Pendulums


At a most elementary description, a pendulum is an object that swings back and forth in a straight line from a fixed point. When observing a pendulum and the forces that affect it, one must observe the period of a pendulum. A pendulum’s period is the amount of time that it takes for the pendulum to swing from one end, to the next, and back. The period of a pendulum is caused by the force of gravity causing the gravitational potential energy of the weight to be turned into kinetic energy and back to gravitational potential energy and so on and so forth. Gravitational potential energy is a form of energy that is stored in objects that are not in contact with Earth that comes from the force of gravity acting upon it. Kinetic energy is a type of energy that comes from the motion of an object, in this case the swinging of the pendulum. [1] [2]
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Hypothesis


We hypothesize that the length of the rope from which the pendulum swings affects the period of a pendulum, which is the basis of our experiment. We observed through experimentation that the length of a pendulum does indeed affect its period by testing the formula that is the accepted equation for solving the period of a pendulum.
The formula to mathematically determine the period of a pendulum is:

external image 50e75c8fc81ed1e9c2f0d191772a2629.png

[3]

To see this formula in action, use the interactive animation below. Edit the length of the rope and enable the photogate timer to see the variations in the period of the pendulum.









Background


Pendula are some of the oldest representations of how Earth’s gravity works on objects. The pendulum has been seen through the ages and performed many different jobs over the years. Pendulums have been around for such a long time, the root of the word “pendulum” comes from the Latin “pendulus” meaning “hanging”. [4] [5]





Uses

Despite the long record of the pendulum, the pendulum is still prevalent in the world today. One notable example is that pendulums were used in old fashion clocks. Galileo first realized that pendulums could alleviate the time discrepancies in typical time-keepers of the age, but he never completed a design. Christiaan Huygens, however, is accredited with the creation of the pendulum clock in 1657. Although this clock had numerous discrepancies in its original design, the blueprints were amended to produce the most accurate time-keeper of its era. [6] [7]

Pendulums have even been used as forms of torture during the Inquisition. For execution, the accused would lay on their back as a swinging axe would slowly descend during its swing and eventually slice open their chests. This method was immortalized in Edgar Allen Poe's The Pit and the Pendulum. Despite their more gruesome points in history, pendulums are also said to have religious qualities.

Over the last few centuries not only have they been used to visualize the force of gravity but also to show how the Earth rotates throughout the day. Because of its exceptional demonstration of the force of gravity, the pendulum can be used in many experiments to represent the force of gravity at a specific time and place. When the pendulum is first started it is lifted above the ground giving the weight at the end gravitational potential energy then the weight is released and swings first converting the gravitational potential energy (G.P.E.) into kinetic energy and then back to G.P.E. and repeat.
[8] [9]







Pendulums in Nature


Most people never notice, but there are naturally occurring pendulums that can be seen everyday. Many of these naturally occurring pendulums appear in living organisms. The human arm is a prime example of a naturally occurring pendulum. It swings back and forth from a fixed point in a straight line unless the outside force of our muscles acts upon it. Our legs do not fit the mold quite as well, but the legs of many animals act as pendulums too. Take for example a horse’s legs. A horse’s legs are nothing more than two pairs of pendulums swinging opposite directions and this is very obvious if you slow down a video of a racing horse. Why is it that these pendulums appear in living organisms? Pendulums make use of gravity to create energy and if they are incorporated in to a body then it makes the body more efficient.






Types of Pendulums


Newton's Cradle
Newton's Cradle
When speaking about the common, everyday pendulum, the inventor cannot be specifically pinned down because pendulums have been around for countless centuries. However, when speaking about particular kinds pendulums, a specific inventor can usually be identified. Take for example Newton’s Cradle . Newton’s Cradle was invented by an unknown inventor in Canada and produced by Simon Prebbel but was named after Newton because the toy showed Newton’s third law in action. Newton’s Cradle is a set of spheres of equal mass suspended by two lines all of which are the same length. In simpler terms, it is a set of pendulums that are suspended by two lines instead of one and are set so that they come in contact with one another. This pendulum is now used as an example of momentum and the transfer of momentum from one object to another. Although this is its only scientific purpose, it is a fascinating toy for people of all ages.





