Chapter 6: Simple Harmonic Motion Gizmo

Student Exploration: Simple Harmonic Motion Make sure you use a name your instructor can recognize when you log in and don’t forget to do the 5 question quiz at the end of the Gizmo. They are part of your mark. Vocabulary: controlled experiment, harmonic motion, oscillation, pendulum, period, spring, spring constant Prior Knowledge Questions (Do these BEFORE using the Gizmo.) A bungee jumper launches herself off a bridge. How would you describe her motion? A child goes to the playground and gets on a swing. How would you describe his motion? What do the motions of the bungee jumper and swinger have in common? _____________ Gizmo Warm-up Harmonic motion is repeating back-and-forth or up-and-down movement. The Simple Harmonic Motion Gizmo™ allows you compare the harmonic motions of a spring and a pendulum. To begin, open the TOOLS tab on the bottom right and drag one arrow to the bottom of the spring so that the weight just touches the tip of the arrow, as shown. Drag a second arrow so that the pendulum just touches the tip of the arrow when it swings to the left. When the spring touches the arrow, click the green button on the stopwatch. Count the movements, or oscillations . Click the green button again after the tenth oscillation. What is the time for 10 oscillations of the spring ? _______ _________________ Divide this time by 10 to find the period of the spring: _______ _________________ Click the red button to reset the stopwatch. U se the same procedure on the pendulum . Activity A: Get the Gizmo ready: Click the red button to reset the stopwatch. Period of a spring Introduction: The spring constant is a measure of the stiffness of a spring. The greater the spring constant, the harder it is to stretch or compress the spring. The Simple Harmonic Motion Gizmo allows you to manipulate the mass on the end of the spring (m), the spring constant (k), and the gravitational acceleration (g). Question: Which factors affect the period of a spring? Predict : Which factors do you think will increase or decrease the period of a spring? Which do you think will have no effect on the period of a spring? Gather data : In a controlled experiment , only one factor changes at a time. Controlled experiments are a fair way to compare the effects of each variable on a system. m (kg) k (N/m) g (m/s2) 0.5 kg 100 N/m 9.8 m/s2 2.0 kg 100 N/m 9.8 m/s2 m (kg) k (N/m) g (m/s2) 1.0 kg 50 N/m 9.8 m/s2 1.0 kg 200 N/m 9.8 m/s2 Time for 10 oscillations (s) Period (s) Time for 10 oscillations (s) Period (s) m (kg) k (N/m) g (m/s2) 1.0 kg 100 N/m 5.0 m/s2 1.0 kg 100 N/m 20.0 m/s2 Time for 10 oscillations (s) Period (s) Analyze : Examine the results of each experiment. Which factors affected the period of the spring? _____________________________ Which factor had no effect on the period? __________________________________ What is the effect of quadrupling the mass? ________________________________ What i s the effect of quadrupling the spring constant? _____________________ __ _ Get the Gizmo ready: Reset the stopwatch. Set Activity B: L to 1.0 m and Period of a pendulum g to 9.8 m/s 2 . Introduction: The Simple Harmonic Motion Gizmo allows you to manipulate three variables for the pendulum: its mass (m), its length (L), and the gravitational acceleration (g). Question: Which factors affect the period of a pendulum? Predict : Which factors do you think will increase or decrease the period of a pendulum? Which do you think will have no effect at all? Gather data : For each of the combinations given in the table below, measure the time for 10 oscillations of the pendulum and calculate the period. If necessary, change the Sim. speed to improve the accuracy of your measurements. m (kg) L (m) g (m/s2) 0.5 kg 1.0 m 9.8 m/s2 2.0 kg 1.0 m 9.8 m/s2 m (kg) L (m) g (m/s2) 1.0 kg 0.5 m 9.8 m/s2 1.0 kg 2.0 m 9.8 m/s2 Time for 10 oscillations (s) Period (s) Time for 10 oscillations (s) Period (s) m (kg) L (m) g (m/s2) 1.0 kg 1.0 m 5.0 m/s2 Time for 10 oscillations (s) Period (s) 1.0 kg 1.0 m 20.0 m/s2 Analyze : Examine the results of each experiment. Which factors affected the period of the pendulum? __________________________ Which factor had no effect on the period? __________________________________ What is the effect of quadrupling the length? _______________________________ What i s the effect of quadrupling the gravitational acceleration? ________________ Get the Gizmo ready: Reset the stopwatch. Activity C: Set g Calculating periods to 9.8 m/s 2 . Introduction: In activity A, you found that the period of a spring depends only on its mass and the spring constant. In activity B, you found that the period of a pendulum depends on its length and gravitational acceleration. Now, you will determine formulas for the period of each object. Question: How are the periods of pendulums and springs calculated? Summarize : Look at your results from prior activities. How did quadrupling m affect the period of the spring? ___ ____________________ How did quadrupling k affect the period of the spring? ________________________ How did quadrupling L affect the period of the pendulum? _____________________ How did quadrupling g affect the period of the pendulum? _____________________ Gather data : Use the Gizmo to find the period of the spring for three sets of m and k values. Then find the period of the pendulum for three sets of L and g values. Spring m Time for Period k( ( 10 Period word/embeddings/oleObject2.bin> ) word/embeddings/oleObj ) (s) Time for Period g L 10 Period word/embeddings/oleObject5.bin> ) word/embeddings/oleOb (s) Think and discuss : Which is more likely to keep accurate time on the Moon, a spring-driven watch or a pendulum clock? Explain your answer.