Physics 1051 Laboratory #2 The Simple Pendulum

The Simple Pendulum

Physics 1051 Laboratory #2 The Simple Pendulum

Contents

Part I: Objective Part II: Introduction The Simple Pendulum Part III: Apparatus and Setup The Pendulum Clamp The Photogate Using LoggerPro

Part IV: Mass Dependence Expectation Data Collection and Analysis Part V: Length Dependence Expectations Data Collection Plotting Your Data 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 massless and unstretchable, and a particle of mass m attached to the string called the pendulum 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 all experiments should be conducted with this small angle.

FT x

y

Fg=

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 direction opposite to the displacement of the pendulum. The resultant motion is oscillatory with the pendulum exhibiting simple harmonic motion. We may analyze the restoring force and resulting motion to determine the period of a simple pendulum

FT x

y

Fg=

T = 2L

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 1: Write the objective of your experiment.

Lab Report 2: Write the relevant theory of this experiment.

Lab Report 3: 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 4: 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. Your masses should range from 50 g to 250 g.

Physics 1051 Laboratory #2 The Simple Pendulum

Part IV: Mass Dependence Data Collection and Analysis

Use a table to record your results.

Lab Report 5: Describe your method to determine how the period of a simple pendulum depends on its mass.

Lab Report 6: 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 7: 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 spanning the entire length of the string (minimum range of 60.0 cm).

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 of period as a function of time for each oscillation will be displayed.

Physics 1051 Laboratory #2 The Simple Pendulum

Part V: Length Dependence Data Collection

You may find the average period by clicking Analyze then Statistics.

Use a table to record your results. Lab Report 8: 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 an appropriate graph to be used to find the acceleration due to gravity.

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.

Format: Include a title and axes labels. Turn off connecting lines.

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 check Show Uncertainty.

Lab Report 9: 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 10: Outline briefly the steps of your experiment. Lab Report 11: List your experimental results and comment on

how they agreed with the expected results. Lab Report 12: List at least three sources of experimental

uncertainty and classify them as random or systematic.

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.