SelfPaced Physics Cover Sheet
Activity 6 - The Period of a Pendulum
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PHYS 1000
Activity: The Period of a Pendulum
Objective: To confirm experimentally that the period of a pendulum is proportional to
L , and to use this to determine the acceleration of gravity at the surface of the Earth,
g.
Background: Physics, Concepts and Connections, Hobson, Chapter 5.
A pendulum is simply a mass hanging from a string which is allowed to oscillate in a
plane. The time for one complete oscillation (back and forth) is called the period of the
pendulum. If the amplitude (angle) of the swing is not too great (less than 15°) the
period does not depend strongly on the amplitude, nor does it depend upon the mass of
the object used as the pendulum bob. However, the period of the pendulum does
depend upon the length of the pendulum and upon the force of attraction between the
bob and the earth, which enters the equations describing the pendulum through the
parameter g, the acceleration due to gravity.
From Newton’s second law of motion, the relationship between period (T), the length
(L), and g can be found to be:
T = 2!
L
.
g
This relationship tells us that the period is period is proportional to the square root of the
length of the pendulum, so that if the length of the pendulum increased by a factor of 4,
the period would only increase by a factor of two. This experiment will test this
prediction.
The period-length relationship can also be expressed so that g is expressed in terms of
T and L:
4! 2 L
g=
T2
Equipment and Supplies : String, a heavy mass, tape measure or meter stick,
stopwatch.
Procedure: NB: The length of the string should be measured from the pivot point to
the center of mass of the pendulum bob.
Pick a pendulum bob that has an evenly distributed mass. Some examples could be a
film box filled with water, a soap bottle or full hand sanitizer dispenser, or a plastic cup
filled with sand. Use a heavy mass so that air resistance is minimized. Tie the
pendulum to a secure overhead point such as a ceiling hook.
Measure the length of the pendulum as per above. Start the pendulum swinging with a
small amplitude: no more than a few inches from the side of the resting position. With a
stopwatch, measure how long it takes for a fixed number of periods (e.g., 50.) (If you
don’t have a stopwatch, count how many periods occur over one minute using a regular
watch.) Remember, one period is the time needed for one complete cycle; and one
complete cycle can be described as the pendulum swinging away from it’s high point
and then back again to the same high point (There and back again!) The more cycles
you count, the more accurate your results will be. Find the measured period Tm by
dividing the total time by the number of cycles (by cycle, we still mean complete cycle or
period.)
Use the measured period and the equation above to determine the value of the
acceleration of gravity, g.
Repeat the experiment for five different lengths. Make sure you use a large range of
values of length. At least one choice for length should be four times another value. Fill
out the table on the worksheet.
Worksheet for Activity 6: The Period of a Pendulum
Length
(cm)
Number
Total
of
time for
Complete N Cycles
Cycles
(s)
N
Measured
Period Tm
(s)
g
(cm/s2)
4! 2 L
g=
T2
Percent
Difference
1) Do your data support the conclusion that the period of a pendulum is proportional
to the square root of the length? Does increasing the length by a factor of 4
increase the period by a factor of 2? ___________________________________
2) Calculate the percent difference between your value of g (the acceleration due
to gravity) and the accepted value of g = 980 cm/s2 by using the formula
| g ! 980 |
Percent Difference =
x 100
980
3) Comment on your values and any discrepancies. What do you think are the
sources of error? (Note: if you are deviating significantly from this value, you
should re-check your calculations.)
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4) Write a paragraph summarizing this experiment. The purpose of this paragraph is
to have you present evidence that you actually did the experiment and
understand what you did.
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