PURPOSE
OF THE EXPERIMENT
The purpose of this experiment is to
realize the equilibrium and torque concept. In other words we try to go deeper
in the sentence that if the net torque is zero then the object will be in
equilibrium. We will also make the determination of the centre of gravity of
the meter stick, comparison of the experimentally determined location
for a given applied force to produce rotational equilibrium with the location
predicted theoretically and finally determination of the mass of
an unknown object.
PROCEDURE
AND THE RESPONSES TO THE QUESTIONS
1)
In this part we draw the figure below showing a
meter stick at equilibrium state when hanged by a string. To make it clear, we
draw the meter stick like this position because it is a common misconception
that if a meterstick is in equilibrium then it will remain parallel to ground.
However in real, if an object is in equilibriom then it will remain at a
position that you leave.
2)
In this part we used a meter stick and tried to
bring it in equilibrium by hanging it. We recorded the mark where meter stick
is hanged as 500 ± 0,1cm.
3)
In this part we observed two situations. One of them
is shifting the position of the string on the meter stick 5cm to the right of
the equilibrium point and the other is shifting the string 5cm to the left of
the equilibrium point. In both of the situations we observed that the meter
stick is not in equilibrium, it oscillated and its movement was fast. This
motion occured because of torque as we changed the distance of meter stick’s
two arms. One arm got shorter and other one got longer. Therefore torque was
formed and the meter stick turned.
4)
In this part we bring the meter stick into
equilibrium state again. We hang 50g mass 5cm away from the meter stick’s
equilibrium point and then released the meter stick. It stroke the table in
short time (1,98s). When we done the same thing with 100g mass, it stroke the
table more violent and shorter time than first one.(1,59s) When we done the
same thing with 200g mass, the meter stick stroke the table as the most violent
one and it took the shortest time among them. (1,11s)
|
Mass
|
Distance
|
Violence
|
Time
|
|
50g
|
5cm
|
Violent
|
1,98s
|
|
100g
|
5cm
|
More violent
|
1,59s
|
|
200g
|
5cm
|
The most violent
|
1.11s
|
5)
In this part we only used 50 g mass but at different
distances as 15cm, 25cm and 35cm away from meter stick’s equilibrium point. In
first trying the meter stick stroke the table in short time.(1.51s) When we
done the same thing for 25cm distance, it stroke the table more violent and
shorter time than first one.(1.32s) When we done the same thing for 35cm
distance, the meter stich stroke the table as the most violent one and it took
the shortest time among them.(1.05s)
|
Mass
|
Distance
|
Violence
|
Time
|
|
50g
|
15cm
|
Violent
|
1,51s
|
|
50g
|
25cm
|
More violent
|
1,32s
|
|
50g
|
35cm
|
The most violent
|
1.05s
|
6)
By considering the measurements in 4 and 5, we can
say that when we fix the distance and increase the masses or when we fix the
masses and increase the distance we obtain same results. (Two of these
situations increase the net torque.)
7)
In this part we measured the weight of meter stick
by dynamometer and recorded it as 165±1g.
8)
In this part we considered the mechanism below.
In order to stabilize the meter stick we predicted to hang the 500g mass from
pointed side because we hang the stick
at the point O which is not the center of gravity.
The longer side of stick is more heavy
so we thought that we hang the mass from that
side.
9)
In this part we hanged 500g mass on meter stick in
real and by moving it we found the point where the stick comes to equilibrium.
We saw that our prediction in 8th part was true.
10)
In this part by using different masses, we repeated
the 9th part and filled the measurement table 1 below. The diagram for this part is also shown below.
Measurement Table 1
|
Trial
Number
|
G
|
d
|
d`
|
|
1
|
500g
|
20cm
|
6,5 ±0,1 cm
|
|
2
|
200g
|
20cm
|
17cm ± 1 mm
|
|
3
|
300g
|
20cm
|
11,2cm ± 1mm
|
11) In this part we
calculated the weight of meter stick and recorded it in calculation table 1.
And compared it with the measurement in step 7. In order to compare we also
calculated the error(%).
Calculation Table 1
|
Trial
|
Calculated Mass
|
Real mass
|
Error(%)
|
|
1
|
162.5g
|
165 ± 1g
|
1.52
|
|
2
|
170g
|
165 ± 1g
|
3.03
|
|
3
|
168g
|
165 ± 1g
|
1.82
|
Measurement
Error (%) = 1.52
Our measurement is consistent with our
calculations. In any case, our error(%) values are less than 5%.
12) In this part we hanged
the meter stick at the 70 cm mark and hanged the 50g mass to 60cm, 100g mass to
80cm and 200g mass to 90 cm. The question was that ‘Is the meter stick in
equilibrium now? Why?’
We said that the meter stick is not in
equilibrium in this situation. Because when we do the necessary calculations
according to the equilibrium point, left
and right sides’torques due to masses including meter stick’s mass are not
equal. The diagram for this situation shown in below.
(Total net torque calculated as 0,38N.m
and the other one calculated as 0,5N.m. Therefore there is a net torque in
clockwise direction with the magnitude of 0,12N.m)
(Here we took g as 10m/s2 )
13) We predicted that we
should hang the 20g mass to the long side of meter stick at the distance of
60cm from string to bring the system in equilibrium.
14) With trial and error we
found the position of 20g mass as 60cm that we predicted before because firstly
we decided to try our predicted value, in which the system is in equilibrium
state.
15) In order to calculate
the torque that causes motion in clockwise and counterclockwise directions, we
tried other distance values too and we recorded them in Measurement Table 2.
