lab 8
docx
keyboard_arrow_up
School
New Mexico State University *
*We aren’t endorsed by this school
Course
MISC
Subject
Aerospace Engineering
Date
Dec 6, 2023
Type
docx
Pages
8
Uploaded by ChefMetalMole42
Lab 8: Centripetal Acceleration and Force
Clayton McCall
October 27
th
2023
Objective:
Create an experiment with a tube a string, two weights and a paper clip.
where you will be able to calculate velocity, centripetal acceleration and
centripetal force.
Data Table 1
Item
Mass (kg)
Small Washer
.006
Large Washer 1
.02825
Large Washer 2
.02825
Large Washer 3
.02825
Large Washer 4
.02825
Activity 1 – Part A
In part one I used the tube with the weights and added one washer each trial
which gave me the different values. I put a paper clip 30 cm away from the
small washer at the other end to keep the moving mass from moving all the
way up the string and to keep the radius at a certain variable.
Data Table 2A
Varying the Hanging Mass
Tria
l
Moving
Mass, m
(kg)
Hanging
mass, M
(kg)
Radius, r
(m)
Time, t
(seconds)
1
.006
.02825
.3
.45
2
.006
.0565
.3
.27
3
.006
.08475
.3
.22
1
© 2021 Carolina Biological Supply Company
4
.006
.113
.3
.26
Data Table 2B
Varying the Hanging Mass - Calculations
Tri
al
Experimen
tal
Velocity,
v
E
(m/s)
Theoreti
cal
Velocity
, v
T
(m/s)
Percen
t Error
in
Velocit
y
v
E
2
(m
2
/s
2
)
Centripetal
acceleratio
n, a
c
(m/s
2
)
m/r
(kg/m)
mv
E
2
(kg· m
2
/s
2
)
Centripet
al Force,
F
c
(N)
Weigh
t, Mg
(N)
1
4.189
3.722
11%
17.5
48
58.493
.02
.105
.35
.277
2
6.981
5.264
24%
48.7
34
162.447
.02
.292
.973
.554
3
8.568
6.447
24%
73.4
10
244.7
.02
.440
1.467
.831
4
7.250
7.445
2%
52.5
63
175.21
.02
.315
1.05
1.10
9
Part 1:
To find the experimental velocity I used the formula (2pir)/t. Once
I had the formula, I plugged in the values to find 2pi(.3)/.45 in the
first trial which equals 4.189. to find the theoretical velocity I used
the formula √(Mgr/m). once I had the formula, I plugged in the
values for the first trial √(.02825*9.81*.3/.006) I then evaluated
this and got the answer 3.722.
Use spreadsheet software (i.e., Excel or Google sheets) to create a graph of
v
E
2
versus the centripetal acceleration, a
c
, from Activity 1. Include a line of
best fit and record the equation of the line.
10
20
30
40
50
60
70
80
0
50
100
150
200
250
300
f(x) = 40.18 exp( 0.03 x )
ve^2 vs. centripetal acceleration
2
© 2021 Carolina Biological Supply Company
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
1.
Using the graph created in Question 1, explain how centripetal
acceleration is affected when the hanging mass changes. Does your
graph verify the relationship in Equation 7?
Changes in the hanging mass can impact centripetal acceleration, with
mass and radius being key factors that determine the magnitude of
this acceleration. My graph shows that as the experimental velocity
squared goes up the centripetal acceleration also goes up up until the
end where I had a random variable.
2.
Use spreadsheet software (i.e., Excel or Google sheets) to create a
graph of centripetal force, F
c
, versus v
E
2
from Activity 1. Include a line
of best fit and record the equation of the line.
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
0
10
20
30
40
50
60
70
80
f(x) = 12.07 exp( 1.31 x )
centripital force vs. ve^2
3.
Using the graph created in Question 3, explain how centripetal force is
affected when the hanging mass changes. Does your graph verify the
relationship in Equation 8?
Changes in the hanging mass in a rotating system directly affect the
centripetal force required to keep the object moving in a circular path. The
force varies based on the mass of the object and the radius of the circular
motion. As the hanging mass gets larger and larger the centripetal force gets
higher and higher up until I had a random variable.
