1. a) A flag waving in the breeze flaps once each s. What is the period and frequency of the flapping flag?

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1 PHYSICS 20N UNIT 4 REVIEW NAME: Be sure to show explicit formulas and substitutions for all calculational questions, where appropriate. Round final answers correctly; give correct units. Be sure to show your work for all calculational problems. This unit contains considerable content knowledge of physics, terms, etc. that may not be completely covered by this review. Be sure to review the text, quizzes, and your outline notes and questions in preparation for the unit exam. 1. a) A flag waving in the breeze flaps once each s. What is the period and frequency of the flapping flag? b) A small hummingbird flaps its wings 70 times per second. What is the period of the wingbeats? c) An electric motor turns at 3600 revolutions per minute. What is the period and frequency of the motor s rotation? d) A weight on a spring bounces from its lowest point to its highest point in a time of s. What is the period and frequency of the bouncing weight? 2. An elastic band is suspended vertically and stretched by adding an increasing number of masses to the end of the band. The weight added (force stretching the band) and the corresponding stretch of the band are shown in the chart below. a) Plot a graph of displacement against force on the axis below. For convenience, use displacement as the independent variable. Disp. (cm) Force (N) b) Through what range of displacement does this rubber band obey Hooke s Law? c) Find the spring constant for the band through the displacement where it obeys Hooke s Law. d) How much energy is stored in the band when it is stretched by 10.0 cm? e) The band is stretched to 8.0 cm and used to project a 55.0 g paper ball horizontally. If 75% of the energy stored in the stretched band is transferred into kinetic energy of the paper ball, what is the ball s initial speed? PHYSICS 20N UNIT 4 REVIEW REVISED FALL 2007 PAGE 1

2 3. A student investigates simple harmonic motion using a meter stick and a weight. The student tapes the weight to the end of the meter stick, then clamps the meter stick, on edge, to a counter. She then pulls the meter stick sideways, and monitors its vibratory motion using a motion sensor and computer. The sketch at right shows the meter stick viewed from above. Position x Motion sensor Centre position Vibrating meter stick a) As it moves from the extreme position at x to the extreme position at y, where does the vibrating meter stick have the greatest speed? The greatest acceleration? Position y Weight Clamp b) Where does the meter stick experience the greatest restoring force? c) Where does the meter stick have the largest amount of kinetic energy? The largest amount of spring potential energy? d) If energy losses in this system are ignored, how does the total mechanical energy of the meter stick change? e) If this meter stick does vibrate with SHM, how should the restoring force change as the stick moves away from the centre position? f) Sketch the likely shape of graphs for speed and acceleration that will be displayed by the connected computer, for one complete vibration. Clearly show positions x and y and the centre position on your graph sketches. PHYSICS 20N UNIT 4 REVIEW REVISED FALL 2007 PAGE 2

3 4. The sketch at right shows a simple spring-mass system. If the mass is 1.50 kg and the spring has a constant of 40.0 N/m, find the period and frequency of the vibrating system. 5. A spring-mass system with the same mass as the one in the preceding question, but using a different spring, moves from the extreme left to the extreme right in a time of 1.30 s. What is the constant for the spring? 6. A pendulum with a length of 0.65 m completes 12 complete oscillations. How much time does this require? 7. Find the length of a pendulum that has a frequency of Hz. 8. A pendulum-based device is used to measure the local gravitational acceleration on a mountaintop. If the pendulum has a length of 1.20 m and a period of 2.21 s, what value of g is found? 9. On a distant planet (not earth), an object dropped from rest requires s to fall m. Find the period of a 1.50 m long pendulum on this planet. (Hint: use the motion information to first find g.) PHYSICS 20N UNIT 4 REVIEW REVISED FALL 2007 PAGE 3

4 10. Siobhan s uncle pushes her on a swing. When her uncle pushes once every 2.0 s, the swing moves back and forth but doesn t go very high. When the uncle changes the time between pushes to 2.5 s, the swing moves easily to a greater height. What is the resonant frequency of the swing? 11. In the preceding question, Siobhan s uncle continues to push at the same rate, but pushes with more force. What motion characteristic of the swing will change? 12. Label the following on the sketch at right. a) crest b) trough c) wavelength d) points with same phase e) points with opposite phase f) amplitude 13. The sketch to the right shows a straight water wave striking a barrier in a ripple tank. Draw the reflected wave; label angles that show how the wave obeys the law of reflection. Incident wave 14. The sketch to the right shows a circular water wave generated at point S as part of the wave strikes a straight barrier. Sketch how the wave reflects. S 15. A wave moves along a rope and reflects from a fixed end, as shown in the sketch. Sketch the reflection. What type of wave is shown? How does the short section of rope labeled x move as the reflected wave passes by? x PHYSICS 20N UNIT 4 REVIEW REVISED FALL 2007 PAGE 4

