PHYS 2211L
Final Examination Laboratory
Simple Pendulum
Study Assignment:
Lesson notes:
This laboratory is the final examination for PHYS 2211L. You should insure that you thoroughly
understand the requirements of the advanced sheet before you come to lab. This lab, including
your report must be completed within the lab period. All work performed after data taking is
completed must be by individuals only. Your final product will consist of four parts to be turned
in:
a. original data sheets
b. figure for the experimental apparatus
c. spreadsheet for calculations
d. word-processed portions of paragraph 3 and 5 of the report
Items a and b will be given to your instructor. Items c and d may be provided to your instructor
by either e-mail (from the classroom) or by flash drive before leaving the room (provided by the
instructor). E-mail will be sent to
[email protected]
Your instructor will confirm receipt of readable files for parts c and d before you leave the
classroom.
Objectives for the Exam:
1. To measure the acceleration due to gravity using a simple pendulum.
2. To demonstrate your ability to individually perform error calculations and analysis.
1. Objective.
The objective of this laboratory is to experimentally determine the acceleration
due to gravity using a simple pendulum.
2. Theory.
a.
A simple pendulum consists of a mass m suspended from a string or cord
of length L. If the mass is pulled aside by some small angle and released,
then the angle that the string makes from the vertical changes with time as
the mass swings back and forth. If we were to plot
a graph of the angle
as a function of time,
we would see that it displays SHM, just as the
position of the mass at the end of a spring as a
function of time. In general, the motion of a
pendulum is not simple harmonic. However, for
small angles, it becomes simple harmonic.
The period of the pendulum is the amount of time required for the
pendulum to complete a full oscillation; that is, the time to return to its
release point. If the angle of release for the pendulum is small (less than
15 degrees from the vertical), the period is given by
T 2
L
g
(1)
where
T
is the period of the pendulum,
L
is the length of pendulum, and
g
is the acceleration due to gravity.
3. Experimental Procedures and Apparatus
Using equation (1) from the theory section one can solve for g:
g=4
2
L / T2
Using the following equipment one can measure the length of the pendulum and
the period of oscillation to experimentally determine a value for g. Measure the
length once. Conduct 5 trials to determine an experimental value for the
acceleration.
2
a.
Equipment.
1)
2)
3)
4)
5)
6)
b.
Stop watch.
Meter stick.
String.
Rods and clamps.
Mass for pendulum bob.
Protractor.
Experimental setup.
The experimental setup will be provided by the student.
c.
Capabilities. To be provided by the student
4. Data.
The following describes what the student must provide in his/her lab report:
1) Provide a figure showing the experimental setup
2) Provide a description of the capabilities of the equipment used in the
experiment.
3) Provide a copy of your original data for the experiment.
4) Provide a copy of your spreadsheet with calculations. Include the following:
a) The period and uncertainty in the period of your simple pendulum.
b) The acceleration due to gravity.
c) The uncertainty in the acceleration due to gravity.
d) The percent fractional error in the acceleration due to gravity.
e) The percent discrepancy in the acceleration due to gravity. Use 9.800
m/s2 as the accepted value for the acceleration due to gravity.
3
5. Results and Conclusions.
1) Provide a statement of the acceleration due to gravity and its uncertainty.
2) Provide a statement of the percent fractional error in the experiment.
3) Provide a statement of the percent discrepancy in the experiment.
4) Provide a statement identifying the dominant type of error in the experiment.
5) Provide a statement identifying the measurement that produces the greatest
amount of random error in the experiment.
6) Describe sources of systematic error in the experiment.
7) Describe sources of random error in the experiment.
ANNEX A
1) Provide a copy of your original data for the experiment.
trial
number of oscillations
total time (s)
1
2
3
4
5
2) Length of simple pendulum (pivot to center of mass).
4
L (m)
L (m)
5