Foucault Pendulum

Another example is the Foucault pendulum, the most well-known form of the modern pendulum. The Foucault pendulum was invented in 1851 by Jean Bernard Leon

Foucault of France(Foucault) who used his pendulum to illustrate the daily rotation of the Earth around its axis. Foucault showed signs of being a great inventor as a child. He studied medicine in college before changing his focus to physical science. Foucault realized that when he set this very large
pendulum into motion and let it continue to move throughout the day that it would continue to swing in a straight line while the Earth rotated beneath it. This experiment is often recreated using a bob or weight that is filled with sand and has a hole in the bottom so that the path it follows can be easily observed In addition to this Foucault is credited as the first person to photograph the sun, also the first person to measure the speed of light, and even credited with improvements on mirrors, telescopes, lenses and more. Over the years many scientists have used Foucault’s pendulum to study the Earth’s rotations just as Foucault did when he first made his discovery and even to determine values such as the mass of the Earth and the force of gravity at a specific point on the Earth. [10] [11] [12]





Experiment






Safety Information

While dealing with pendulums, it is pertinent that the location of the experiment is clear of obstacles and bystanders. A ladder is involved and therefore users should revert to the safety precautions that are posted on the ladder. A helmet would be beneficial to anyone standing near the trajectory of the pendulum.






Materials

  1. 3 PVC pipes 1.5 inches in diameter and in 10 feet long segments
  2. 8- 90 degree elbows
  3. 3- T joints
  4. 3 different bobs with varying weights and masses
  5. 30 feet of rope
  6. Gridded board with marked increments
  7. Camcorder and tripod
  8. Measuring tape
  9. Meter stick
  10. Duct tape
  11. Ladder
Diagramofcontraption.JPG






Procedure

Setup

  1. Measure and cut materials for contraption (see diagram)
    1. Cut 2 segments of PVC to ~10 cm (brick width) [segments 1a and 1b]
    2. Cut 4 segments of PVC to 0.75 meters [segments 2a, 2b, 2c, and 2d]
    3. Cut 2 segments of PVC to 0.4 meters [segments 3a and 3b]
    4. Cut 2 segments of PVC to 0.25 meters long [segments 4a and 4b]
    5. Cut 2 segments of PVC to 0.2 meters long [segments 5a and 5b]
    6. Cut 1 segment of PVC to 0.5 meters long [segment 6a]
  2. Construct contraption (see diagram for name references and orientation)
    1. Join 2b and 3a with a 90 degree elbow
    2. Join 3a with 2a with a 90 degree elbow
    3. Place 90 degree elbows on the top of 2a and 2b
    4. Set these pieces aside for later construction
    5. Join 1b and 4b with T joint
    6. Join 2c to remaining opening in T joint connecting 1b and 4b
    7. Join 4b and 5a with 90 degree elbow
    8. Join 5a and 5b with T joint
    9. Join 5b and 4a with 90 degree elbow
    10. Join 4a and 1a with T joint
    11. Join 2d to remaining opening in T joint connecting 4a and 1a
    12. Join 3b to 2d with 90 degree elbow
    13. Join 3b to 2c with 90 degree elbow
    14. Join 6a to T joint mentioned in step h
    15. Fit the contraption (except for piece mentioned in step d) around the brick wall of PCHS Science Building Atrium so that piece 6a is hanging out toward the middle of the building
    16. Take piece mentioned in step d and join it to the larger contraption so that it locks around the brick
    17. Ensure that the contraption is stable and duct tape it to the wall to ensure that it doesn’t slide
  3. Weigh each of the three weights and record them in a table
  4. Create smallest pendulum
    1. Cut a rope 1.3 meters long
    2. Tie weight to the bottom of the rope
    3. As the experiment calls for it, tie it to the contraption (on piece 6a) so that the length of the rope is approximately 1 meter long
    4. Measure actual length of rope and record in table
    5. Replicate the same steps with different sizes of weights as the experiment calls for it
  5. Create medium pendulum
    1. Cut a rope around 2.8 meters long
    2. Tie weight to the bottom of the rope
    3. As the experiment calls for it, tie it to the contraption (on piece 6a) so that the length of the rope is approximately 2.5 meters long
    4. Measure actual length of rope and record in table
    5. Replicate the same steps with different sizes of weights as the experiment calls for it
  6. Create largest pendulum
    1. Cut a rope around 5.3 meters long
    2. Tie weight to the bottom of the rope
    3. As the experiment calls for it tie it to the contraption (on piece 6a) so that the length of the rope is 5 meters long
    4. Measure actual length of rope and record in table
    5. Replicate the same steps with different sizes of weights as the experiment calls for it
  7. Set up the camera and tripod at an angle where the entire period of the pendulum is seen




