This is an example lab report. It is meant to illustrate the format of lab reports as
well as to clarify what this format accomplishes. It is not necessary for you to imitate the
style of this paper, so long as you accomplish the objectives outlined in each section.
In the experiment portrayed here, a spring is hung vertically and various masses are
attached. The displacement is measured and used to determine the force law.
My name
Lab partner name
PHYS 0040
Lab 0
Objective
This portion of the report should include a brief explanation of why you are doing
the experiment and/or what you expected to report. This allows an outside reader (who is
unfamiliar with the experiment) to determine what they are reading and why they may or
may not be interested in continuing to read it. It also makes the rest of the paper easier to
follow since they already know the direction it is taking.
This experiment is intended to determine the force constant of a spring and confirm
Hooke’s law F = kx by measuring the displacement of the spring with various masses
hanging from it.
Procedure
Here you provide a detailed account of the procedure you followed including unforeseen
modifications you needed to make. This is an account of the past. It is meant to allow
the reader to repeat what you did, but it is not a set of directions. Generally speaking this
section should include a detailed description of your apparatus, but because we are all using
the same lab manual it is sufficient that you mention it briefly.
Five metal cylinders were were weighed one at a time on a triple beam balance to
determine their masses. The length of the spring being used was measured against a meter
stick with the spring lying on the table and then again with the spring hanging from
the mount. The cylinder masses were then attached one at a time and the length of the
spring was recorded for each one. The mount needed to be repositioned when measuring
the displacement with the fourth and fifth cylinders because the length of the spring and
cylinders combined were sufficient to reach the table beneath the mount.
Data
The data provided should include all of the measurements used in the calculations.
Everything necessary for a repetition of your calculations by the reader should be provided
with units and uncertainties. A number without both units and an uncertainty is useless
because it does not specify the result (Fahrenheit, Celsius, Kelvin, or a personal system
of units can make the number 10 mean anything from sub-liquid nitrogen temperatures to
those at the center of the Sun) and its level of precision. (Does 10 degrees Celsius mean
10 and not 15, or 10 and not 10.0001 ?).
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The data we obtained are presented in Table 1.
Table 1. Measurements of Spring Extension.
Cylinder
1
2
3
4
Cylinder Mass (±1) g
37
55
63
84
Spring Length (±0.1) cm
6.4
7.2
7.6
8.6
5
101
9.4
Spring length on the table: 4.7 ± 0.1 cm
Spring length on the mount: L0 = 5.5 ± 0.1 cm
Calculations
In this section there should be a derivation of the pertinent quantities from first principles. This means that the basic physics equation and the equations derived from it should
appear in their general forms with an explanation of how you arrive at each step (unless it
is basic algebra or otherwise readily apparent). A sample calculation is also good to include.
These things provide the transparency necessary for a reader to follow your logic and make
it possible for them to identify individual errors in an otherwise correct calculation. This
example isn’t typical in that the only derivation takes place in the next section, but take
note of how each calculation is specified exactly so that there is sufficient information to
repeat it.
The masses were plotted versus the lengths as shown in Figure 1, and a linear least
squares fit was applied. The resulting line equation was f (x) = 21.22x − 98.35. The slope
error was calculated using the formula
σs2
=N
N
P
σy2
P
,
x2 ( x)2
with σy = 1 g, N = 5 and x being the length measurements. The slope error was
σs2 = 0.1801, so the slope is 21.2 ± 0.4 g/cm.
Results
This section should give your final answers regarding the questions posed in the objective section. In many cases this is as simple as writing the sentence “The experimentally
determined value of x is y ± z (units).” for each result. This example is probably a bit
more complicated to wrap up than most of what you will see in this course, but note that
both objectives (determining the spring constant and confirming Hooke’s law) are addressed
quantitatively.
Hooke’s law states F = mg = Kx, or m = (K/g)x. This predicts a a linear relationship between mass and displacement with a slope of (K/g), where K is the spring constant
and g is the gravitational acceleration. The data matches a line with slope 21.2 ± 0.4 g/cm
with a Chi-squared value of
P
(yi − y(xi ))2
2
= 0.76,
χ =
σ2
where yi is the ith mass, y(xi ) is the mass calculated using the line equation with ith
measurement of spring length, and σ is the uncertainty in the mass measurements. This
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result confirms Hooke’s law, and using g = 9.8 m/s2 gives us a spring constant K =
9.8(slope) = 207 ± 4 g/s2 , or using 10 g/s2 = N/cm, K = 20.7 ± 0.4 N/cm.
Figure 1. Mass versus spring length. Best fit
line mass = 21.22length − 98.35 is also shown.
Discussion
This section should address the significance of the results using a quantitative analysis
of the agreement between your result and the theory or accepted values. A good way to do
this is by reporting c, the difference in values as a multiple of σ, the uncertainty. For an
experimentally determined value X ± σ, c is given by the relationship |T − X| = cσ with T
being the accepted value or theoretical result. The point is to be able to give the certainty
of your results agreement or disagreement with T. This can also be done using the relative
uncertainty on the right hand side if you divide the left hand side by T . Then c is the ratio
of the percentage difference to the relative uncertainty. Additionally, you should speculate
on why your result is accurate/inaccurate and precise/imprecise and what could be done to
improve it.
The χ2 value 0.76 is somewhat lower than expected. For this many degrees of freedom,
the value should be ∼ 3. Nevertheless the agreement is very good, indicating a good match
of the data to Hooke’s law. The reason the above number is too low is likely because the
data was invented, and the experiment never actually took place. A good way to improve
upon this would be to actually do the experiment. Agreement between a theoretically
predicted mass (based on Hooke’s law with K/g = 21.2 g/cm) and an experimentally
determined mass is provided here for a more typical example of a discussion, though for
this report it is not actually necessary. The data used is for cylinder 2.
The experimental value of the mass is 55±1 g, which differs by 1 g from the theoretical
value of 54 g, a difference of 1σ. This is quite a good agreement and indicates that the
data supports the theory.
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