2 Springs Hooke’s Law F = -kx Potential Energy in a Spring PEsp=1/2 kx2 The force exerted by a spring is equal to the spring constant times the distance the spring is compressed or stretched from its equilibriumPotential Energy in a Spring PEsp=1/2 kx2
3 Spring Practice Problem A spring stretches by 18 cm when a bag of potatoes weighing 56 N is suspended from its end.Determine the spring constantHow much elastic potential energy is stored in the spring when it is stretched this far?
4 Periodic MotionEquilibrium – When the forces on an object are balanced or equal zero and the acceleration is zero.Periodic Motion – Motion that repeats in a regular cycleSimple harmonic motion – when the force on an object is directly proportional to the displacement of the object
6 Periodic Motion Period – (T) time for one complete cycle Amplitude – maximum distance that the object moves from equilibrium (measured in radians or meters)Frequency – (f) number of cycles or vibrations per unit of time (measured in hertz, Hz = s-1)
7 Pendulums Period of a Pendulum Example: A pendulum with a length of 36.9 cm has a period of 1.22 s. What is the acceleration due to gravity at the pendulum’s location
8 Springs Period of Spring Example: The body of a 1275 kg car is supported on a frame by four springs. Two people riding in the car have a combined mass of 153 kg. When driven over a pothole, the frame vibrates with a period of s. For the first few seconds, the vibration approximates SHM. Find the spring constant of a single spring.K=2.00 X 104 N/m
9 Resonance Swinging – How do you make yourself go higher? Occurs when small forces are applied at regular intervals to a vibrating or oscillating object and the amplitude of the vibration increases.
10 ResonanceMany objects have a natural frequency – vibrates in a regular pattern.Resonance occurs when whenever a sound wave has the same frequency as the natural frequency of an object. The sound will cause the object with the same natural frequency to vibrate.
11 Waves A disturbance that carries energy through matter or space. Types of Mechanical WavesTransverse WavesLongitudinal WavesSurface WavesMechanical Waves – Waves that require a medium.Medium – A material that a disturbance travels
12 Wave Pulse – a single bump or disturbance that travels through a medium
13 Periodic Wave – When a wave moves at the same rate
14 Longitudinal Waves (think slinky) Longitudinal Waves – disturbance is in the same direction or parallel to, the direction of the wave’s motion.Transverse Waves (think rope)Transverse Wave – one that vibrates perpendicular to the direction of the wave’s motion
15 Longitudinal waveOn a longitudinal wave the area squeezed together is called the compression. The areas spread out are called the rarefaction.The wavelength is the distance from the center of one compression to the center of the next compression.
16 Surface Waves (think water) Surface Waves – Lake or ocean; Longitudinal at the surface, the particles move in a direction that is both parallel and perpendicular to the direction of wave motion.
17 Measuring a WaveWavelength (l) – shortest distance that the wave pattern repeats OR distance from peak to peak or trough to troughPhase – Same displacement and same velocityA crest and trough are exactly 180o out of phase.Period – time for one wavelength (T)Frequency - # of cycles per unit time (Hz)
18 Measuring a Wave Speed – displacement of wave peak over time. Amplitude – the distance of the wave peak/trough to equilibriumCrest – High Point of the waveTrough – Low Point of the wave
20 Wave AmplitudeThe amplitude of a wave is directly related to the energy of a wave.The amplitude of a longitudinal wave is determined by the closeness of the longitudinal waves. The closer the longitudinal waves and the farther the rarefaction lines.
29 1. If you moved the slider to the far right, doubling the amplitude, the period would be… twice as big1/2 as bigStays the same1/4 times as bigNot enough information to decideC they are independentFrom Pollock:
30 2. What will this wave look like after it reflects? B.c.D.Fixed endC
31 3. What will this wave look like after it reflects? B.c.D.Loose endB
32 Amp time t1 t2 t3 t4 4. What is the period of this wave? t1 t2 t2-t1 None of the aboveAmptimet1t2t3t4DAdapted From Pollock at CU 1240 courseHis notes follow:Chris said that from here on out, participation was dwindling, I may have overdosed on CT’s today? But, this one got 85% correct, at least!
33 What is the wavelength (“”)? 5.The picture shows “displacement as a function of location along a string”What is the wavelength (“”)?ABCDE none of theseAAdapted from From Pollock at CU 1240 courseRemember X axis is position not timeFundamentals of waves
34 6.The picture shows “displacement as a function of location along a string” What is the amplitude?ABCDE none of theseCAdapted from From Pollock at CU 1240 courseRemember X axis is position not timeFundamentals of waves
35 Not enough information 7. Looking at the following waveform, what is the period? assume it repeats itself over and over12time (sec)1 sec2 sec1 m/s2 m/sNot enough informationBAdapted From Pollock at CU 1240 course
36 Not enough information 8. Looking at that same wave,what is its speed?12Time (sec)1/2 m/s2 m/s5 m/s20 m/sNot enough informationE.Adapted From Pollock at CU 1240 courseHis notes follow:Obviously important that “not enough info” occasionally be the RIGHT answer! (80% correct)Now given that λ=10 m what is the speed ofthe wave?
37 E) None of the above/not enough info/not sure CT9. The wavelength, λ, is 10 m. What is the speed of this wave?Time (sec)11 m/sjust under 7 m/sC) 10 m/sD) 15 m/sE) None of the above/not enough info/not sureD 10/(2/3)Adapted From Pollock at CU 1240 courseHis notes follow:Propaganda about talking to neighbors, kind of needed/helpful on a day like today with so many CT’s.Answer d only got 49% of vote! So, some “hints” might be appropriate here…
38 10. Which one of the following is most likely to be impossible? A. Transverse waves in a gasB. Longitudinal waves in a gasC. Transverse waves in a solidD. Longitudinal waves in a solidE. They all seem perfectly possibleEFrom Pollock at CU 1240 courseHis notes follow:Last year Everyone got this wrong. It’s a good question, and serves to stimulate really good conversation /discussion. (E was 45%, but C and D both popular) A good one to talk about “why not”.This year we did a little better (30% said A, many of the rest said E)Ran out of time, but ended here.
39 Not enough information to decide 11. If you moved the frequency slider to the left so that it changed from 500 to 250 the period would betwice as big1/2 as bigStays the same1/4 times as bigNot enough information to decideAAdapted From Pollock at CU 1240 course
42 What is diffraction?Diffraction occurs when an object causes a wave to change direction and bend around it.
43 Diffraction also occurs when passing through a small opening Diffraction also occurs when passing through a small opening. They diffract and spread out as they pass through the hole.
44 Standing WavesA wave pattern that results when two waves of the same frequency, wavelength, and amplitude travel in opposite directions and interfere
45 Standing WavesNode – a point in a standing wave that always undergoes complete destructive interference and therefore is stationaryAntinode – a point in a standing wave, halfway between two nodes, at which the largest amplitude occurs