Physics 1051 Laboratory #2 The Simple Pendulum
The Simple Pendulum
Physics 1051 Laboratory #2 The Simple Pendulum
Contents
Part I: Objective Part IV: Mass Dependence
Expectation
Part II: Introduction Data Collection and Analysis
The Simple Pendulum
Part V: Length Dependence
Part III: Apparatus and Setup
Expectations
The Pendulum Clamp
Data Collection
The Photogate
Plotting Your Data
Using LoggerPro
Analysis
Part VI: Summary
Physics 1051 Laboratory #2 The Simple Pendulum
Part I: Objective
In this experiment, you will determine how the period of a
simple pendulum depends on the mass of the pendulum.
You will also determine how the period of the pendulum
depends on the length of the pendulum.
You will be designing your own experiment based on the
information in the following slides.
Physics 1051 Laboratory #2 The Simple Pendulum
Part II: Introduction
The Simple Pendulum
In this experiment you will investigate the motion
of a simple pendulum.
The simple pendulum is a system consisting of a
string of length L, which is assumed to be y
massless and unstretchable, and a particle of
mass m attached to the string called the pendulum x
FT
bob.
When the mass is displaced a small angle from
equilibrium and then released, the pendulum will
undergo simple harmonic motion.
This treatment is valid for angles less than 10° and
Fg =
all experiments should be conducted with this
small angle.
Physics 1051 Laboratory #2 The Simple Pendulum
Part II: Introduction
The Simple Pendulum
The forces acting on the bob are the tension in
the string FT and the gravitational force Fg.
When the pendulum is displaced and released,
the tangential component of Fg produces a
restoring force, which always acts in the y
direction opposite to the displacement of the x
pendulum. The resultant motion is oscillatory FT
with the pendulum exhibiting simple harmonic
motion.
We may anlayze the force and resulting motion
to determine the period of a simple pendulum
L
T = 2" Fg =
g
Physics 1051 Laboratory #2 The Simple Pendulum
Part III: Apparatus and Setup
Apparatus
You have been provided with
• A pendulum clamp
• String
• Metre stick
• Mass set
• Support rod
• Photogate
• Stopwatch
Physics 1051 Laboratory #2 The Simple Pendulum
Part III: Apparatus and Setup
The Pendulum Clamp
The pendulum clamp may be
attached to a support rod.
To make a pendulum, hang a
string from any of the three
suspension points.
The string may be shortened
by looping the string about
the suspension points.
Physics 1051 Laboratory #2 The Simple Pendulum
Part III: Apparatus and Setup
The Photogate
The photogate emits a beam of infrared light
from one side which is received by a sensor
on the other side.
With the software, data is collected by
recording the times when the infrared light
beam between the jaws of the photogate is
interrupted.
To time a pendulum using the photogate and
LoggerPro, the pendulum is allowed to swing
between the jaws of the photogate. The
period is then plotted as a function of time on
LoggerPro.
Physics 1051 Laboratory #2 The Simple Pendulum
Lab Report
Lab Report: Write the objective of your experiment.
Lab Report: Write the relevant theory of this experiment.
Lab Report: List your apparatus and sketch your setup.
Physics 1051 Laboratory #2 The Simple Pendulum
Part IV: Mass Dependence
Expectation
Your goal is to determine how the period of the pendulum depends on the
mass of the pendulum.
Lab Report: How do you expect the period of a simple pendulum to
depend on mass? Explain.
Physics 1051 Laboratory #2 The Simple Pendulum
Part IV: Mass Dependence
Data Collection and Analysis
Using the given apparatus, test your hypothesis.
The pendulum clamp can support masses up to 250 g.
The length of the pendulum is defined as the distance from the
top of the string to the middle of the mass.
Clustering the masses on the loop will keep the pendulum
length approximately constant.
A stopwatch is recommended for this portion of the
experiment.
Use a table to record your results.
Lab Report: Describe your method to determine how the
period of a simple pendulum depends on its
mass.
Lab Report: Discuss your results of how the period of a
simple pendulum depends on its mass.
Physics 1051 Laboratory #2 The Simple Pendulum
Part V: Length Dependence
Expectations
Your goal is to predict and then test how the period of the pendulum
depends on the length of the pendulum.
Lab Report: How do you expect the period of a simple pendulum to
depend on length? Explain.
Physics 1051 Laboratory #2 The Simple Pendulum
Part V: Length Dependence
Data Collection
Using the given apparatus, test your
hypothesis.
Typically, the length of the pendulum is
defined as the distance between the top of the
string and the middle of the mass.
We recommend the use of the photogate and
LoggerPro for this portion of the experiment.
For reliable results, you will need a minimum
of 5 data points.
Physics 1051 Laboratory #2 The Simple Pendulum
Part III: Apparatus and Setup
Using LoggerPro
Plug the photogate into Dig/Sonic 1 of the LabPro.
Make sure the LabPro is connected to the computer and plugged in.
Click here to launch LoggerPro.
Test that the photogate is working by moving your hand in and out of the gate.
The gate status displayed directly above your graph should change between
blocked and unblocked as you move your hand.
LoggerPro is now ready to collect data.
You may begin the collection by clicking Collect.
When you take data, LoggerPro will calculate the period of the motion by timing when
the pendulum passes through the sensor (similar to your measurement with the
stopwatch).
A graph displaying the period for each oscillation will be produced.
Physics 1051 Laboratory #2 The Simple Pendulum
Part V: Length Dependence
Data Collection
Use a table to record your results.
Lab Report: Describe your method of collecting
data for determining how the period
of a simple pendulum depends on
its length.
Physics 1051 Laboratory #2 The Simple Pendulum
Part V: Length Dependence
Plotting Your Data
Click here to open Graphical Analysis.
Plot a graph showing the relationship between period and length of a
pendulum.
HINT: A linear graph is the easiest to analyze. Examine the equation
relating period and length and rearrange it to find a linear relationship.
Plot the appropriate variables.
Have an instructor come check your graph and initial your report.
Print your graph and include it with your lab report.
Physics 1051 Laboratory #2 The Simple Pendulum
Part V: Length Dependence
Analysis
To obtain a linear fit to your data, click Analyze then Linear Fit.
To find the uncertainties in the slope and intercept, double click on the
box that appears and in the Standard Deviations section check both the
Slope and Intercept.
Lab Report: Use the results from your graph to determine the
acceleration due to gravity. Show your workings.
Compare your result with the accepted value of 9.81 m/s2.
Comment on the agreement.
Having trouble?
Click here to open your notes from the graphing workshop.
Physics 1051 Laboratory #2 The Simple Pendulum
Part V: Summary
Lab Report: Outline briefly the steps of your experiment.
Lab Report: List your experimental results and comment on
how they agreed with the expected results.
Lab Report: Listat least three sources of experimental
uncertainty and classify them as random or
systematic. Justify the classification.
Physics 1051 Laboratory #2 The Simple Pendulum
Wrap it up!
Check that you have completed your Lab Report.
Be sure to include your printed graph.