Student Exploration: Simple Harmonic Motion
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1 Nae: Date: Student Exploration: Siple Haronic Motion Vocabulary: controlled experient, haronic otion, oscillation, pendulu, period, sprin, sprin constant Prior Knowlede Questions (Do these BEFORE usin the Gizo.) 1. A bunee juper launches herself off a bride. How would you describe her otion? 2. A child oes to the playround and ets on a swin. How would you describe his otion? 3. What do the otions of the bunee juper and swiner have in coon? Gizo War-up Haronic otion is repeatin bac-and-forth or upand-down oveent. The Siple Haronic Motion Gizo allows you copare the haronic otions of a sprin and a pendulu. To bein, open the POINTER tray on the botto of the Gizo. Dra one arrow to the botto of the sprin so that the weiht just touches the tip of the arrow, as shown. Dra a second arrow so that the pendulu just touches the tip of the arrow when it swins to the left. 1. When the sprin touches the arrow, clic the reen button on the stopwatch. Count the oveents, or oscillations. Clic the reen button aain after the tenth oscillation. A. What is the tie for 10 oscillations of the sprin? B. Divide this tie by 10 to find the period of the sprin: 2. Clic the red button to reset the stopwatch. Use the sae procedure on the pendulu. What is the period of the pendulu?
2 Activity A: Period of a sprin Get the Gizo ready: Clic the red button to reset the stopwatch. Introduction: The sprin constant is a easure of the stiffness of a sprin. The reater the sprin constant, the harder it is to stretch or copress the sprin. The Siple Haronic Motion Gizo allows you to anipulate the ass on the end of the sprin (), the sprin constant (), and the ravitational acceleration (). Question: Which factors affect the period of a sprin? 1. Predict: Which factors do you thin will increase or decrease the period of a sprin? Which do you thin will have no effect on the period of a sprin? 2. Gather data: In a controlled experient, only one factor chanes at a tie. Controlled experients are a fair way to copare the effects of each variable on a syste. For each of the cobinations iven in the table below, easure the tie for 10 oscillations of the sprin and calculate the period. If necessary, reduce the Si. speed to iprove your accuracy. () (N/) (/s 2 ) Tie for 10 oscillations (s) Period (s) N/ 9.8 /s N/ 9.8 /s 2 () (N/) (/s 2 ) Tie for 10 oscillations (s) Period (s) N/ 9.8 /s N/ 9.8 /s 2 () (N/) (/s 2 ) Tie for 10 oscillations (s) Period (s) N/ 5.0 /s N/ 20.0 /s 2 3. Analyze: Exaine the results of each experient. A. Which factors affected the period of the sprin? B. Which factor had no effect on the period? C. What is the effect of quadruplin the ass? D. What is the effect of quadruplin the sprin constant?
3 Activity B: Period of a pendulu Get the Gizo ready: Reset the stopwatch. Set to 1.0 and to 9.8 /s 2. Introduction: The Siple Haronic Motion Gizo allows you to anipulate three variables for the pendulu: its ass (), its lenth (), and the ravitational acceleration (). Question: Which factors affect the period of a pendulu? 1. Predict: Which factors do you thin will increase or decrease the period of a pendulu? Which do you thin will have no effect at all? 2. Gather data: For each of the cobinations iven in the table below, easure the tie for 10 oscillations of the pendulu and calculate the period. If necessary, chane the Si. speed to iprove the accuracy of your easureents. () () (/s 2 ) Tie for 10 oscillations (s) Period (s) /s /s 2 () () (/s 2 ) Tie for 10 oscillations (s) Period (s) /s /s 2 () () (/s 2 ) Tie for 10 oscillations (s) Period (s) /s /s 2 3. Analyze: Exaine the results of each experient. A. Which factors affected the period of the pendulu? B. Which factor had no effect on the period? C. What is the effect of quadruplin the lenth? D. What is the effect of quadruplin the ravitational acceleration?
4 Activity C: Calculatin periods Get the Gizo ready: Reset the stopwatch. Set to 9.8 /s 2. Introduction: In activity A, you found that the period of a sprin depends only on its ass and the sprin constant. In activity B, you found that the period of a pendulu depends on its lenth and ravitational acceleration. Now, you will deterine forulas for the period of each object. Question: How are the periods of pendulus and sprins calculated? 1. Suarize: oo at your results fro prior activities. A. How did quadruplin affect the period of the sprin? B. How did quadruplin affect the period of the sprin? C. How did quadruplin affect the period of the pendulu? D. How did quadruplin affect the period of the pendulu? 2. Gather data: Use the Gizo to find the period of the sprin for three sets of and values. Then find the period of the pendulu for three sets of and values. Sprin () (N/) Tie for 10 oscillations (s) Period (s) Period Pendulu () (/s 2 ) Tie for 10 oscillations (s) Period (s) Period 3. Calculate: Calculate the ratios listed in the last three coluns of each table. (Activity C continued on next pae)
5 Activity C (continued fro previous pae) 4. Analyze: Exaine your data tables. A. No atter what values of and you used for the sprin, what is the ratio of the period to? B. No atter what values of and you used for the pendulu, what is the ratio of the period to? 5. Challene: Put toether what you learned in this activity to coe up with forulas for the period (T) of a sprin based on its ass () and sprin constant () and for the period of a pendulu based on its lenth () and ravitational acceleration (). T Sprin = T Pendulu = Have your teacher chec your forulas when they are coplete. 6. Apply: How lon would a pendulu on Earth (where = 9.8 /s 2 ) have to be to have the sae period as a sprin with a ass of 10.0 and a sprin constant of 25 N/? 7. Thin and discuss: Which is ore liely to eep accurate tie on the Moon, a sprin-driven watch or a pendulu cloc? Explain your answer.
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