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2011 Honors Notes Chapter 13 Vibrations and Waves 1. How does the force on a spring is related to the distance a spring is stretched? a. What is Hooke’s Law? b. If a spring is cut in half, what happens to its spring constant? c. If you know the force on the block below, how can you determine the acceleration of the block? Is it constant? d. For each of the pictures draw the force and acceleration directions. Label the equilibrium point and the amplitude. In which picture is the force maximum? Minimum? 2011 Honors Notes Chapter 13 2. What is the period of the motion? a. Through what total distance does the block travel in one period? A/2 A 2A 4A 3. What is the frequency of the motion? 4. The motion of Earth going around the Sun is periodic with a period of 1 year. Is this motion simple harmonic? 5. How is it possible to find the work done by a variable force? a. What is the potential energy stored by a spring? 2011 Honors Notes Chapter 13 b. What does the potential energy change to as the block moves? c. Is mechanical energy conserved in this system? End 0 midpoint 0 End 0 Fill in the chart with constant, max or zero Velocity Kinetic Potential Force Acceleration ETotal Energy energy mid End 6. Find the velocity as a function of the position. 2011 Honors Notes Chapter 13 7. A mass of 0.5 kg oscillates with amplitude of 0.2 meters on a horizontal spring with spring constant of 100 N/m. a. What is the total energy? b. What is the velocity at a position of 0.1 meters from equilibrium? 8. A slingshot consists of a light leather cup, containing a stone that is pulled back against two parallel rubber bands. It takes a force of 15 N to stretch either one of these bands 1.0 cm. a. What is the potential energy stored in the two bands together when a 50 g stone is placed in the cup and pulled back 0.20 m from the equilibrium position? b. With what speed does the stone leave the slingshot? 9. At an outdoor market, a bunch of bananas is set into oscillatory motion with an amplitude of 20.0 cm on a spring with a spring constant of 16.0 N/m. It is observed that the maximum speed of the bunch of bananas is 40.0 cm/s. What is the weight of the bananas in Newton’s? 2011 Honors Notes Chapter 13 10. Comparing simple harmonic motion with uniform circular motion a. Draw a clock hand at 1 o’clock. b. Draw a line from the end of the clock hand to the x axis. Describe the motion of the point on the x-axis as the clock hand travels counterclockwise. c. Relate the amplitude (the length of the clock hand) of the motion to the position of the point on the x axis. d. Draw a graph of the position of the point on the x axis as a function of time. xmax x t ½T T -xmax - e. Write the equation for the two motions given in class. 2011 Honors Notes Chapter 13 f. What if the blocks don’t travel at the same angular velocity? g. Substitute angular displacement to relate to angular velocity/frequency. Substitute in for angular velocity/frequency so that it is terms of period. h. Write the equations for the two motions given in class. i. What if the motion starts with an angular displacement? j. Write the equations for the two motions given in class. 2011 Honors Notes Chapter 13 11. The position of a 0.2 kg object attached to a spring is described by x= (0.5m) cos(0.5πt+π/2) a. What is the position of the object at 2 seconds? At 0 seconds? b. What is the spring constant? c. What is the frequency? 12. Start with the velocity equation as a function of position. Find velocity as a function of time. a. Graph velocity as a function of time. vmax v t ½T T -vmax 13. How is angular velocity/frequency related to the spring constant and mass? 2011 Honors Notes Chapter 13 14. Find the period of simple harmonic motion. 15. Find the period of a simple pendulum. 16. A pendulum clock that works perfectly on Earth is taken to the Moon. Does it run fast or slow there? 2011 Honors Notes Chapter 13 17. A simple pendulum is 5.00m long. a. What is the period of simple harmonic motion for this pendulum if it is located in an elevator accelerating upward at 5.00 m/s2? b. What is the period if the elevator is accelerating downward at 5.00 m/s2? 18. What is a wave? 19. What is a medium? 20. What is an example of waves transferring energy? 21. Types of Waves Mechanical Waves Electromagnetic waves Mediums What oscillates? Examples 2011 Honors Notes Chapter 13 22. Types of Mechanical Waves Longitudinal Waves Transverse waves Mediums Direction of oscillations Examples 23. Describing waves a. Frequency b. Amplitude c. Wavelength d. Wave speed 24. How are the terms above related? 2011 Honors Notes Chapter 13 25. In a long line of people waiting to buy tickets at a movie theater, when the first person leaves, a pulse of motion occurs as people step forward to fill in the gap. The gap moves through the line of people. What determines the speed of this pulse? Is it transverse or longitudinal? 26. Speed of waves on strings 27. In mechanics, massless strings are often assumed. Why is this not a good assumption when discussing waves on strings? 28. A simple pendulum consists of a ball of mass 5.00 kg hanging from a uniform string of mass 0.060 kg and length L. If the period of oscillation for the pendulum is 2.00s, determine the speed of a transverse wave in the string when the pendulum hangs vertically. 2011 Honors Notes Chapter 13 29. Interference of Waves a. Constructive interference b. Destructive interference 30. Reflection of waves a. What happens at a fixed end? b. What happens at a free end?

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posted: | 9/16/2011 |

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