PHY11L A4 E204
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Transcript of PHY11L A4 E204
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E204: TORQUE: SECOND CONDITION OF EQUILIBRIUM
FRISNEDI, Nadine T.
OBJECTIVE
Torque, which is developed by Archimedes, is the
ability of force to change the rotational motion of
a particle and an influence to change the rotational
motion of an object. For a body to be in equilibrium
the sum of all the torques acting on it, clockwise
and counter clockwise, should be zero.
Equilibrium implies a state of balance. Its second
condition states that the net torque acting on the
body should be zero for angular acceleration to be
zero.
The purpose of this experiment is to study the
principles of torque through the application
of Newton’s second condition of equilibrium.
The students were tasked with obtaining the
weight and forces of certain apparatuses
through the analysis of equilibrium so as
to practice and understand more clearly the
significance of torque in the process. In order to
evaluate their findings, the students were
prompted to compare their gathered data
with actual values through the computation
of the percent differences. This relationship
between torque and equilibrium is the main
background of the experiment which was
conducted.
By the end of the experiment, it is expected for
students to know the second condition of
equilibrium. They will learn how the second
condition affects an object or a body. They will also
learn how to apply the second condition in
computing the unknown data in the experiment.
Through this experiment, the students will gain
more knowledge and appreciation about the
concepts on torque and how different is first
condition of equilibrium to the second one.
Students will also appreciate the concept of second
condition of equilibrium and how it is important in
studying Physics.
MATERIALS AND METHODS
The performed experiment used the following
materials and equipment which are: two pieces of
weight pans, a model balance, a protractor, a
meter stick, a spring balance, set of weights and
an electronic weighing scale.
Figure 1. The materials and equipment used in the experiment.
Before conducting the experiment, the table
should be made stable, stationary and leveled. The
model balance, meter stick, and the weight pans
were the main materials for this experiment. The
model balance was set-up based on the figure
given on the laboratory manual wherein the axis
of rotation passes through the center of gravity of
the beam. Since there is a missing nail on the
beam, in which there is hole left on it to be used
later on the experiment, it is necessary to put a
piece of paper, it can be rolled so that it fits on the
last empty hole on the right side of the beam.
Adjust the amount of that piece of paper until the
beam is balanced.
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Figure 2. Set-up for the determination of the weight of the
pans.
After the set-up is done, a 10-gram weight is
considered to be the W1, was placed on the pan,
P1. The pans are to be placed on the beam in which
the hooks or nails can be used to hang the pans.
The pan, P1 is positioned on the right side of the
beam while the pan, P2 is positioned on the left
side of the beam. The two pans were placed on
the beam while it is made sure that the beam
becomes horizontally orientated or be seen as
balanced in both of its sides which states that the
system is in equilibrium. It is not necessary that
the pans must be placed on the hooks or the nails,
they can be hanged on top of the body of the beam
inwardly to make the pans become balanced.
Figure 3. P1 with a W1 and P2 in equilibrium.
The L1 is the distance between the pan, P1 and the
axis of rotation, L2 on the other hand is the
distance between the pan, P2 to the axis of
rotation. L1 and L2 was measured using the meter
stick.
Figure 4. Measuring L1 using the meter stick.
Figure 5. Measuring L2 using the meter stick.
After that, the 10g weight was taken off from the
pan, P1. A weight of 5g, which is considered the
W2, was placed on P2. The two pans were placed
again on the beam for the system to be in
equilibrium.
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Figure 6. P1 and P1 with W2 in equilibrium.
The L3 this time is also the distance between the
pan, P1 and the axis of rotation, L4 on the other
hand this time is the distance between the pan, P2
to the axis of rotation. Using the meter stick, L3
and L4 were measured. The previous procedure
was repeated for the second and the third trial
however the amount of weights placed on the pans
were different. After conducting all the trials, the
mass of P1 and P2 was computed for each trial.
For the second part of the experiment, a weight of
50g is considered as W1, was placed on P1 which
is at the left side of the beam. The spring balanced
was also placed on the left side of the beam in a
manner that will make the beam balanced.
Figure 7. Set-up for determining the force needed for
equilibrium
The angle of inclination of the spring balance was
measured using the protractor, which is less than
90 degrees in which the beam was kept in
horizontal position. The reading of the spring
balance was recorded and was marked as the
F(Measured).