Experiment

  1. Perform the following instructions 9 times (3 different weights on smallest pendulum, 3 different weights on medium pendulum, 3 different weights on largest pendulum)
    1. Ensure that the pendulum is in order as directed in the set up
    2. Set camera to recording mode
    3. Hold weight out as far as rope will allow to either the right or left of the contraption
    4. Release the weight to let the pendulum swing
    5. Allow the pendulum to swing through several periods
    6. Stop recording
  2. Upload videos
  3. For each video, determine the time it takes to complete three periods and divide that time by three
  4. Record the average time of the periods in the table




Data


Lenght of Rope (meters)
Weight of Mass (grams)
Observed Avg Period (seconds)
Period Derived From Equation (seconds)
3.78
600
3.93
3.90
3.78
300
4.00
3.90
3.78
150
4.03
3.90
2.04
600
2.80
2.87
2.04
300
3.00
2.87
2.04
150
2.93
2.87
1.04
600
2.53
2.05
1.04
300
2.47
2.05
1.04
150
2.47
2.05









Summary of Results:

We concluded that although there were some discrepancies, there is enough data to make a reasonable assertion that the period of a pendulum is indeed affected by the length of the rope. Our data supports the accepted formula for the period of a pendulum.






Discussion


We added differences of weights as another variable to see if it affected the swing. There was no trend in the data to suggest that there was a relation to the weight of the bob to the period of the pendulum.
We could have improved our project by changing the lengths of some of the parts. 6a did not need to be so long, but it did not affect the outcome of the experiment.
We could not get the smallest pendulum would not swing in a straight path. While we looked for every possible flaw as to why this was happening, we could come up with no reasonable conclusion behind the skewed path. This incorrect path may be the reason that our data for the smallest pendulum is the farthest off from the expected period. Our data, however, is close enough to notice trends.


































References


  1. ^ Beynon, Z. (1999). What is a pendulum? Retrieved from California Academy of
    Sciences website: California Academy of Sciences
  2. ^ Kurtus, R. (2009, October 17). Pendulum exhibits periodic motion. Retrieved from
    School For Champions
  3. ^




    Beynon, Z. (1999). What is a pendulum? Retrieved from California Academy of
    Sciences website: California Academy of Sciences
  4. ^ Beynon, Z. (1999). What is a pendulum? Retrieved from California Academy of
    Sciences website: California Academy of Sciences
  5. ^ pendulum. (n.d.). Dictionary.com Unabridged. Retrieved May 12, 2011, from Dictionary.com website: Dictionary.com
  6. ^ Usher, A. P. (n.d.). A history of mechanical inventions (Harvard University
    Press & Dover, Eds., 1988 ed.). (Original work published 1929) Retrieved
    from A History of Mechanical Inventions
  7. ^ Beynon, Z. (1999). What is a pendulum? Retrieved from California Academy of
    Sciences website: California Academy of Sciences
  8. ^
    Baker, G. L., & Blackburn, J. A. (2005). The pendulum: a case study in physics
    (Oxford University Press, Ed.). Retrieved from [[http://books.google.com/ books?id=PePX073k_qsC&dq=pendulums+in+the+inquisition&source=gbs_navlinks_s|books.google.com]]
  9. ^ Baker, G. L., & Blackburn, J. A. (2005). The pendulum: a case study in physics(Oxford University Press, Ed.). Retrieved from books.google.com
  10. ^




    University of Louisville. (n.d.). The Foucault pendulum. In The Foucault
    Pendulum. Retrieved from University of Louisville website:
    The Foucault Pendulum
  11. ^ Palmer, G. (2010, September 10). Different types of pendulums. Retrieved April/
    May, 2011, from eHow website: Different Types of Pendulums
  12. ^ Beynon, Z. (1999). What is a pendulum? Retrieved from California Academy of
    Sciences website: California Academy of Sciences