Pendulum Lab
Gage Ames
Jamie Rapaport, Zack Armagost, and Mike Rejeki
Physics - Period 2
Friday, April 03, 2009
Purpose
The purpose of this lab is to identify factors that affect the period of a pendulum.
The factors that will be examined are length of string, mass of bob, amplitude, and air
resistance. It is important to determine how these factors change the period of a
pendulum, if at all. If a factor changes the period, a trend should be identified.
Background Information
Pendulums have been used for hundreds of years as more than just
demonstrations and forms of minor entertainment. The pendulum was discovered by
Galileo Galilei around 1602. One of its most important uses was timekeeping. In fact,
the pendulum served as the most accurate way to keep time up until the 1930s. A
pendulum works by constantly trying to return to its equilibrium position. When a
pendulum is at rest and hanging straight down, it is in its equilibrium position. If the bob
is lifted and released, gravity causes it to fall down. It attempts to restore its equilibrium,
which inadvertently makes it oscillate. The time it takes for the bob of a pendulum to
return to its initial position from which it was dropped is called the period. The period
represents the rate at which the pendulum swings and can be used to figure out home
many times the pendulum swings in a certain amount of time.
By changing different parts of a pendulum one at a time and measuring its
period, one can determine how that factor affects the period. The length of string, mass
of bob, amplitude, and air resistance will each be changed to analyze their effect on the
period of a pendulum.
Equipment and Setup
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Ring stand
Pendulum rod
String
Assorted bobs (spheres)
Stopwatch
Protractor
Paper
Scissors
Ruler
Tape
Digital mass balance
Setup
Pendulum rod
String
Bob
Ring
Stand
Procedure
1. Assemble the ring stand by attaching the pendulum rod to the stand.
2. Using a ruler, hang one of the bobs so that it is 10 cm from the bottom of the
pendulum rod to the top of the bob. Tighten the screw on the pendulum rod to
hold it in place.
3. Pull the bob up to one side of the pendulum so that it forms a perpendicular line
with the pendulum rod.
4. Release the bob and immediately begin timing using the stop watch. Stop timing
when the bob goes through two periods (when the bob returns to its original
position the second time).
5. Record the time from the stopwatch in a data table.
6. Repeat steps 2-5, each time adding 5 cm to the length of the string. Do this until
you record a time for a length of 30 cm.
7. Hang one of the bobs so that it is 20 cm from the pendulum rod to the bob.
8. Using a protractor, pull the bob up so that it forms a 90° angle with the rod of the
ring stand.
9. Release the bob and immediately begin timing using the stop watch. Stop timing
when the bob goes through two periods.
10. Record the time from the stopwatch in a data table.
11. Repeat steps 8-10, each time subtracting 20° from the angle (or amplitude). Do
this until you record a time for an amplitude of 10°.
12. Choose five different bobs and use a digital mass balance to find each of their
masses. Record them in a data table.
13. Hang one of the bobs so that it is 20 cm in length.
14. Pull the bob up to one side of the pendulum so that it forms a perpendicular line
with the pendulum rod.
15. Release the bob and immediately begin timing using the stop watch. Stop timing
when the bob goes through two periods.
16. Record the time from the stopwatch in a data table.
17. Repeat steps 13-16, each time using a bob of a different mass. Do this until you
have recorded a time for all five bobs.
18. Hang one of the bobs so that the pendulum is 20 cm in length.
19. Use a pair of scissors and a ruler to cut out a piece of paper that is 5 cm in length
and 5 cm in width.
20. Tape the paper to the bob.
21. Pull the bob up to one side of the pendulum so that it forms a perpendicular line
with the pendulum rod.
22. Release the bob and immediately begin timing using the stop watch. Stop timing
when the bob goes through two periods.
23. Record the time from the stopwatch in a data table.
24. Remove the paper from the bob.
25. Repeat steps 19-24, each time increasing the length and width of the paper by 2
cm. Do this until you have recorded a time for the bob with a piece of paper 13
cm in length and width.
