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Physics 104 β Spring 2014 Intro and Harmonic Oscillator Energy β’ Maglev Tour β Magnetic force ππ£ × π΅ www.win.net/~dorsea/nehager/south/atlanta_maglev.htm β’ Introduction and Syllabus β’ Procedures (same as 103) β’ Topics covered β’ Differences with Phy 103 American Maglev Technology, Inc. Powder Springs, GA Jan 2011 β’ Harmonic Oscillator Intro and Syllabus Physics 104 General Physics: Thermodynamics, Electromagnetism, Optics Spring 2014 Syllabus β’ β’ β’ β’ β’ β’ β’ β’ β’ β’ β’ β’ β’ β’ β’ β’ β’ β’ β’ β’ β’ β’ β’ β’ Instructor: Nat Hager, Research Scientist, Physics and Engineering 173 Masters/Esbenshade (behind mineral gallery) Email: [email protected] - also forwards to smartphone. (OK to nag if I donβt reply in a day or 2). Web: msi-sensing.com/etown.htm or public directory βhagerneβ Phone: Office/Lab 361.1377. Home: 898.3053 before 9:00 PM. Please leave a message. Office Hours: Monday, Tuesday 1:00 β 2:00 PM Or by appointment. Please feel free to stop by my lab anytime, if my door is closed please leave a note. Class Hours: Mon/Tue/Fri 11:00 AM β 12:20 PM All classes in Nicarry 228. All class periods are the same format. Discussion topics will be covered in all sessions. Lab: Tue/Fri 2:00 β 3:50 PM Prerequisites: Physics 103 or equivalent Textbook: Giancoli, D.C., Physics, Sixth Edition, Prentice Hall, 2004. Supplemental Texts: Many Resources in the Physics Hideaway in Esbenshade including: Boyle, J, Study Guide: Physics (Giancoli), Prentice Hall, 2004. Procedures β’ Same as Physics 103 β WebAssign (setup) β Quizzes (5) β Exams (3) β Lab β Final β Powerpoints β Equation sheets Topics β’ β’ β’ β’ Waves and Sound Thermodynamics Electricity and Magnetism Optics (Ch. 11-12) (Ch. 13-15) (Ch. 16-22) (Ch. 23) Weβre trying to cover a lot, so weβll have to skip around some. (almost never do starred sections) General Differences with Physics 103 β’ Use βEnergyβ in broader context β β β β Kinetic energy of ideal gas. (6.02 x 1023 molecules) Potential energy stored in chemical bonds (fuel). Energy stored/carried in EM field. Anything that can do work! β’ Define new Forces β Electrostatic πΉ = ππΈ β Magnetic πΉ = ππ£ × π΅ β But use same F = ma relations β’ Reinterpret old concepts β Gravitational Field g = 9.8 π ππ (π πππ ππ π π 2 ) β Electric Field πΈ = π₯π₯ π πΆ β Magnetic Field π΅ = π₯π₯ π π΄ β π F = mg F = ππΈ F = qv × π΅ β’ Develop analogous methods β Flow of fluid (continuity) -> flow of electrical current (Kirchoff) Simple Harmonic Oscillator β’ A little Physics 103 β’ Jumping-off point for Waves Simple Harmonic Oscillator β’ Object subject to restoring force around equilibrium: F = - kx β β β β