Figure 8. Determining the angle of inclination of the spring
balance.
The distance of the pan, P1 from the axis of
rotation is measured as the L1 and the distance of
the spring balance from the axis of rotation was
measured and was marked as L2. The force
exerted by the spring balance was measured using
the second condition of equilibrium. The
procedures were repeated for the second trial but
the spring balance was placed at the right side of
the beam.
For the third part of the experiment, the second
hole on the beam was used as the axis of rotation.
The weight 50g was, which is again considered as
the W1, was placed on the pan, P1. The location of
pan was adjusted for the system until equilibrium
is achieved. The distance of P1 from the axis of
rotation was measured as the L1. The distance
from the axis of rotation to Wb, which is the
previous axis of rotation from the first two parts of
the experiment, was measured and marked as the
L2.
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Figure 9. Set-up for determining the weight of the beam.
Figure 10. Measuring L1 using the meter stick.
Figure 11. Measuring L2 using the meter stick.
The previous procedure was repeated for the
second and the third trial however the amount of
weights placed on the pans were different. For the
second trial, the W1=60g while on the third trial,
the W1=70g were used. After this the weight of the
beam was computed using the second condition of
equilibrium.
OBSERVATIONS AND RESULTS
In the first part of the experiment, the L1, L2, L3,
L4, P1(Computed), and P2(Computed) were needed. The
weights were already given. The L1 and L2 was
measured by the distance of the P1 with W1 of P2
to the axis of rotation. The L3 and L4 was measured
by the distance of the P1 and P2 with W2 to the
axis of rotation. The P1(Computed) and P2(Computed) were
computed using the elimination method of two
equations from the procedures. The average
weight of pans, were obtained by getting the
average of P1 and P2 in the three trials. The percent
difference for both of the pans were computed in
which the actual value of the pans was the first
variable while the average experimental weight
was the second variable.
Table 1. Determining the Weight of the Pan
Actual Value of pan 1, P1 = 24.8g
Actual Value of pan 2, P2 = 24.8g
TRIAL L1 L2 L3 L4
1 W1= 10g
17.7
cm
24.7
cm
21.1
cm
17.7
cm W2= 5g
2 W1= 15g
10.2
cm
16.3
cm
19.9
cm
10.1
cm W2= 25g
3 W1= 30g
10.1
cm
22.1
cm
18.2
cm
10.1
cm W2= 20g
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TRIAL P1
(COMPUTED)
P2
(COMPUTED)
1
W1 = 10g 25.59g 25.5g
W2 = 5g
2 W1 = 15g
25.58g 25.39g W2 = 25g
3
W1 = 30g 25.06g 25.17g W2 = 20g
Average Weight of P1 = 25.41g
Average Weight of P2 = 25.35g
Percent Difference for P1 = 2.43%
Percent Difference for P2 = 2.21%
Sample Computations:
Getting the P1(Computed) and P2(Computed) for the first
trial:
(𝑃1 + 𝑊1)𝐿1 = (𝑃2𝐿2)
(𝑃2 + 𝑊2)𝐿4 = (𝑃1𝐿3)
𝑃2 =𝐿1(𝑊2𝐿4 + 𝑊1𝐿3)
𝐿2𝐿3 − 𝐿1𝐿4
𝑃2 =17.7((5)(17.7) + (10)(21.1))
((24.7)(21.1) − (17.7)(17.7))
𝑃2 = 25.5𝑔
𝑃1 =(𝑃2 + 𝑊2)𝐿4
𝐿3
𝑃1 =(25.5 + 5)17.7
21.1
𝑃1 = 25.59𝑔
Average weight of pans:
𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑃1 = 25.59 + 25.58 + 25.06
3
𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑃1 = 25.41𝑔
𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑃2 = 25.5 + 25.39 + 25.17
3
𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑃2 = 25.35𝑔
Percent Difference
% 𝑑𝑖𝑓𝑓 𝑃1 =|𝐸𝑉1 − 𝐸𝑉2|
(𝐸𝑉1 + 𝐸𝑉2
2)
% 𝑑𝑖𝑓𝑓 𝑃1 = |24.8 − 25.41|
(24.8 + 25.41
2)
%𝑑𝑖𝑓𝑓 𝑃1 = 2.43%
% 𝑑𝑖𝑓𝑓 𝑃2 =|𝐸𝑉1 − 𝐸𝑉2|
(𝐸𝑉1 + 𝐸𝑉2
2)
% 𝑑𝑖𝑓𝑓 𝑃2 = |24.8 − 25.35|
(24.8 + 25.35
2)
%𝑑𝑖𝑓𝑓 𝑃2 = 2.21%
For the second part of the experiment, the L1 and
L2 was measured using the same procedure in the
first part of the experiment by replacing the P2
with the spring balance. The angle of inclination
was measures using the protractor. The force F by
the spring balance on the beam was computed
using the second condition of equilibrium. The
percent difference for both trials were computed
in which the F(MEASURED) was the first variable and
the F(COMPUTED) as the second variable.
