LAB #6- PHY 111
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School
College of Business & IT Batkhela, Malakand Agency *
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Course
111
Subject
Aerospace Engineering
Date
Nov 24, 2024
Type
Pages
4
Uploaded by AgentFangOryx3
Understanding the Centripetal force on a Object in Rotation
Purpose:
The purpose of this investigation is to analyze the relationship between the centripetal
force acting on the object in rotational motion and the speed of the object in rotational motion.
Material:
The material used in this investigation uses a straw or thin tube, string, two paper clips,
washers, ruler, a stopwatch or phone with stopwatch features, and an optional lab assistant.
Procedure:
1.
Take a string and cut it to a length of 1.0 meter. Then, take the string and run it through a
straw. Afterwards, tie two washers to the top end of the string and a paperclip on that
paperclip add five washers at the bottom of the string.
2.
After this setup, add the second paperclip below the straw to secure the straw to not slide
up or down. However, ensure that the paperclip does not come into contact with the
straw. Alternatively, a knot can be placed in place of the paperclip to secure the straw.
3.
Measure and record the length of the string between the washer and the straw. This
measurement will be considered as the radius of the rotation. This should be constant for
all trials conducted.
4.
Holding the straw, begin to rotate the washers over one’s head in horizontal circles
parallel to the ground.
5.
In addition, while in rotation, ensure the paperclip attached remains at a constant distance
throughout from the straw. This is done to ensure that the speed of the washers remains at
constant speed, this can take several practice and tries.
6.
Measure and record the time it takes for the two washers to perform ten revolutions.
Repeat the trial run and take the average of this result.
7.
Secondly, add an additional five more washers to the bottom of the string to the
paperclip.
8.
Then, again, measure and record the time it takes for the two washers to perform ten
revolutions. Repeat the trial run and take the average of this result.
9.
Continue this process for a total of five or more trials. For each trial, add two more
washers. Each trial should have atleast a repetition.
10. From the collected data, calculate the rotational speed and the centripetal force. In
addition graph the centripetal force vs speed.
Data:
-
Radius = 13 cm or 0.13 m
-
Washer mass of 1 = 5.73g or 0.00573 kg
# of Washers
Trial #1 (s)
One Rotation (s)
Trial #2 (s)
One Rotation (s)
Average (s)
5 washers
7.28
0.728
7. 13
0.713
7.21
10 washers
4.94
0.494
4.92
0.492
4.93
12 washers
4.8
0.48
4.88
0.488
4.84
14 washers
4.34
0.434
4.31
0.431
4.33
16 washers
4.17
0.417
4.14
0.414
4.16
# of Washers
Average (s)
Rotational Speed (m/s)
Centripetal Force (N)
5 washers
7.21
0.113
0.28
10 washers
4.93
0.166
0.562
12 washers
4.84
0.169
0.674
14 washers
4.33
0.189
0.786
16 washers
4.16
0.196
0.898
Calculations:
The following calculations are examples of the calculations did for all trials
-
One Rotation for Trial #1 - 5 washers:
One Rotation
= (rotation time (sec)) /(number of rotations)
= (7.28 sec) / (10 rotations)
= 0.728 secs
-
Average for Trial #1 and #2 - 5 washers:
Average=
(Trial #1 +Trial #2) / 2
=
(7.28 +7.13)/ 2
= 14.41s/ 2
= 7.21 s
-
Rotational Speed for 5 washers using the Average
v= (2πr)/ T
avg
v= (2)(3.14)(0.13 m)/ 7.21 s
v= 0.113 m/s
-
Centripetal Force for 5 washers using the Average
Washer mass = (0.00573kg) (5 washers)
Mass = 0.02865 kg for 5 washers
ΣF= W= mg
ΣF= (0.02865 kg) (9.8 N/kg)
= 0.28 N
Graphs:
Results:
As depicted in the data column and the graph, the addition of washers to the bottom of
the string leads to a decrease in time per rotation of the two washers at the top of the string. The
graph depicted shows a positive linear trendline with the equation y= 7.13x + -0.548. With the
graph and data, it is safe to conclude that the centripetal acceleration is greatest at higher speeds.
Conclusion:
The investigation explored centripetal force and rotational speed to understand and
analyze the relationship between these forces. In having to horizontally rotate two washers with a
constant radius, the relationship was understood via the collected data. In simpler terms, the data
and graph showed that the relationship between centrifugal force and rotational speed are linear.
Hence, the centripetal acceleration will be the highest wherever the speed is the greatest. In
comparing this data set to the formulas in physics, it is easy to understand how the centripetal
force is proportional to the square of the velocity.
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Taking the five washers versus ten washers as an example, the five washers took 7.21
seconds on average for ten rotations, whereas, one rotation would take 0.721 seconds on average.
In comparison, for ten washers, it took 4.93 seconds on average for ten rotations, whereas, in one
rotation on average it takes 0.493 seconds. This difference indicates that with more washers, the
time decreased, this increased the speed to ensure that the two washers are kept at a constant
radius.
A source of error in this investigation is that although one can ensure that the radius is
maintained in rotation, it is possible that the string moved or was not at the same distance
throughout. Although this should not affect the results by too much, preventative measures were
taken such as repetitive trials to ensure errors do not occur as well as marking the string with a
marker to ensure the radius is at proper distance. It is also possible that stopping the timer was
not at the exact point as one person was doing both rotations and tracking time; here, the timer
was stopped as soon as possible and can only be a few milliseconds off.
Analysis:
1.
Look up the equation for centripetal force in your book. Does this equation match your
graph relating centripetal force and speed? Explain.
The equation in the textbook for centripetal force is Fc=mv2r or Fc=mrω2. Yes,
this equation does and is represented in the linear graph. As mentioned prior, the
centripetal force is proportional to the square of the rotational speed. Here, the graph and
data match the physics formula. This equation is seen as taking the rotational speed and
squaring it to see if that matches the centripetal force. Here, this may not be exact in my
data set, however, it is close and the graph is depicting this overall trend.