 1.0 cm3
Error analysis discussion:
It was easy to get volume measurements with the graduated cylinder and
even easier to propagate uncertainties. However, it was difficult to
precisely read the scale because of the curved surface of the water.
Furthermore, water droplets kept falling off the sides of the cylinder
(and raising the water level in the cylinder). The deformed lead
sample was not a problem using this method, though.
PART 5:
Sample
mass (g)
---------------------------Aluminum
100.00 +/- .05
Tin
110.00 +/- .05
Copper
105.00 +/- .05
Lead
150.00 +/- .05
No calculations needed for this part.
Error analysis discussion:
It was possible to get quite precise mass measurements using the
triple-beam-balance. The only real source of uncertainty was in trying
to determine just how closely we could read the scale.
PART 6:
NOTE--Data from parts (4) and (5) were used to calculate the following
values:
Sample
density (g/cm3)
--------------------------Aluminum
13.3 +/- 1.8
Tin
31.4 +/- 9.0
Copper
35.0 +/- 11.7
Lead
75.0 +/- 37.5
Sample data and error analysis calculations:
m
D = V
100
D = ----- = 13.3
7.5
Density = 13.3 g/cm3
We used a shortcut formula again:
∆D
∆m
∆V
-- =
D
-- + -m
V
∆D = D
∆m
∆V
-- + -m
V
∆D = 13.3
.05
1
--- + --100
7.5
= 1.8
Uncertainty in density = 1.8 g/cm3.
Error analysis discussion:
There were no measurement uncertainties in this part (no new
measurements were made). However, uncertainties in the values of mass
and especially volume propagated into our values for density. Thus the
density values have very large uncertainties. It would be better to use
the volumes obtained with the calipers in part 3 in our calculations;
that way we could get more precise density values.
CONCLUSION:
Quantitative observations or measurements are central to physics. The
ability to make and interpret measurements is essential not only in
physics but in any other science or field where experimental work is
important. In this laboratory we measured simple physical quantities
and used the results of those measurements to calculate other physical
quantities. We also kept track of the precision of our measurements
via recording experimental uncertainties and found that the
uncertainties in our measurements propagate into any quantity
calculated using those measurements, sometimes giving very large
uncertainties in the calculated quantities.