Ball Drop Lab
S. Lee, J. Huang, K. Yu, K. Lee, S. Zeng
The purpose of this lab was to determine the gravitational constant by means of testing.
This was done with the following materials:
●​ A device running Windows OS (a very new Thinkpad)
●​ Universal Lab Interface software
●​ Logger Pro 3.8.7
●​ Vernier Motion Detector
●​ Racquet ball
●​ Ping pong ball (for extension)
In the experiment, testing will happen involving gravity and objects, and the relationship
between the position, velocity, and acceleration of said objects. It is expected that the outcome of
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the gravitational constant will be close to the accepted value of 9.80 𝑚/𝑠 .
For the experiment, the following instructions were followed. First, one student stood on
a chair and held the Vernier Motion Detector as high as possible, with the screen facing down,
level to the floor. It was made sure that nothing was in the way that could be sensed by the
detector. The second student held the lacrosse ball 0.5 meters under the detector, making sure
their body was not in the way. A third student started recording, and student number 2 waited a
second for the machine to start beeping, before dropping the ball. Student 2 made sure to remove
their hand immediately. The ball was allowed to bounce until the graphing was finished. The
computer produced distance, velocity, and accelerating vs time on 3 separate graphs. For the
extension, a ping pong ball was used, with the same methods as stated above.
1.​ Graph Analysis :
At the start, the graphs show when the ball was still in the hands. As shown on the velocity and
acceleration graphs, there is a big, sharp spike right at the beginning. This jump shows the quick
push from the hand before the ball was let go. This part makes the acceleration graph jump up
and down away from normal gravity. This could be due to fingers slipping right before release.
Once the ball was let go, it fell freely and bounced a few times. While the ball was moving up,
the position graph shows a smooth curve. At the same time, the velocity graph shows a straight
line moving up toward zero. During this upward move, the acceleration graph stays flat. This
shows that gravity pulled on the ball in a steady way.
When the ball reached the top and fell down, the graphs kept showing these same patterns. The
position graph kept curving smoothly back down. At the same time, the velocity graph crossed
the zero line and kept moving down. As shown on the acceleration graph, the numbers stayed flat
at around 9.80 during the whole drop.
Although done well overall, the tiny bumps in the lines show small changes during the fall. This
could be due to the ball moving a little bit out of line with the sensor.
2. The coefficient of the x^2 term for d vs t was 4.819 with a calculated error of ±0.0236. The
value of g is 9.80, so ½ g is 4.90. Calculating the percent error of the approximation with the
equation:
gives 1.65% error.
3. The coefficient of the x term for a vs t was 9.663. Using the same percent error calculation
from above, the percent error was 1.43%.
4. The mean constant value of the acceleration was 9.672, and using the percent error calculation
gives a percent error of 1.31%.
The percent error for acceleration for the following graphs vs. time are as follows:
Position % error: 1.65%
Velocity % error: 1.43%
Acceleration % error: 1.31%
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Following the directions of this lab meticulously, the different percent errors obtained for
position, velocity, and acceleration were 1.65%, 1.43%, and 1.31%, respectively. These were
calculated using the difference between the values obtained and the accepted value, divided by
the accepted value. This resulted in using the values 0.162, 0.137, and 0.128, all divided by 9.80
respectively. Although not very erroneous, there were several possible sources of error. From the
person shaking while holding the Motion Detector to the ball not dropping straight, there are
several possible ways that this would have affected the data. As shown on the velocity and
acceleration graphs, there are a few bumpy areas on each. This could be due to the Motion
Detector picking up another side of the ball if the ball was not perfectly aligned and dropped in a
straight line, which would cause the graphs to waver slightly. Although done precisely overall,
the errors that occurred while testing caused the fallible values for the changes in position,
velocity, and acceleration.
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Our results conclude that the gravitational constant is 9.638 𝑚/𝑠 when measured with
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the position vs. time graph, 9.663 𝑚/𝑠 when measured with velocity vs. time, and 9.672 𝑚/𝑠
when measured with acceleration vs. time. Compared to the value of 9.80, this results in a
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percentage error of 1.65%, 1.43%, and 1.31% respectively, signifying that our measurements
were accurate and close to the true value. When adding the calculated error, as seen in the graph,
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to the measured value of 9.672, the result is approximately 9.71 𝑚/𝑠 , which is still not enough
to reach the true value of 9.80.
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METHODS
RESULTS
ANALYSIS 2, 3, 4
ANALYSIS 5