Center of Gravity
& Equilibrium
AJ Klatch
Mat Chabalko
Mr. Edmondson
H. Engr Science I
November 5th, 2001
5/6
I. Abstract
The purpose of this lab is to understand the conditions for equilibrium of
parallel forces and to also learn how to calculate any additional forces that are
needed in order to establish equilibrium. Also, this lab is to coincide with the
information on torque that was taught to us in class.
This lab required the use of a meterstick, many hooked masses, a platform
balance, meterstick clamps, and string. In order to successfully do this lab the
procedure needed to be followed flawlessly. My team did this the best way
possible and achieved the appropriate answers.
The data we achieved for the lab is listed in the proceeding sentences. The
mass of our meterstick was .0837kg. The location of the center of gravity on our
meterstick was found .498m on the meterstick (49.8cm). For trial 1 the mass
required for equilibrium was .04631kg; for trial 2 the mass required for
equilibrium was .0863kg; for trial 3 the mass required for equilibrium was
.0363kg. The locations of the masses are as follows: for trial 1 the mass was at
.95m, for trial 2 the mass was at .986m, for trial 3 the mass was at .187m. These
values are for our first data table.
Our second data table values are as follows: For trial 1, the weight of the
required mass was .490N. For trial 2, the weight of the required mass was .490N.
For trial 3, the weight of the required mass was .196N. For trial 1, the torque arm
for required mass was found at .251m. For trial 2, the torque arm for required
mass was found at .208m. For trial 3, the torque arm for required mass was found
at .314m. For all three trials, the weight of the actual meterstick was found to be
.820N. Torque arm for weight of meterstick for trial 1 was .100m, for trial 2 was
.098m, and for trial 3 was .102m. The amount of torque that was produced from
our torque masses for trial 1 was .123N*m, for trial 2 .135N*m, for trial 3
.06N*m. The weight of the meterstick for our experimental values were .850N
for trial 1, .830N for trial 2, .832N for trial 3.
Finally, we calculated our errors. Our absolute error for trial 1 was .030N
and a relative error 3.60%. Our absolute error for trial 2 was .012N and a relative
error of 1.40%. Our absolute error for trial 3 was .010N and a relative error of
1.21%.
II. Procedure
1. The center of gravity of the meterstick was determined.
2. Trial one had the meterstick supported at the .65m mark, with a
mass hung at some distance to the right of this until a perfect
balance was achieved. The results of amount of mass and distance
from the pivot point were recorded.
3. For trial 2 the .75m mark was chosen to support the meterstick, and
a mass was hung to the right of this until a perfect balance was
achieved. The results of amount of mass and distance from the
pivot point were recorded.
4. For trial 3 the .4 meter mark was chosen to support the meterstick,
and a mass was hung to the left of this until a perfect balance was
achieved. The results of amount of mass and distance from the
pivot point were recorded.
5. The meterstick was repositioned for three more advanced trials.
6. For trial one, the .3m mark was chosen as the pivot point. A .2kg
mass was hung at the .1m mark, a .1kg mass was hung at the .2m
mark, and a .020kg mass was hung at the 90m mark. A final .050
mass was positioned to the right of the pivot until a balance of the
meterstick was obtained. The resulting distance was recorded.
7. For trial two, the .4m mark was chosen as the pivot point. A .1kg
mass was hung at the .1m mark, a .020kg mass was hung at the
.25m mark, and a .020kg mass was hung at the 90m mark. A final
.050 mass was positioned to the right of the pivot until a balance of
the meterstick was obtained. The resulting distance was recorded,
and a diagram was drawn of the setup.
8. A final trial, trial three, saw the .6m mark was chosen as the pivot
point. A .1kg mass was hung at the .4m mark, a .20kg mass was
hung at the .7m mark, and a .50kg mass was hung at the 90m mark.
A final .050 mass was positioned to the left of the pivot until a
balance of the meterstick was obtained. The position of the mass
was recorded.
