Experiment 10
Rotational Dynamics
by
Eugenio Panero
PHY 2091-06
experiment performed: Nov 1, 2006
report submitted: Nov 8, 2006
Lab Partner:
Chip Widmer
Instructor:
Ismael Diaz
Introduction
The purpose of this experiment is to explore centripetal force. A Beck Centripetal
Force Apparatus will be used for this purpose.
Data
(See attached pages)
Data Analysis
The velocity of an object moving in a circle is given by the formula
.
The centripetal force exerted on the object can be therefore expressed
as
, where
.
For instance, to determine the centripetal force in trial number one:
Many measured quantities determine the outcome of this experiment. All
uncertainties and errors will affect the final result.
Neither the uncertainty in mass nor the uncertainty in radius, however, is the
largest source of error for this experiment. Since time measurements were based
on human observation, uncertainty if frequency is the measurement that affects
the results the most. An estimate for error is ±0.1 sec, but this value is not
determinable. This value will be used to propagate the error in the final result.
The theoretical result for centripetal force, determined using static forces is
5.3493 N. The difference between theoretical and experimental value, whose
error is 0.1 N, therefore, is given by the following equations.
Discussion
Experimental Force Error in Experimental Force Theoretical Force Error in Theoretical Force
5.6853 N
± 0.22 N
5.3493 N
± 0.1 N
Table 1: Summary of Results
The result obtained is not within experimental limits. The discrepancy between
the theoretical value and the experimental one are beyond what the error
accounts for. A target precision of 5 % was set, while the precision obtained was
6.28 %. Several further trials were made to increase precision, but obtained the
negative effect and were discarded.
Nevertheless, there may be errors in the error propagation itself as well. An
accurate estimation of the error in revolutions per second could not be made. The
estimate tries to reflect the human error in keeping time. A more sophisticated
approach to the experiment would have called for the use of a photogate or
similar device to keep track of revolutions. This would have eliminated systematic
error in measurement.
Other systematic errors occurred throughout the experiment. The theory does
not account for external forces that might affect the centripetal force, such as air
resistance, gravity, or friction. Taking into account these factors could increase
the precision of the results.
Conclusion
The results obtained where close, but beyond, experimental limits. A sound
approximation of centripetal force was obtained, but a series of errors and
imprecision in measurements affected the final outcome.