Table 2. Determining the Force Needed to be
in Equilibrium
TRIAL L1 L2 W1+P1
1 17.7
cm 7.3cm 74.8g
2 17.7
cm 15.1 cm 74.8g
TRIAL F
(COMPUTED)
F
(MEASURED) %Diff
1 224.18g 240g 6.82%
2 108.38g 90g 18.53%
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Sample Computations:
Getting the F(COMPUTED) for the first trial:
Given: L1 = 17.7cm, L2 = 7.3cm, W1 = 50g,
P1 =24.8g, θ=54°
𝑊1 + 𝑃1 = 50𝑔 + 24.8𝑔 = 74.8𝑔
𝐹(𝐶𝑂𝑀𝑃𝑈𝑇𝐸𝐷) =(𝑃1 + 𝑊1)𝐿1
sin 𝜃 𝐿2
𝐹(𝐶𝑂𝑀𝑃𝑈𝑇𝐸𝐷) =(74.8)17.7
(sin 54°)7.3
𝐹(𝐶𝑂𝑀𝑃𝑈𝑇𝐸𝐷) = 224.18𝑔
Percent Difference for the first trial:
F(MEASURED) = 240g
% 𝑑𝑖𝑓𝑓 =|𝐸𝑉1 − 𝐸𝑉2|
(𝐸𝑉1 + 𝐸𝑉2
2)
% 𝑑𝑖𝑓𝑓 = |240 − 224.18|
(240 + 224.18
2)
%𝑑𝑖𝑓𝑓 = 6.82%
For the third part of the experiment, the L1 and L2
was measured by getting the distance between P1
and Wb from the axis of rotation respectively. The
weight if the beam was computed using the given
formula. The average weight of pans, were
obtained by getting the average of P1 and P2 in the
three trials. The percent difference for both trials
were computed in which the WB(MEASURED) was the
first variable and the average of the WB(COMPUTED) as
the second variable.
Table 3. Determining the Weight of the Beam
TRIAL L1 L2 W1+P1
1 14.1cm 7.3cm 74.8g
2 12.4cm 7.3cm 84.8g
3 11.1cm 7.3cm 94.8g
TRIAL wB (COMPUTED) wB (MEASURED)
1 144.48g
137g
2 144.04g
3 144.15g
Average Weight WB =
Percent Difference =
144.22g 5.14%
Sample Computations:
Getting the WB (COMPUTED) for the first trial:
Given: L1 = 14.1cm, L2 = 7.3cm, W1 = 50g,
P1 =24.8g
𝑊1 + 𝑃1 = 50𝑔 + 24.8𝑔 = 74.8𝑔
𝑊𝐵 =(𝑃1 + 𝑊1)𝐿1
𝐿2
𝑊𝐵 =(74.8)14.1
7.3
𝑊𝐵 = 144.48𝑔
Average weight of the beam:
𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑊𝐵 = 144.48 + 144.04 + 144.15
3
𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑊𝐵 = 144.22𝑔
Percent Difference
Actual Value of 𝑊𝐵 = 137g
% 𝑑𝑖𝑓𝑓 =|𝐸𝑉1 − 𝐸𝑉2|
(𝐸𝑉1 + 𝐸𝑉2
2)
% 𝑑𝑖𝑓𝑓 = |137 − 144.22|
(137 + 144.22
2)
%𝑑𝑖𝑓𝑓 = 5.14%
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DISCUSSION & CONCLUSION
Torque is a measure of how much a force is acting
on an object causes that object to rotate. It is also
called as the moment of force. On the experiment
the model balance serves as the axis of rotation.
