Exploring Jupiter's Moon Io: Motion, Waves, and Damped Systems in Physics
In this lecture, Professor Lee Carkner delves into the motions of celestial bodies, particularly focusing on Jupiter's moon Io. Students will learn how Io's speed across the sky varies based on its distance from Jupiter and explore the principles behind damped systems and energy loss. The lecture also covers different wave types—transverse and longitudinal—and their characteristics, including wave speed and properties. Key concepts discussed include gravitational forces, resonance, and calculations involving maximum velocity and distance in astronomical contexts.
Exploring Jupiter's Moon Io: Motion, Waves, and Damped Systems in Physics
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Presentation Transcript
Waves Physics 202 Professor Lee Carkner Lecture 6
Suppose you are watching Jupiter’s moon Io in a telescope. Where will Io appear to be moving fastest across the sky? • When it is furthest away from Jupiter • When it is closest to Jupiter • When it is half the maximum distance away from Jupiter • The speed is the same everywhere • We can’t tell without more information
Which of the following would increase the rate at which a damped system loses energy the most? • Doubling b • Doubling m • Halving b • Halving m • a and d only
Imagine a swing with a resonance at a period of T. What other period will also produce resonance? • 1/10 T • ¼ T • ½ T • 2 T • 2.5 T
PAL #5 Damped SHM • What is r if vmax = 13600 m/s and T = 3.6 days? • vmax = wxm so xm = vmax/w • w = 2p/T = 2p/(3.6)(24)(60)(60) = 2.02 X 10-5 rad/sec • xm = • What is mass of planet? • Gravitational force = centripetal force • GMm/r2 = mv2/r • M = v2r/G =
Test Next Friday • About 15 multiple choice • Mostly concept questions • About 4 problems • Like PALs or homework • Bring calculator and pencil • Formulas and constants provided (but not labeled) • Worth 15% of grade
What is a Wave? • Example: transmitting energy, • A sound wave can also transmit energy but the original packet of air undergoes no net displacement
Transverse and Longitudinal • Transverse waves are waves where the oscillations are perpendicular to the direction of travel • Examples: • Longitudinal waves are waves where the oscillations are parallel to the direction of travel • Examples: • Sometimes called pressure waves
Waves and Medium • The wave has a net displacement but the medium does not • This only holds true for mechanical waves • Photons, electrons and other particles can travel as a wave with no medium (see Chapter 33)
Wave Properties • The y position is a function of both time and x position and can be represented as: y(x,t) = ym sin (kx-wt) • Where: • k = angular wave number
Wavelength and Number • One wavelength must include a maximum and a minimum and cross the x-axis twice k=2p/l
Period and Frequency • Frequency is the number of oscillations (wavelengths) per second (f=1/T) w=2p/T • The quantity (kx-wt) is called the phase of the wave
Speed of a Wave y(x,t) = ym sin (kx-wt) • But we want to know how fast the waveform moves along the x axis: v=dx/dt • If we wish to discuss the wave form (not the medium) then y = constant and: • e.g. the peak of the wave is when (kx-wt) = p/2 • we want to know how fast the peak moves
Velocity • We can take the derivative of this expression w.r.t time (t): • Since w = 2pf and k = 2p/l v = w/k = 2pfl/2p v = lf • Thus, the speed of the wave is the number of wavelengths per second times the length of each • i.e.
Next Time • Read: 16.6-16.10 • Homework: Ch 16, P: 12, 15, 18, 24
