Lab Report
Determining the Acceleration Due to Gravity with a Simple Pendulum
Quintin T. Nethercott and M. Evelynn Walton
Department of Physics, University of Utah, Salt Lake City, 84112, UT, USA (Dated: March 6, 2013) Using a simple pendulum the acceleration due to gravity in Salt Lake City, Utah, USA was found to be (9.8 +/- .1) m/s2 . The model was constructed with the square of the period of oscillations in the small angle approximation being proportional to the length of the pendulum. The model was supported by the data using a linear fit with chi-squared value: 0.77429 and an r-square value: 0.99988. This experimental value for gravity agrees well with and is within one standard deviation of the accepted value for this location.
I.
INTRODUCTION
The study of the motion of the simple pendulum provided valuable insights into the gravitational force acting on the students at the University of Utah. The experiment was of value since the gravitational force is one all people continuously experience and the collection and analysis of data proved to be a rewarding learning experience in error analysis. Furthermore, this experiment tested a mathematical model for the value of gravity that that makes use of the small-angle approximation and the proportional relationship between the square of the period of oscillations to the length of the pendulum.Sources of error for this procedure included precision in both length and time measurement tools, reaction time of the stopwatch holder, and the accuracy of the stopwatch with respect to the lab atomic clock. The final result of g takes into account the correction for the error introduced using the approximation. There are opportunities to correct for the effects of mass distribution, air buoyancy and damping, and string stretching[1]. Our results do not take these effects into account at this time.
A.
Theoretical Introduction
The general form of Newton’s Law of Universal Gravitation can be used to find the force between
Quintin T. Nethercott and M. Evelynn Walton
Department of Physics, University of Utah, Salt Lake City, 84112, UT, USA (Dated: March 6, 2013) Using a simple pendulum the acceleration due to gravity in Salt Lake City, Utah, USA was found to be (9.8 +/- .1) m/s2 . The model was constructed with the square of the period of oscillations in the small angle approximation being proportional to the length of the pendulum. The model was supported by the data using a linear fit with chi-squared value: 0.77429 and an r-square value: 0.99988. This experimental value for gravity agrees well with and is within one standard deviation of the accepted value for this location.
I.
INTRODUCTION
The study of the motion of the simple pendulum provided valuable insights into the gravitational force acting on the students at the University of Utah. The experiment was of value since the gravitational force is one all people continuously experience and the collection and analysis of data proved to be a rewarding learning experience in error analysis. Furthermore, this experiment tested a mathematical model for the value of gravity that that makes use of the small-angle approximation and the proportional relationship between the square of the period of oscillations to the length of the pendulum.Sources of error for this procedure included precision in both length and time measurement tools, reaction time of the stopwatch holder, and the accuracy of the stopwatch with respect to the lab atomic clock. The final result of g takes into account the correction for the error introduced using the approximation. There are opportunities to correct for the effects of mass distribution, air buoyancy and damping, and string stretching[1]. Our results do not take these effects into account at this time.
A.
Theoretical Introduction
The general form of Newton’s Law of Universal Gravitation can be used to find the force between