Data
Varying Length of Pendulum
Trial
Mass (g)
24
24
24
24
24
1
2
3
4
5
Length (cm)
10
15
20
25
30
Amplitude (°)
90
90
90
90
90
Time (2 periods) (s)
1.35
1.75
2.06
2.32
2.50
Length (cm)
Amplitude (°)
Time (2 periods) (s)
24
24
24
24
24
20
20
20
20
20
90
70
50
30
10
2.10
1.91
1.72
1.71
1.69
Mass (g)
3.6
5.6
23.9
71.6
87.4
Length (cm)
20
20
20
20
20
Amplitude (°)
90
90
90
90
90
Time (2 periods) (s)
2.00
2.03
2.00
2.00
2.06
Varying Amplitude of Pendulum
Trial
Mass (g)
1
2
3
4
5
Varying Mass of Bob
Trial
1
2
3
4
5
Varying the Attached Surface Area
Trial
1
2
3
4
5
Mass (g)
24
24
24
24
24
Length
(cm)
20
20
20
20
20
Amplitude (°)
Calculations
Calculating the length of the period
Varying Length
Trial 1: (1.35 s)/2 = 0.675 s
Trail 2: 0.875 s
Trial 3: 1.03 s
Trial 4: 1.16 s
Trail 5: 1.25 s
Varying Amplitude
Trial 1: 1.05 s
90
90
90
90
90
Time (2 periods)
(s)
2.03
2.06
2.07
1.91
1.96
Period
(s)
1.015
1.03
1.035
0.955
0.98
Paper Side
Size (cm)
0
5
7
9
11
Trial 2: 0.955 s
Trial 3: 0.860 s
Trial 4: 0.855 s
Trial 5: 0.845 s
Varying Mass
Trial 1: 1.00 s
Trial 2: 1.02 s
Trial 3: 1.00 s
Trial 4: 1.00 s
Trial 5: 1.03 s
Varying Surface Area
Trial 1: 1.02 s
Trial 2: 1.03 s
Trial 3: 1.04 s
Trial 4: 0.955 s
Trial 5: 0.980 s
Calculating the Area of the Paper
Trial 1:
Trial 2:
Trial 3:
Trial 4:
Trial 5:
(0 cm)2 = 0 cm2
25 cm2
49 cm2
81 cm2
121 cm2
Graphs
Error Analysis
The error in this lab came from a few different sources depending on the
manipulated variable we tested. When we changed the length of the pendulum some
error came from the string being so long that it made the bob bounce when we dropped
it. This really only happened with the 25 cm and 30 cm lengths, but it still had a bad
effect on our periods. Another type of error occurred when we changed the air
resistance by attaching paper of different areas. We found that the paper taped on the
bob make the arc of the pendulum decrease in size at a much faster rate. This means
that, with our large surface areas especially, the period time was not very accurate. The
bob didn’t get very close to the position we dropped it from, so we had to stop the timer
when the bob went as far as it would in its arc. Error may have also resulted from the
pendulum swaying forward or backward during its motion. Sometimes the bob was not
dropped exactly straight and caused the bob to take on a slightly diagonal motion. This
would have changed the times of our periods slightly.
Questions and Conclusions
Questions
There were no questions for this lab.
Conclusion
Overall this was a successful lab. We were able to successfully test four different
variables and analyze their effect on the period of the pendulum. The only
significant trend we found was between length of the pendulum and period. Our
data showed that as the length of the pendulum increased, the period of the
pendulum also increased. There was a slight positive trend between the amplitude
and the period of the pendulum, but it was not correlated enough to state with any
confidence that a trend exists. We found absolutely no correlation between the
period and the mass or surface area.
If I were to perform this lab again I would try to come up with different variables to
test. Some of the variables we tested did not have a good effect on the pendulum.
Another variable I would like to test is how porous the bob’s material is. I think it
would be interesting to see how air going through the bob would change the period.