Sample Lab Report
Academy Physics
Using Kinematic Measurements to Determine the
Acceleration of Gravity
Date Data Taken: 9/13/12
Date Report Submitted: 9/20/12
Lab Report By
Alfred Adams
Members of Lab Group
Bob Brown
Cindy Clark
Darlene Davis
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1. Design Experiment
1.a Purpose In this lab we used kinematic measurements to measure the acceleration of
gravity at our location on earth. We then compared that result to the established value to
determine the degree to which our experimental results agree with the prediction.
Reference value for acceleration of gravity
We were provided with a reference value for the local acceleration of gravity in New
York City to be 9.802 m/s2.
In this experiment we will be dropping objects and measuring the time that it takes to
move a given distance. Assuming that the gravitational attraction is constant and that we
can neglect the air resistance, we can use the relationship:
x  x0  v0t  12 at 2 (1)
Assuming that the object starts at rest, and letting downward be the positive direction, we
can rewrite this expression as
y  12 gt 2 (2) .
In this lab we will measure y and t and use that data to determine a value for g.
1.b Equipment The equipment consists of a Pasco electromagnetically controlled release
mechanism and a sensitive impact device. The impact device is hooked up to a Pasco
timing gate that produces a value for the time difference between the moment of release
and the time of impact. A diagram of the apparatus is shown below.
We also used a vernier caliper to determine the height of the bottom of the ball above the
impact sensor.
1.c Experimental setup
Release
mechanism
y
Timing gate
Impact sensor
A photo of this equipment is shown at right.
1.d Experimental procedure
a) Height measurements were the most critical part of the lab. We use a vernier caliper
that allowed us to measure the height with a precision of 0.1mm. We checked the
repeatability of the height by having two group members make blind measurements (we
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Academy Physics
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did not share the results until all of use had made the measurements) of the height and
then comparing the results. We both members of our group got consistent results (within
±0.1mm) we felt that we had developed a reproducible technique.
b)Time measurements were made by using the timing gate discussed above. We found
that if we did not bump our setup we could repeat our measurements with a precision of
±0.0001 seconds.
c) The general procedure was that we approximately selected a height for the holding
fixture, measured the height, and then released the ball.
2.0 Observe and measure real phenomena
2.a Pros and Cons of Approach
The setup worked fairly well. We would have liked to be able to vary the distance more,
but we were constrained by the setup to stay within a total distance of 1.0m in height.
Also, we found that we could not make reproducible measurements for distances less
than 0.1m.
2.b Care required in measurements
Each time we repositioned the height we needed to be sure that the setup was secure
(tight) and that the ball was falling to the center of the impact sensor. We made three
measurements to confirm that our times were reproducible and, if there were no
significant outliers, we took the average of the three measurements.
2.c Additional relevant observations
We needed to consider whether there were effects due to air resistance. The ball was a
steel ball and seemed to fall quite well. The results that we got were consistent with a
constant acceleration, so we were able to ignore air resistance effects.
We made our measurements by increasing the height each time. When we finished a set
of five measurements, we repeated the first measurements and observed that our data was
consistent with the earlier results.
3. Analyze Data
3.a Data Table
The measured values and computed values
for time squared are shown in the table at
right.
units
error +/-
time
s
0.002
0.146
0.193
0.284
0.302
0.365
0.454
t^2
s^2
0.021
0.037
0.081
0.091
0.133
0.206
height (m)
m
0.0001
0.1011
0.2034
0.3876
0.4456
0.6771
0.9765
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3.b Results of linearized fits
Based on equation (2) above, if we plot y as a function of the square of time, the slope
should equal g/2.
Results of drop ball experiment
y = 4.8375x + 0.0053
R2 = 0.9999
1.2
height (m)
1
0.8
0.6
0.4
0.2
0
0
0.05
0.1
0.15
0.2
0.25
time^2 (s)^2
3.c Calculations
Based on the slope, our measured value for that acceleration of gravity can be computed
by taking twice the fitted slope. The result is 9.67m/s2.
3.d Extrapolations and interpolations of data
None needed for this lab.
4.Analyze errors
4.a Sources of error
The primary sources of error were the ability to accurately measure the height and the
ability to accurately measure the time.
4.b Percent error relative to established value.
Comparing our measured value of 9.67m/s2 against the accepted value of 9.802 m/s2 we
have an error given by
% error 
meas  ref
=1.4%
ref
4.c Significant figures
Since time was measured with ±0.002 s, we used up to the milli second point for our
significant figures. Since height was measured ±0.0001 m, we used up to the fourth digit
to the right of the decimal point for our measurements.
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4.d Ways to reduce error
To improve our time measurements, we would get the most improvement by improving
the variability of the drop mechanism. This would require improved electronics.
Another way to get improved results would be to increase the time of the fall by
increasing the height. The error in time measurements did not increase as the height
increased, so increasing the height would reduce the percent error in the time, and thus
reduce the impact of time errors on the overall result.
5. Communicate results
5.a Inferences and conclusions
The purpose of the experiment was to attempt to validate the kinematic equations for
constant acceleration by analyzing times for various drops. Our results showed very
good overall agreement (~1%) between measured and predicted results.
5.b Improvement to experimental procedure
An alternative method to achieve the same result would be to make video observations of
the ball dropping. This would eliminate the issue of controlling the release times because
you could observe the actual time of release as the ball dropped. This would essentially
allow many measurements to be made for a single drop, eliminating a number of
systematic errors from the measurement.
5.c Questions for further study
We could go further with this experiment by determining at what masses and ball
diameters the air resistance begins to become significant. By repeating the same
measurements for a number of different masses and diameters, we should be able to
determine when the observed values significantly vary from the accepted value for g.