3
© 2021 Carolina Biological Supply Company
Activity 1 – Part B
Data Table 3A
Varying the Radius of the Moving Mass
Tria
l
Moving
Mass, m
(kg)
Hanging
mass, M
(kg)
Radius, r
(m)
Time, t
(seconds)
1
.006
.02825
r
1
= .3
.45
2
.006
.02825
r
2
= .25
.24
3
.006
.02825
r
3
= .205
.26
4
.006
.02825
r
4
= .15
.18
Part 2:
In part two I changed the radius of the moving mass by putting a paper clip
30cm away from the small washer then 25cm then 20cm then 15cm. the
weights stayed the same in this part and the only thing that changed was
the radius. I used the same data that I received in the first trial for the first
part for the first trial in this part.
Data Table 3B
Varying the Radius of the Moving Mass - Calculations
Tria
l
Experimen
tal
Velocity, v
E
(m/s)
Theoretic
al
Velocity,
v
T
(m/s)
Percent
Error in
Velocity
v
E
2
(m
2
/s
2
)
Centripetal
acceleratio
n, a
c
(m/s
2
)
mv
E
2
(kg· m
2
/s
2
)
Centripetal
Force, F
c
(N)
Weight,
Mg (N)
1
4.189
3.722
11%
17.5
48
58.49
.105
.35
.277
2
6.545
3.398
48%
42.8
37
171.348
.257
1.028
.277
3
4.954
3.077
37%
24.5
42
119.717
.147
.717
.277
4
5.236
2.63
49%
27.4
2
182.8
.165
1.1
.277
4
© 2021 Carolina Biological Supply Company
Part 2:
In this part to find the centripetal acceleration I used the formula v^2/r. once
I had this formula, I used the variables that I had and plugged them in to find
the centripetal acceleration. In the first trial my equation was 17.548/.3
which equals 58.49. when I was finding the centripetal force, I used the
formula mv^2/r. once I had the formula I plugged in the values for the first
trial and found .105/.3 the equation evaluated out to be .35.
1.
Use spreadsheet software (i.e., Excel or Google sheets) to create a graph
of v
E
2
versus radius, r, from Activity 2. Include a line of best fit and record
the equation of the line.
15
20
25
30
35
40
45
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
f(x) = 0.24 exp( − 0 x )
ve^2 vs. radius
2.
Using the graph created in Question 5, explain how centripetal
acceleration is affected when the radius changes. Does your graph verify
the relationship in Equation 7?
Centripetal acceleration is directly affected by changes in the radius of
the circular path. A smaller radius increases the centripetal acceleration,
while a larger radius decreases it. When the radius decreases the
centripetal acceleration is supposed to increase. In my values it does not
look like this happens
3.
Use spreadsheet software (i.e., Excel or Google sheets) to create a graph
of mv
E
2
versus radius, r, from Activity 2. Include a line of best fit and
record the equation of the line.
5
© 2021 Carolina Biological Supply Company
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.22
0.24
0.26
0.28
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
f(x) = 0.24 exp( − 0.45 x )
mve^2 vs. radius
4.
Using the graph created in Question 7, explain how centripetal force is
affected when centripetal force is affected when the radius changes.
The centripetal force is directly affected by changes in the radius of the circular
path. A smaller radius requires a greater centripetal force, while a larger radius
demands less centripetal force.
5.
Discuss whether the percent error calculated in Activities 1 and 2 are
acceptable experimental errors. Explain any discrepancies between your
experimental and theoretical velocity values which exceed the acceptable
range of experimental error.
In my first experiment with adding more hanging mass I feel like my error
was decent, but it could be better. In the second part of the experiment my
error was very off I feel this is so because of the time I was valuing in each of
the separate trials.
6.
Compare the centripetal force to the weight of the hanging mass in each
Activity. Does your data verify the relationship in Equation 10?
The centripetal force in the first experiment seems to have a relationship
where when the weight increases the centripetal force increases up until
my last trial where I had a random error. In my second part I feel like the
relationship is much more random. I feel like my first part verifies the
relationship of equation 10 while my second part does not.
6
© 2021 Carolina Biological Supply Company
Conclusion:
I really enjoyed this lab it was very different from a lot of the labs I
have done before. One part I really enjoyed about the lab was
that the contraption I created was fun to experiment with and fun
to build. One part I didn’t like very much in the lab was the
amount of calculating I had to do I feel like the calculations could
have been much more fun to evaluate and I didn’t understand the
calculations as much as I would’ve hoped. I am excited to learn
more after doing more of these labs in the future and overall I
enjoyed this lab.
References
Walker, J., Resnick, R., & Halliday, D. (2014).
Fundamentals of physics
. John
Wiley & Sons, Inc.
7
© 2021 Carolina Biological Supply Company