lab 9
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New Mexico State University *
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MISC
Subject
Aerospace Engineering
Date
Dec 6, 2023
Type
docx
Pages
9
Uploaded by ChefMetalMole42
Lab 9: Torque and Equilibrium Lab
Clayton McCall
November 3
rd
2023
Page
1
of
9
Objective:
In this lab you create an experiment with a ruler washers and string to create
a balance to find how torque is used on a balance. In this experiment you
can understand more how to find counterclockwise torque and clockwise
torque.
Part 1:
In part one you create the device that works as a balance and you put one
small washer on one side and one large washer on the other. To balance out
the ruler you move the string with the large washer along the ruler until it
balances out. You can use the distance on the ruler as one of the variables to
find the torque. To continue the experiment you add another small washer
and move the large washer until it balances out you do this once more to
find each
length of the large washer from the center of mass to use to calculate torque
Data Table 1
Mass Values
Item
Mass [g]
Ruler
12.9
Small Washer 1
5.8
Small Washer 2
6.0
Small Washer 3
6.1
Large Washer 1
28.8
Large Washer 2
25.6
Loop of
String 1 with Paper Clip at 0
cm
.4
Loop of
String 2 with Paper Clip
.4
A: Equilibrium with Two Masses
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Data Table 2
Location of Masses for Balancing the Ruler
Number of
Small
Washers at 0
cm
Location of
Center of
Mass of the
Ruler, x
cm
[cm]
Location of
the Large
Washer for
Balance, x
[cm]
Lever Arm of
Small
Washer(s)
x
cm
– 0 [cm]
Lever Arm of
Large Washer
x - x
cm
[cm]
1 washer for
1
st
Trial
22.86
12.065
22.86
10.795
1 washer for
2
nd
Trial
22.86
12.0227
22.86
10.837
2 washers for
1
st
Trial
22.86
10.16
22.86
12.7
2 washers for
2
nd
Trial
22.86
9.99
22.86
12.87
3 washers for
1
st
Trial
22.86
7.451
22.86
15.409
3 washers for
2
nd
Trial
22.86
7.281
22.86
15.579
Data Table 3
Torques
Number of Small
Washers at 0 cm
Anti-clockwise
Torque [cm g]
{Show a sample
Calculation}
Clockwise Torque
[cm g] {Show a
sample
Calculation}
% Difference in
Torques
1 washer for 1
st
Trial
3049.890
1300.688
80.41%
1 washer for 2
nd
Trial
3061.756
1300.688
80.74%
2 washers for 1
st
Trial
3588.106
2646.228
30.22%
2 washers for
2
nd
Trial
3636.135
2646.228
31.51%
3 washers for 1
st
Trial
4353.474
4014.193
8.11%
3 washers for 2
nd
Trial
4401.504
4014.193
9.204%
Part 2:
In part two we calculate the torque for the large washer and for the small
washer. To find the torque you use the formula t=rFsin(theta) where force is
the weight multiplied by gravity radius is the distance from the axis of
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rotation and theta is the angle at which the force is pulling the object. When
plugged in for the first values you get the formula.
T=10.795(5.8*9.81)sin(90). when you simplify this equation you get the
answer 3049.890.
B: Equilibrium with Three Masses
Part 3:
In part three you do the same process as the first part except for the fact
that you do not balance the ruler on the center of mass and instead you
balance it at 20.5 cm on the ruler. Another thing that is also changed is that
instead of only one large washer you use two large washers.