5 16. What type of waves are shown on the coil spring sketched at right? Label a compression, a rarefaction, and a wavelength. Describe the motion of the short section of spring labeled at x as the waves pass by. x 17. A student generates waves in a coil spring by moving the end of the spring from side to side at a rate of two complete over-and-back motions each second. The motion of the end of the spring creates periodic waves with a wavelength of 45.0 cm. a) What type of wave is produced? What other motion would produce the same kind of wave? b) What is the speed of the periodic waves? c) The three main characteristics of waves are frequency, speed and wavelength. Two of these characteristics are determined by the wave source and medium; the third is then set by the values of the other two. Using the description above, explain how each wave characteristic could be changed. d) If the student continues to move the end of the spring at the same rate but stretches the spring more tightly, what would change? 18. Periodic waves in a ripple tank have a wavelength of 2.50 cm and are generated with a period of s. How fast do the waves move across the tank? 19. Sound waves with a frequency of 850 Hz travel through air at 335 m/s. What is their wavelength? 20. Pressure or P-waves in an earthquake travel through the earth s crust at 5.00 km/s. A monitoring station is located 2500 km from the source of the earthquake. a) How long will it take for the first P-wave to reach the monitoring station? PHYSICS 20N UNIT 4 REVIEW REVISED FALL 2007 PAGE 5

6 b) If the P-waves are generated with a frequency of 3.00 Hz, what is the wavelength of the waves? 21. What are the shortest three lengths of a pipe (closed at one end) that will resonate with a 256 Hz tuning fork? Assume the speed of sound to be 330 m/s for this question. 22. A loudspeaker produces sound with a frequency of 1100 Hz; the sound resonates when the speaker is placed above a tube open at both ends that is 15.2 cm long. a) Find the speed of sound. b) Two longer pipes of the same diameter also resonate with this frequency. What are their likely lengths? 23. The sketch to the right shows a standing wave produced by moving the end of a coil spring completely up and down 20 times in 10 s. a) Label nodal and antinodal points on the sketch. Name the type of interference that occurs at each point. 6.0 m b) Find the speed of the waves on the spring. PHYSICS 20N UNIT 4 REVIEW REVISED FALL 2007 PAGE 6

7 24. Use the principle of superposition to sketch the wave that results from the interference of each pair of waves shown. 25. The sketch to the right shows a moving tuning fork; as it moves horizontally at 3.00 m/s, the fork is vibrating at 512 Hz and producing sound. The speed of sound is 343 m/s. a) Which way is the fork moving? b) Is the pitch higher for the sound reaching the boy or the girl? Why? Tuning fork Sound waves c) What is this effect called? d) Find the frequency of the sound as it reaches the boy. e) Find the frequency of the sound as it reaches the girl. 26. How does a shock wave occur? PHYSICS 20N UNIT 4 REVIEW REVISED FALL 2007 PAGE 7

8 27. A two-source interference pattern in a ripple tank is shown at right. a) Name the lines indicated at I and II; explain how each is formed. I II b) What alternate names can be given to the lines at I and II? Incident wave S 1 S 2 NUMERICAL AND SHORT ANSWERS 1. a) s; 2.50 Hz b) s c) s; Hz d) s; 1.43 Hz 2. b) 0-12 cm c) 25 N/m d) 0.13 J e) 1.5 m/s 3. a) centre; x or y b) x or y c) centre; x or y d) constant e) F α x s; Hz N/m s m m/s s Hz 11. amplitude 15. transverse 16. longitudinal 17. a) transverse b) 90.0 cm/s d) speed increases m/s m 20. a) 500 s b) 1.67 km m; m; 1.61 m 22. a) 334 m/s b) m; m 23. b) 8.0 m/s 25. a) left b) girl c) Doppler Effect d) 508 Hz e) 517 Hz 27. a) antinodal; nodal b) second order maximum second order minimum PHYSICS 20N UNIT 4 REVIEW REVISED FALL 2007 PAGE 8