III. Data tables
Trial 1 2 3
Mass of meterstick .0837kg .0837kg .0837kg
Location of center .498m .498m .498m
of gravity
Location of .650m .750m .400m
meterstick support
Mass required for .0463kg .0863kg .0363kg
equilibrium
Location of required .950m .986m .187m
mass
Trial 1 2 3
Weight of required .490N .490N .196N
mass
Torque arm for .251m .208m .314m
required mass
Weight of .820N .820N .820N
meterstick, actual
Torque arm for .100m .098m .102m
weight of meterstick
Torque produced by .123m*N .135m*N .06m*N
required mass
Weight of .850N .830N .832N
meterstick,
experimental
Absolute Error .030N .012N .010N
Relative error 3.60% 1.40% 1.21%
IV. Math Calculations
The force weights of the added masses were calculated by multiplying their
masses by 9.8. Ex: .05kg*9.8=.49N
The torque produced by the required masses added was found by multiplying
the distance from the pivot point by the force weight.
Ex: .49N*.1m=.123m*N
The experimental weight of the meterstick was calculated by solving the
torque equation that says the counterclockwise torques are equal to the
counterclockwise torques.
Ex: .1m*.2kg*9.8+.2m*.2kg*9.8= X*49.75+.6*.020*9.8
X=.850N
The absolute error was then calculated by subtracting the value that had been
calculated for the mass of the stick, and then by subtracting the actual weight.
Ex: .850-.820=.030
The relative error was then found by dividing the absolute error by the
accepted weight of the stick, and multiplying by 100.
Ex: .030/.820*100=3.6%
V. Conclusion
In conclusion, this lab was very successful. My team was able to understand
the learning objectives presented in this laboratory exercise, which made it
exciting to complete. Also, this lab was able to clear up some of the fuzziness
between seeing items on a blackboard and doing them yourself.
One notable factor about this lab is that as the trials continued, our percentage
of error decreased. Thus, we can say that our precision improved upon becoming
a learned person. Again, in order to prove our successfulness in this lab our
values we achieved are as follows.
The data we achieved for the lab is listed in the proceeding sentences. The mass
of our meterstick was .0837kg. The location of the center of gravity on our
meterstick was found .498m on the meterstick (49.8cm). For trial 1 the mass
required for equilibrium was .04631kg; for trial 2 the mass required for
equilibrium was .0863kg; for trial 3 the mass required for equilibrium was
.0363kg. The locations of the masses are as follows: for trial 1 the mass was at
.95m, for trial 2 the mass was at .986m, for trial 3 the mass was at .187m. These
values are for our first data table.
Our second data table values are as follows: For trial 1, the weight of the
required mass was .490N. For trial 2, the weight of the required mass was .490N.
For trial 3, the weight of the required mass was .196N. For trial 1, the torque arm
for required mass was found at .251m. For trial 2, the torque arm for required
mass was found at .208m. For trial 3, the torque arm for required mass was found
at .314m. For all three trials, the weight of the actual meterstick was found to be
.820N. Torque arm for weight of meterstick for trial 1 was .100m, for trial 2 was
.098m, and for trial 3 was .102m. The amount of torque that was produced from
our torque masses for trial 1 was .123N*m, for trial 2 .135N*m, for trial 3
.06N*m. The weight of the meterstick for our experimental values were .850N
for trial 1, .830N for trial 2, .832N for trial 3.
Finally, we calculated our errors. Our absolute error for trial 1 was .030N
and a relative error 3.60%. Our absolute error for trial 2 was .012N and a relative
error of 1.40%. Our absolute error for trial 3 was .010N and a relative error of
1.21%.
In closing, this lab was able to be completed in the allotted time. And, this lab
was completed to the best of our abilities.
VI. Questions
1.Does the accuracy of your results in finding the weight of the meterstick imporve when
knife-edge support is placed farther from the center of gravity? Explain.
No, it does not. As long as the stick is in equilibrium, the mathematics should
remain the same, and produce very similar results no matter where support is
placed. The only thing that changes is the place where it is supported, not the
actual numbers that have the true bearing on the outcome of the results.
2.Under what conditions would it be impossible to produce equilibrium in this
experiment with the addition of a single mass?
It would be impossible whenever either the torque arm required for the mass that
is to be added is too short, or when the mass itself is too small in order to
effectively counteract the torque pulling in the opposite direction.