Our data in the first table shows that we have
determined the weight of the pan. The concept of
torque and the second condition of equilibrium was
used in this part. Based on our data, as the weight
increases the P1 and the P2 also increases. It shows
that as the force applied increases, torque also
increases. Therefore, torque is directly
proportional with the force applied on the object
and is also dependent on the perpendicular
distance of the applied force to the axis of rotation.
Since the summation of torque in the body must
be equal to 0, the clockwise torques must be equal
to the counterclockwise torques, the P1 should be
equal to P2 so that the beam will not rotate. The
% difference that we got for the P1 and P2 are
2.41% and 2.35% respectively, which is small.
Our data on the second table shows that we have
determined the force exerted by the spring
balance to the beam. The force needed for the
system to be in equilibrium is greater when the
angle is greater than zero but less than 90
degrees. As the angle is reaching zero, the system
is reaching equilibrium. For this part of the
experiment, we got a high percent difference.
Maybe it is due to the wrong measurements of the
distances and the angles and we assumed that the
beam is balanced already.
On the third activity we need to use the second
hole in the beam as the axis of rotation. The data
from the third table shows that we have
determined the weight of the beam. The weight
was computed using the concept of the second
condition of equilibrium. The weight we have come
up is quite close to the actual value and this means
that we did the experiment properly.
In the three parts of experiment which finds the
weight of the pan, force exerted and weight of the
beam respectively, we noticed how torque is
affected by the forces acting on the system and
their radial distance from the axis and also, how
the rotational equilibrium is applied. We have
come up to the conclusion when second condition
of equilibrium is satisfied, there is no angular
acceleration and body will not be moving and will
be in rotational equilibrium.
Since all the parts of the experiment have been
applied by the second condition of equilibrium and
we have analyzed each part to get the unknown
data, the first objective of second condition of
equilibrium was fulfilled. Since we have applied the
second condition of equilibrium, we have known its
importance for solving the unknown and learning
how to use it. This fulfills the second objective of
the experiment. This makes our experiment
successful since all the objectives were achieved
The possible sources of error for this experiment
are wrong judgement of balancing the beam and
inaccurate measurement of the distances of the
object to the axis of rotation. We might say that
the beam is already balance but maybe it is not
really balanced totally. If the beam is not
balanced, it will affect our data since we applied
the second condition of equilibrium. For the
measurement of the distances, since they are all
measured manually, there is a tendency to
approximate the measurement since the object we
are measuring are not stable.
We could recommend to the students in the future
that will also conduct this experiment is that they
make sure that the beam is totally balanced and
make sure that when measuring distances, it
should be done properly and accurately. Also,
doing a sub-trial per added weight is
recommended to verify the measurements so that
the data to be used will be of the least error.
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ACKNOWLEDGMENT & REFERENCE
I would like to thank my groupmates for being so
cooperative upon doing the experiment. Although
it was a lot of pressure doing two experiments in
one period they kept cool and relaxed even if time
is really limited. I appreciate all of their efforts
since without their initiative in doing the tasks
assigned to them, our experiment will have a great
chance of failure. I would also like to thank our
professor, Prof. Ricardo F. De Leon, Jr. for guiding
all throughout the experiment and for pointing out
the things we should remember in conducting the
experiment. I would also like to thank him for
giving us additional points for our performance in
this experiment. I would like to thank my friends,
Vivi, Elijah, and Alvin for giving me ideas on how I
should properly layout my report and how my
ideas should flow. They were very nice when I ask
for their help. I also would like to acknowledge the
lab assistants for reminding us how to properly
handle the materials and equipment they are
lending us so that it would be easy for us to set it
up and we won’t damage those materials. Lastly,
I would like to thank my family for their never
ending support and encouragement for me in my
studies as I pursue my degree in Mapúa. They
have been so understanding and I am so blessed
to have them.
Reference:
Calderon, Jose C., (2000) College Physics
Laboratory Manual, Mapúa Institute of
Technology, Manila: Department of Physics.