2016 AP Physics Unit 6 Oscillations and Waves.notebook December 09, 2016
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1 AP Physics Unit Six Oscillations and Waves 1
2 2
3 A. Dynamics of SHM 1. Force a. since the block is accelerating, there must be a force acting on it b. Hooke's Law F = kx F = force k = spring constant x = distance spring is stretched or compressed c. this force is always trying to return the mass to the equilibrium position 3
4 A. Dynamics of SHM 1. Force d. Example a 12 cm long spring has a spring constant of 400 N/m. How much force is required to stretch the spring to a length of 14 cm? 4
5 A. Dynamics of SHM 2. Amplitude a. amplitude is the maximum displacement from the equilibrium position b. at the equilibrium position, the amplitude is 0 5
6 B. SHM in terms of energy 1. elastic potential energy a. a stretched or compressed spring stores energy as work is done to stretch or compress the spring b. U s = 1/2 kx 2 U s = spring potential energy k = spring constant x = position 6
7 B. SHM in terms of energy 1. elastic potential energy c. Example A 0.5 kg block oscillates on a spring whose spring constant is 500 N/m. The amplitude of the oscillations is 4.0 cm. Calculate the maximum speed of the block. 7
8 B. SHM in terms of energy 1. elastic potential energy c. Example A 2.0 kg block is attached to an ideal spring with a spring constant of 500 N/m. The amplitude of the oscillations is 8.0 cm. Determine the total energy of the system and the speed of the block when it is 4.0 cm away from its equilibrium position. 8
9 B. SHM in terms of energy 1. elastic potential energy c. Example A 8.0 kg block is attached to an ideal spring with a spring contant of 500 N/m. The block is at rest at its equilibrium position. An impulse force acts on the block, giving it an initial speed of 2.0 m/s. Find the amplitude of the resulting oscillations. 9
10 B. SHM in terms of energy 2. Period and Frequency a. period = number of seconds per complete cycle of oscillations b. frequency = number of complete oscillations per second c. period = 2π m/k m = mass of object k = spring constant 10
11 B. SHM in terms of energy 2. Period and Frequency d. Examples A block oscillating on the end of a spring moves from its position of maximum stretch to maximum compression in 0.25 s. Determine the period and frequency of this motion. 11
12 B. SHM in terms of energy 2. Period and Frequency d. Examples A student observing an oscillating block counts 45.5 cycles of oscillations in one minute. Determine the frequency in hertz and the period in seconds. 12
13 B. SHM in terms of energy 2. Period and Frequency d. Examples A 2.0 kg block is attached to a spring with a spring constant of 300 N/m. What is the frequency and period of the oscillations. 13
14 B. SHM in terms of energy 2. Period and Frequency d. Examples 14
15 II. Spring/Block Vertical Motion A. Consider a spring suspended from the ceiling. A block is attached to it and the spring stretches a certain distance, d. At this point the spring is in equilibrium B. at this point, kd = mg C. now the vertical spring can be treated the same as a horizontal spring 15
16 II. Spring/Block Vertical Motion D. Examples A 1.5 kg block is attached to the end of a vertical spring with a spring constant of 300 N/m. After the block comes to rest, it is pulled down a distance of 2 cm and released. 1. what is the frequency of the oscillations? 2. what are the maximum and minimum amounts of stretch of the spring during the oscillations? 16
17 III. Pendulums A. a pendulum is a mass attached to a string that swings without friction about a vertical equllibrium position B. the restoring force is F = mg sinө C. frequency of the oscillations of a pendulum D. period of the oscillations of a pendulum 17
18 IV. Waves A. Transverse traveling waves 1. the waves oscillates perpendicular to its direction of travel. 2. crests points of maximum vertical displacement from the equilibrium position 3. troughs points of maximum vertical displacement from the equilibrium position 4. wavelength distance between consecutive troughs or crests 5. amplitude maximum displacement from the equilibrium position 6. the velocity of a wave is determined by the wavelength and the frequency of the wave v = λf v = velocity (m/s) λ = wavelength (m) f = frequency (Hz) 18
19 IV. Waves B. Big Wave Rules 1. the speed of a wave is determined by the type of wave and the characteristics of the medium. 2. when a wave passes into another medium, its speed changes but its frequency does not. 19
20 IV. Waves C. superposition of waves 1. when 2 waves meet, the displacement at any point of the medium is the sum of the displacements due to the individual waves. 2. constructive interference if the displacements of two waves have the same sign, the combined wave will have a greater displacement 3. destructive interference if the displacements of the two waves have opposite signs, the combined wave will have a smaller displacement 4. in phase waves will constructively interfere 5. out of phase waves will destructively interfere 20
21 IV. Waves D. Standing Waves 1. if the string is attached to the wall, and a wave is sent down the string, it will strike the wall and bounce back. If the string is just the right length, it will produce a standing wave where the crests and troughs do not travel down the string 2. standing waves have two landmarks called nodes and antinodes 3. nodes and antinodes always alternate along the standing wave and are equally spaced apart at a distance of 1/4 the wavelength 21
22 IV. Waves E. Sound Waves 1. produced by a vibrating object that causes pressure variations in the medium 2. compressions areas in the medium where the particles are pressed together 3. rarefactions areas in the medium where the particles are spread out 4. sound waves are longitudinal waves because the medium and the wave travel in the same direction 22
23 IV. Waves F. Sound level 1. referred to as intensity, it is measured in decibels 2. the greater the amplitude the greater the intensity 23
24 IV. Waves G. Doppler Effect 1. an apparent change in frequency due to the motion of two objects 2. as the source of the sound gets closer to the detector, the frequency increases 3. as the source of the sound moves away from the detector, the frequency decreases 24
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