AST Lab Assignment - Pendulum Motion and Gravity(1)
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Rowan-Cabarrus Community College *
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Course
151
Subject
Astronomy
Date
Dec 6, 2023
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Uploaded by GrandAnteaterPerson235
Astronomy Lab Assignment – Motion of a Pendulum and Gravity
Introduction:
The motion of a swinging pendulum is very closely tied to the effects of the local
acceleration due to gravity. It is also a periodic motion, and we will be able to discuss some
similarities to the motion of an orbiting planet. In this lab, you will build a pendulum and
perform an experiment to explore the nature of its motion under gravity.
You will be looking at the oscillation period of the pendulum’s motion. One swing of the
pendulum will consist of release from start point, swing to the opposite end, and return to its
start location. You will release the pendulum, and use a timer to measure the length of 10 such
oscillations.
These oscillations happen due to the influence of gravity. From the measurements you
make from the pendulum, you will be able to calculate the strength of gravity here on Earth –
and theoretically it would work on any other planet/moon/object in the solar system.
Learning Objectives
:
After completing this lab, you will be able to:
-
Describe the motion of a simple pendulum under the influence of gravity.
-
Determine the acceleration of gravity on Earth.
-
Determine a percent error for your experimentally determined value.
-
Discuss the effects of human reaction time on a simple experiment.
Materials needed
:
-
String
-
Tape
-
Sticks, ruler, broom handle or some sort of stand for your pendulum
-
Washers, small weights, or some other sort of mass for the pendulum bob
-
Paper clips
-
Stopwatch (can be a phone app, or computer app)
Part 1: Building Your Pendulum
1.
For best results, cut a length of string between 30-100cm, and tie your chosen pendulum
weight to the end of it. Affix the end of the pendulum at a height above the ground so
that the bob can swing freely. You want the pendulum to pivot freely from the
attachment point. Ensure there is no movement of your pendulum mount – you want to
minimize extraneous movement for best results.
2.
Measure the length of your assembled pendulum (in Centimeters)
from the attachment point to the center of the object
. Record the
value in the location indicated below.
3.
Now, pull the pendulum out a small angle (ideally not greater than
45 degrees), and release it smoothly – don’t throw it, just let go and
allow it to swing fully extended on the rope.
4.
Use a stopwatch/timer to measure the time it takes to complete 10 full oscillations. You
do not need to drop it and start the timer at the same time. Wait until the pendulum
swing to it’s farthest point on either side, and begin your stopwatch then, and start
counting the following swings.
5.
From starting swing location, to the other side, and back is 1 oscillation.
Run the stopwatch for a total of 10 full oscillations. Stop the timer at
the end of the 10
th
swing.
6.
Record this time in the table below. Repeat this 9 more times, for a total
of 10 measurements.
7.
For each of the pendulum trials above, compute the time for a single oscillation by
dividing your recorded value by 10. Round to 2 decimal places.
8.
Calculate the
Average time
for 1 Oscillation by adding up all of the individual computed
values (single oscillation time) and dividing by 10.
Record Data from Step 1-8 below:
Pendulum Length in centimeters:
Time for 10 Oscillations
Time for 1 Oscillation (divide by 10)
Run 1:
13.99 s
1.399s
Run 2:
14.18s
1,418s
Run 3:
13.97s
1.397s
Run 4:
14.15s
1.415s
Run 5:
14.38s
1.438s
Run 6:
14.35s
1.435s
Run 7:
14.45s
1.439 s
Run 8:
14.27s
1.427s
Run 9:
14.33s
1.433s
Run 10:
14.05s
1.405s
Average time for 1 Oscillation
Lab Procedure Questions:
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1.
Take a look at your values from trails 1-10 above. Are there any data points that stand
out as significantly different (bigger/small) than the rest?
14.45 is the biggest and 13.97 is the smallest.
2.
Would you expect to get the same exact value (down to the nearest millisecond) on the
stopwatch for each run? Why or why not?
It wouldn’t be exact but it would be close since it is swinging from almost
the same spot.
3.
The average human reaction time is about 0.25 seconds. For this pendulum, you react
twice – once to start the stopwatch, and once to stop it. That could be as much as 0.5
seconds for a single pendulum run!
The percent error for this can be calculated as follows:
a. Calculate the percent error 0.5 seconds of rection time would create for 10 oscillations
from your data (use any 1 of your trial times for 10 oscillations):
0.03533568904
b. Calculate the percent error 0.5 seconds of rection time would create for 1 oscillation
from your data (avg value for 1 oscillation above):
0.35335689045
4.
Based on the values you calculated in 3 (a) and (b), why do you think you were asked to
measure and record 10 oscillations for each trial rather than 1 oscillation?
Lab Calculation – Determining Gravity on Earth:
Recall Kepler’s 3rd law for planetary orbits:
P
2
=
a
3
Remember, the orbital period only depends on the length of the semi-major axis. An
oscillating pendulum obeys the following relationship:
T
=
2
π
√
L
g
Where T is the time for 1 oscillation in seconds, L is the length of the pendulum in meters,
and “g” is the acceleration due to gravity. This equation shows that a pendulum on earth
only varies with the Length of the pendulum! (assuming constant “g” anywhere on earth). A
longer pendulum string, and/or weaker gravity would make the oscillation time greater
according to this relationship.
1.
The equation for a pendulum above has been algebraically altered here for you to solve
for “g.”
-
L is your pendulum length in Meters (Convert your value from centimeters to meters by
dividing it by 100).
-
T is the average time for one
oscillation you determined above.
-
Your answer will have units of m/s
2
Use your data for the average time for 1 oscillation (T) and length of pendulum (L) to
solve for the acceleration due to gravity here on Earth.
Show your calculation for full credit!
g
=
4
π
2
(
47
)
(
1.415
)
2
=
926.71185
2.
Recall the textbook value for g, which is
9.81
m
/
s
2
. Calculate the percent error
between your answer and the textbook value.
862.06 m/s^2
3.
What possible sources of error did you have had in this experiment to explain why your
value may differ from the textbook value?
I used a different length of pendulum and was swinging it from places and directions.
4.
Suppose you wake up on an alien planet. You don’t know where, but gravity feels…
different. You build a pendulum from a bit of string 0.3 m long, and count that it takes
17.86 seconds to oscillate 10 times. What is the local gravity on this planet? Do you think
the planet is bigger or smaller than the Earth?
After calculating the equation, I have discovered the answer 25.61 m/a^2. Since the local gravity
is larger than earths means the alien planet is bigger than earth.
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