Force proportional to and opposite displacement Oscillatory motion around equilibrium Rate determined by mass m and k Frictional damping β’ Examples β β β β β Block on a spring (car on springs) Meter stick anchored one end (diving board) String in guitar (sound wave) Object bobbing in water Molecule in crystal lattice Energy in Harmonic Oscillator β’ Potential Energy β Work done by expanding spring: β (force x distance) π₯π βππ₯ π₯π β π= ππ₯ = β 1 ππ₯π 2 2 1 2 β ππ₯π 2 β Looks like decrease in potential energy β’ Kinetic Energy β Energy gained by block being pushed: 1 2 1 2 β π = ππ£π 2 β ππ£π 2 β Appears as increase in kinetic energy β’ Total Energy β Loss of potential = gain in kinetic, vice-versa β Sum of Kinetic and Potential Constant 1 2 1 2 β πΈ = ππ£ 2 + ππ₯ 2 = ππππ π‘πππ‘ 1 β Limiting points πΈ = 2 ππ£πππ₯ 2 1 2 πΈ = ππ΄2 Harmonic Oscillator Terminology β’ Cycle β One complete oscillation β’ Amplitude β x = -A to x = +A β’ Period β time to make one cycle β’ Frequency β # cycles per second β’ Frequency vs. Period β β f = 1/T T = 1/f Example 11-4 - Part 1 β’ Vertical - Find spring constant πΉπ¦ = 0 ππ₯π β ππ = 0 π= ππ π₯π = 0.3 ππ 9.8 π π 2 15 π π = 19.6 π π Example 11-4 - Part 2 β’ Horizontal - Find total energy 1 1 πΈπ‘ππ‘ = 2 ππ₯ 2 + 2 ππ£ 2 β’ At maximum amplitude A π 1 1 πΈπ‘ππ‘ = π πππ + 2 ππ£ 2 = 2 ππ΄2 1 πΈπ‘ππ‘ = 2 19.6 π π 0.1 π πΈπ‘ππ‘ = 0.098 J 2 Example 11-4 - Part 3 β’ At x=0 - maximum velocity vmax 1 π 1 πΈπ‘ππ‘ = 2 ππ₯ 2 + π πππ = 2 ππ£πππ₯ 2 1 0.098 π½ = πΈπ‘ππ‘ = 2 ππ£πππ₯ 2 π£πππ₯ = 2 β0.098 π½ 0.3 ππ = 0.81 π π β’ At x= 0.05 - velocity πΈπ‘ππ‘ = 0.098 π½ 1 ππΈ = 2 19.6 π π 0.05 π 2 = .0245 π½ πΎπΈ = 0.098 π½ β 0.0245 π½ = 0.0735 π½ 1 ππ£ 2 2 = .0735 π£ = 0.7π/π Example 11-4 - Part 4 β’ Maximum acceleration at maximum stretch πΉ = ππ = ππ₯ = ππ΄ π= ππ΄ π π= 19.6 π π 0.1 π 0.3 ππ π = 6.53 π π 2 Example β Problem 23 β’ At center point A 1 π 1 πΈπ‘ππ‘ = 2 ππ₯ 2 + π πππ = 2 ππ£πππ₯ 2 1 πΈπ‘ππ‘ = 2 0.755 ππ 2.96 π πΈπ‘ππ‘ = 3.31 J β’ Amplitude 1 3. 31 π½ = πΈπ‘ππ‘ = 2 ππ΄2 π΄= 2 β3.31 π½ 124 π π = 0.231 π 2 Example β Problem 13 β’ At any point x π π πΈπ‘ππ‘ = π πππ + π πππ 1 πΈπ‘ππ‘ = 2 280 π π .02 π 2 1 + 2 3 ππ .55 π π πΈπ‘ππ‘ = 0.056 J + 0.45375 J = 0.51 J β’ Amplitude 1 0. 51 π½ = πΈπ‘ππ‘ = 2 ππ΄2 π΄ = .06 π β’ Max velocity 1 0. 51 π½ = πΈπ‘ππ‘ = 2 ππ£πππ₯ 2 π£πππ₯ = .58 π π 2 Vertical Harmonic Oscillator Summary - Harmonic Oscillator Energy β’ At any position 1 1 2 2 πΈ = ππ£ + ππ₯ 2 2 β’ At full amplitude: 1 π π 1 2 2 πΈ = ππ£ + ππ = ππ΄ 2 π 2 β’ At max-velocity midpoint: π 1 2 1 π πΈ = ππ + ππ₯ = ππ£πππ₯ 2 π 2 2 β’ Same for all 3, find for one case know it for all. β’ Find total energy, find one component, subtract for other.