Measurement Table 2
|
Mass
|
Force
|
Lever arm Length
|
Torque
|
Direction
|
|
20g
|
0,2N
|
0,6m
|
0,12N.m
|
counterclockwise
|
|
165g
|
1,65N
|
0,2m
|
0,33N.m
|
counterclockwise
|
|
50g
|
0,5N
|
0,1m
|
0,05N.m
|
counterclockwise
|
|
100g
|
1N
|
0,1m
|
0,1N.m
|
clockwise
|
|
200g
|
2N
|
0,2m
|
0,4N.m
|
clockwise
|
The necessary diagram for the equilibrium
conditions is shown below.
16) We calculated the total
torque that causes motion in clockwise and counter-clockwise directions
separately and record them into Calculation Table 2 shown below.
Calculation Table 2
|
Total torque that causes motion in clockwise
direction
|
Total torque that causes motion in
counterclockwise direction
|
|
0,5N.m
|
0,5N.m
|
17) What is the direction
of the total torque?
Total torque is zero so there is no
direction for the total torque because the meter stick is in equilibrium at last
situation (20gr at 10cm shown in figure above.)
18) We know
that the torque is a measure of how much a force acting on an
object causes that object to rotate. There were more than one force acting the
meter stick in our experiment, and each of these forces acted on different point on the meter stick.
Then, each force caused a torque. We also know that the net torque is the sum of the individual torques. In
rotational equilibrium as we saw in this experiment’s last step, the sum of the
torques is equal to zero. In other words, there is no net torque on the object.
19)
We found an object with unknown mass and tried to measure its weight by
hanging known masses on the meter stick as we done in previous steps. The final
arrangements of masses are shown in the figure below.
Our unknown mass made our system in
equilibrium with the distance of 23cm from equilibrium point of meter stick.
|
Mass
|
Force
|
Lever arm Length
|
Torque
|
Direction
|
|
Unknown mass
|
0,522N
|
0,23m
|
0,12Nm
|
counterclockwise
|
|
165g
|
1,65N
|
0,2m
|
0,33N.m
|
counterclockwise
|
|
50g
|
0,5N
|
0,1m
|
0,05N.m
|
counterclockwise
|
|
100g
|
1N
|
0,1m
|
0,1N.m
|
clockwise
|
|
200g
|
2N
|
0,2m
|
0,4N.m
|
clockwise
|
20) We calculated unknown
mass as 52,2 g. In laboratory we measured its mass as 52g.
Measurement Error (%) = 0,38(%)
As seen above our error value is less
than 1%. Therefore our calculations and
measurements are consistent.
CONCLUSION:
We said that torque is a measure
of how much a force acting on an object causes that object to rotate. In other
words, torque is a force that creates rotation.
For example: ‘When you're tightening the lug nuts on your wheels, you're
providing torque when you rotate the nuts with a wrench. Similarly, your
vehicle's engine applies torque to the axles so that your wheels will rotate.’(adventure.howstuffworks.com)
In this experiment we worked on
equilibrium concept firstly. We draw a figure which shows a meter stick at
equilibrium state when hanged by a string. We draw the meter stick like this
position because it is a common misconception that if a meterstick is in
equilibrium then it will remain parallel to ground. However in real, if an
object is in equilibrium then it will remain at a position that you leave.
Then we arranged the meterstick to
its off-center position and experimentally estimate the mass of it. In this
part we calculated the weight of meter stick and recorded it as 165 ± 1g and we
also calculated the error(%) as 1,52% which related to human ability related
faulties;
therefore we
can say that our measurement is consistent with our calculations. In any case,
our error(%) values are less than 5%.
Then we analyze rotation and its
reasons by doing some mini tests. These tests connected us to the torque concept because forces acting on a body of finite size tend to both
translate and rotate the body. The theoritical background is stated below.
With reference to an arbitrarily chosen
origin, the torque due to a force F applied to the body is given by
τ =r´F
where r is the position vector of
the point of application of the force F with respect to the origin. If the body is to be in equilibrium, it must
be in equilibrium both with respect to translation and to rotation.
In translational
equilibrium the vector sum of all forces acting on a body must be zero.
In rotational equilibrium, which
means that the sum of all torques due to those forces must be equal to zero as
said before.
(physics.uoguelph.ca)
We showed this theoretical part with
this experiment. From step 12 to 18 we worked on this theoretical parts’
experimental section in which we investigated the arrangement of
masses on a center-pivot lever required to produce balance. We developed the
idea that both force and lever arm produce torque. That both quantities must be
considered when trying to produce equilibrium. Force vectors are used in
diagrams shown below.
Finally, we used masses to predict an
unknown mass from the arrangement used in the previous activity at the step 19
and our
unknown mass made our system in equilibrium with the distance of 23cm from equilibrium
point of meter stick shown in the figure below. We calculated unknown mass as
52,2 g. In laboratory we measured its mass as 52g. As seen below our error
value is less than 1% which related to human ability related faulties.
Therefore our calculations and
measurements are consistent.
Measurement
Error (%) = 0,38(%)
SUGGESTIONS
AND COMMENTS:
Firstly, we did not found meaningful
the third step. After showing equilibrium situation at step one students could continue
with fourth and fifth steps in which they saw the mass and distance
relationship with different systems.
Secondly, there is 20 steps in this
experiment. They could be separated from each other by dividing them into
triple or quadruple subparts Because with as are it is messy. In any case, the
experiment have four main parts in real.
REFERENCES:
·
[online document] Retrieved from http://adventure.howstuffworks.com/outdoor-activities/off-roading/torque-off-roading.htm
torque/Q.torque.intro.html
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