Question description
Lab
Assignment 10: The Simple Pendulum
Instructor’s Overview
The pendulum is an excellent illustrative
example of simple harmonic motion.
Walker’s Physics has a great
anecdote of Galileo’s observation of oscillating chandeliers and his subsequent
experiments on the simple pendulum. In
this lab, we will replicate Galileo’s experiment to gain insight into the
physics of the pendulum. We’ll improve on
the accuracy of his results by using a stop watch instead of our pulses to measure
the period of the pendulum!
This activity is not based on an eScience
experiment, although we will some material from the kit for the
experiment. For further background on
the pendulum, refer to Walker’s Physics,
Section 13-6.
Lab Instructions
1. ¨ Cut a one meter length of fishing line.
2. ¨ Tie six washers onto the end of the fishing line.
3. ¨ Tie the other end of the line to a feature attached
to a ceiling such as a stationary ceiling fan.
If this is not available, you can recruit an assistant to hold the line
in a very stable fashion.
4. ¨ Measure the distance from the holding point to the
center of the washers. This is the
effective length of the pendulum. Record
this value in the table below.
5. ¨ Move the weights no more than 20 degrees from
equilibrium and let go.
6. ¨ With a stopwatch, time 10 periods (complete
oscillations).
7. ¨ Divide the total time by 10 to get the average period
for this pendulum. Record this value in
the table below.
8. ¨ Repeat steps 4-7 for four other lengths. Suggested lengths: 100 cm, 80 cm, 60 cm, 40
cm, 20 cm. It is good experimental
practice to randomize your trials. For
example, you could run in this order: 80 cm, 40 cm, 100 cm, 20 cm, 60 cm.
Take detailed
notes as you perform the experiment and fill out the sections below. This document serves as your lab report. Please include detailed descriptions of your
experimental methods and observations.
Date:
Student:
AbstractBackgroundObjectiveHypothesis
Introduction
Material and Methods
Results
Data Table
Length (meters)
Average period, T (sec)
Average period squared, T2 (sec2)
Plots/Analysis
Create a plot
of length (x-axis) versus average period (y-axis). You can use a program such as Excel to
generate your plot. Make sure to clearly
label your axes and indicate units.
Create a plot
of length (x-axis) versus (average period)2 (y-axis). Use Excel to add a linear trend line. Record the slope of the best fit line.
Recall that
the period of an ideal simple pendulum is given by the following relation:
Squaring both
sides of the equation gives us this relation:
Using the
slope of your T2 versus L plot, determine the acceleration due to
gravity.
Based on your
results, please answer the following questions:
1.
How close is your experimentally determined gravitational
acceleration to 9.81 m/s2?
What are potential sources for error in the experiment?
2.
For small angles, does the pendulum’s period of oscillation depend
on the initial angular displacement from equilibrium? Explain.
3.
Why is it a good idea to use a relatively heavy mass in this
experiment? What would you say to a
colleague that wanted to use only one washer as the pendulum mass?
4.
Use
the relation of the period of an ideal simple pendulum, , to calculate the
ratio of the periods of identical pendulums on the Earth and on Mars. Note:
The gravitational acceleration on the surface of Mars is approximately 3.7 m/s2.
Conclusions
References
