Formal Report Lab 3 Peterman
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School
Saginaw Valley State University *
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Course
111L
Subject
Mathematics
Date
Apr 3, 2024
Type
Pages
5
Uploaded by PrivateButterfly4714
1 Formal Lab Report 1 By: Paige Perman Lab Partner: James Radomski PHYS –
111L Winter 2024 Lab Completed: February 13
th
, 2024 Report Submitted: February 20
th
, 2024 I.
Introduction This experiment tests the idea of Galileo that objects fall speed is independent of the objects weight to challenge the idea of Aristotle’s
theory that objects fall speed is proportional to the objects weight. This idea is tested with the use of Pasco Interference Box connected to a computer through the Capstone
software. Using an open circuit clamp to allow a metal ball to free fall towards a touch pad that will then close the circuit and record the fall time in Capstone
. Data will be collected at seven (7) different heights recorded in meters, with five (5) collections occurring at each height and then analyzed to determine the acceleration of the object; also known as gravity. It is expected that gravity will be 9.8 meters per second squared. II.
Theory Galileo ran a set of tests of rolling balls down an inclined board. Using a water-clock he concluded that the distance a ball rolls down an incline is proportional to the square of the time it rolls. Where d= distance, a= acceleration, and t=time in seconds 𝑑 =
1
2
?𝑡
2
Galileo
’
s equation can be rewritten to find 𝑡
2
by rearrangement, because we are looking at the rate of gravity, we will be relabeling our acceleration constant of “
a
”
to “
g
”
. 𝑡
2
=
2
𝑔
𝑑 + 0
This equation above can be compared to the standard slope-intercept equation. ? = 𝑚? + ?
Where 𝑡
2
=y, 2/g= m or slope, d=x, and 0=b or y intercept. We then construct a plot of t 2 (on the y-axis) vs. d (on the x-axis) for our data. Putting all the data on the same plot as they represent the same experiment to make comparison of results simpler. Set a trend line for each data set and displaying the equation in the legend; ensuring there are also axis titles, and appropriate error bars for each data set.
2 III.
Apparatus and Methods Figure 1: A labeled diagram of the apparatus used in the experiment, throughout the experiment the open circuit vertical drop clamp was adjusted to various heights to collect data. We log into the desk top computer and locate the file labeled “
108_measurement_of_g_pt.cap
”
and allow Pasco Capstone to open the file, once the program launches, we conduct some test drops from a height of 2 meters to ensure the ball was making proper contact to open and close the circuit, as well as ensuring that capstone was properly updating the display. Conduct five data collections from the 2 meter height, when ready to move the vertical clamp, rotate the screws away from you and with both hands gently slide the clamp down to the new height on 1.8 meters and retighten the screws so that way the clamp will not slide. Repeat this process moving down 0.2 meters until we achieve a height of 1.0 meters. IV.
Analysis Methods Dropping from heights of 2, 1.8, 1.6, 1.4, 1.2, 1.1, and 1.0 meters, each trial height obtained a mean fall time in seconds by adding all five data points and dividing the sum by five, this is done for all seven heights listed above. This data is displayed in Table 1. From the mean we find the standard deviation, listed as “
stdev
”
in Table 1, we also calculated 1
2
𝑡
2
and appropriate error bars, the horizontal error bars were estimated at 0.005 meters, or 5 millimeters.
3 Table 1: A table that displays the drop height in meters, as well as the obtained mean fall time in seconds, standard deviation, calculated 1
2
𝑡
2
and appropriate error bars, and the horizontal error bars for the data to be graphed. From the table above we were able to graph our seven trails against each other on a scatter plot with a trend line and the trend lines equation. Ensuring to include a legend, as well as appropriate titles and labels where necessary. Figure 2: A graph with 1/2t^2 plotted against the drop distance in meters, each point indicates the mean data for all five collections at that specific height. Each data point had its own error bar calculated, this is why it is harder to see the error bars in certain points compared to others. The trend line equation is located in the legend. y = 0.1126x - 0.0089
0.09
0.11
0.13
0.15
0.17
0.19
0.21
0.23
0.80
1.00
1.20
1.40
1.60
1.80
2.00
2.20
1/2 t^2
Drop Distance in Meters
1/2t^2 vs Drop Height in Meters
1/2t^2
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4 V.
Discussion Graphing and analyzing provides a gravity value of 8.88 meters per second squared with a ±0.027 error, the expected value of gravity is 9.8 meters per second squared. A possible explanation for the different between the obtained value and the expected value of gravity is the speed of which we release the vertical clamp, when the clamp is slowly released the ball falls at a speed of 0.57 seconds versus when the clamp is released quickly the ball falls at a speed of 0.52 seconds; both were tested at a height of 1.10 meters. This is a noticeable difference and when done consistently would result in a significantly lower gravity value than the expected gravity value. Another systematic error could be not accounting for the height of the pressure plate compared to the drop height, which would very slightly adjust the calculations. VI.
Conclusion The measured gravity value is 8.88 meters per second squared, and this value agrees with the expected value of gravity of 9.8 meters per second squared within a value of 91%. VII.
Raw Data Raw data as shown in excel is located on the following page (page 5).
5