Data Table 4
Location of Masses for Balancing Three
Masses
Number
of Small
Washers
at 0 cm
Location
of Center
of Mass of
the Ruler,
x
cm
[cm]
Location
of the 2
Large
Washers
for
Balance,
x [cm]
Lever
Arm of
Small
Washer(s
)
20.5 - 0
[cm]
Lever Arm
for the
Ruler Mass
20.5
- x
cm
[cm]
Lever Arm
of Large
Washer
X – 20.5
[cm]
1 washer
for 1
st
Trial
22.86
7.451
20.5
2.36
13.049
1 washer
for 2
nd
Trial
22.86
7.281
20.5
2.36
13.219
2
washers
for 1
st
Trial
22.86
5.5
20.5
2.36
15
2
washers
for
2
nd
Trial
22.86
5.237
20.5
2.36
15.263
3
washers
for 1
st
Trial
22.86
3.217
20.5
2.36
17.283
3
washers
for 2
nd
22.86
2.879
20.5
2.36
17.621
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Trial
Data Table 5
Torques
Number of Small
Washers at 0 cm
Anti-clockwise
Torque [cm g]
{Show a sample
Calculation}
Clockwise
Torque [cm g]
{Show a sample
Calculation}
% Difference in
Torques
1 washer for 1
st
Trial
6963.782
1166.409
142.61%
1 washer for 2
nd
Trial
7054.504
1166.409
143.25%
2 washers for 1
st
Trial
8004.96
2373.039
108.54%
2 washers for
2
nd
Trial
8145.314
2373.039
109.76%
3 washers for 1
st
Trial
9223.315
3599.780
87.71%
3 washers for 2
nd
Trial
9403.693
3599.780
89.267%
%
Difference
=
(
⌈
Στ
ccw
−
Στ
cw
⌉
)
{
(
Στ
ccw
+
Στ
cw
)
2
}
x
100
Part 4:
In the next part you use the values you received as counterclockwise torque
and clockwise torque to find the difference in the torques using the formula
above. When this formula is used you can have the equation ((|69.782-
1166.409)/((6963.782+1166.409)/2))100 when this equation is solved you
get the answer 142.61%.
A: Equilibrium with Two Masses
1.
Draw a diagram of your ruler and mass system in equilibrium identifying
the anti-clockwise torque and clockwise torque.
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9
2.
Calculate the anti-clockwise torque and the clockwise torque of the
system with the ruler and the washers. Record these values in Data Table
3.
3.
Calculate the % Difference in the Torques and record the values in Data
Table 3.
4.
Did your experiment results in Data Table 3 verify, to within a reasonable
experimental error, the condition of equilibrium of Equation 6?
Support
your response with experimental data.
There is one trial in data table three which shows an 8% difference which
verifies the equation but my other values do not confirm the equation.
anti-clockwise
=
clockwise
Equation 6
Part II Equilibrium with Three Masses
1.
Draw a diagram of your ruler and mass system in equilibrium
identifying the anti-clockwise torque(s) and clockwise torque(s).
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2.
Calculate the anti-clockwise torque and the clockwise torque of the
system with the ruler and the washers. Record these values in Data
Table 5.
3.
Calculate the % Difference in the Torques and record the values in Data
Table 5.
4.
Did your experiment results in Data Table 5 verify, to within a
reasonable experimental error, the condition of equilibrium of Equation
6? Support your response with experimental data.
None of my trials verified the equation.
Questions
1.
Explain how your experiment met the condition for equilibrium in
Equation 4.
In my first set of trials most of my values have low percentages on
the percent difference which proves the equation by the
counterclockwise torque and the clockwise torque being very close.
F
vertical
=
F
y
= 0
Equation 4
2.
Discuss the accuracy of balancing the system using your finger
rather than another type of support, such as support stand with
knife edge clamps.
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The accuracy of using a finger instead of a support stand or
something else would make the values much more sporadic and not
very accurate.
3.
A window washer stands on a uniform plank of mass M = 142 kg
and length l = 2.80 m supported by 2 ropes attached at the ends of
the plank. The window washer has a mass m = 68.0 kg. What is the
tension in each of the ropes, T1 and T2, if the window washer's
displacement from the center of mass of the plank is x = 0.930 m
as shown in Figure 5 Window Washer Problem?
to solve this problem you need the formula t*l=m*g*d but the
torque has to be halved in each of the equations because of the
center of mass of the plank. So to find t1 you have the formula
t*1.4m=-142kg*9.81m/s^2*.47. once simplified you get the answer
t1=-571.56.
using the same formula you can find the answer for t2 as
t2=582.79.
Figure 5 Window Washer Problem
Image by R. Harr.
Conclusion:
I enjoyed doing this lab. I feel like at some parts this lab was a little
confusing which is why I feel like some of the values I had were
incorrect. I hope in the future I will start to understand better how to
calculate torque but I feel like this lab did not help me very much. I
look forward to other labs in the future and I hope I will learn more
from future labs than I have in this lab.
References:
Walker, J., Resnick, R., & Halliday, D. (2014).
Fundamentals of physics
. John
Wiley & Sons, Inc.
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