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04.10 Radical Equation Activity
Transcript of 04.10 Radical Equation Activity
28 inch String
Materials Used Measure a length of string in inches. The exact length of the string is your decision; however, you will be required to cut the string a few times later in the procedure, so make sure that it is long. Record this measurement.
Tie one end of the string around the weight. Attach the other end of the string to a fixed object such as a table or a header of a doorway.
Lift the weight to a 45° angle and then let it go. Using the stopwatch, note the number of seconds it takes to complete one full swing back and forth. This is called the period of the pendulum. If the time is too fast for you to record, let the weight complete 10 full swings and divide the time by 10.
Record the string length and time in the chart
Cut the string length. Note the time it takes for the new pendulum to complete one period and record this time along with the new string length. Repeat this procedure until you have 5 different string lengths with five different times recorded.
In the following equation, T = 2 pi Square Root of 1/32 , l stands for the length of the string in feet. Convert your 5 string lengths into feet by dividing by 12 (12 inches = 1 foot). Then, substitute each of these values into the given equation and solve for T (time for one period). Use 3.14 for . Record these new measurements in the chart. Procedures Data Tables Side in Length One Period in Seconds 28
18 / 10 = 1.8
16 / 10 = 1.6
14 / 10 = 1.4
12 / 10 = 1.2
10 / 10 = 1.0
Data Table String length (in feet) One Period (in Seconds) 2.3
1 1.68 (approx) Seconds
1.45 (approx) Seconds
1.27 (approx) Seconds
History of Pendulum The word "pendulum" comes from the Latin word "pendulus" which means "hanging". A pendulum is an object hanging from a fixed point that when pulled back and released, swings freely. A pendulum swings due to gravity and inertia. Gravity pulls the pendulum toward the center of the Earth and inertia causes a moving pendulum to continue moving, or a pendulum at rest to remain still.
Galileo became interested in investigating pendulums as he watched a lamp swinging in a cathedral in Pisa, Italy while he was a university student. In 1602, Galileo began experimenting with pendulums and discovered that the period of a pendulum is not affected by the amplitude. In 1665, a Dutch scientist named Christiaan Huygens was the first person to create a clock using a pendulum.
Answers to Questions 1. The longer the string length the more periods there are.
2. The heavier the weight the more periods there are and more swings there will be.
3. The times are quite similar to the formula.
4. Key and Paperclip
Conclusion I thought this project was an interesting way to implement the pendulum. I learned the history of the pendulum and who discovered it and how it was used to create a clock.