Physics 172H Modern Mechanics

Transcription

1 Physics 172H Modern Mechanics Instructor: Dr. Mark Haugan Office: PHYS 282 TAs: Alex Kryzwda John Lorenz Exam II: Wednesday 8:00-9:30pm in FRNY G140 Lecture 14: Matter & Interactions, Ch and Ch. 8

2 Dissipative Interactions: When interactions like friction and aerodynamic drag between a system like this block-wall system and its surroundings are negligible the system s energy is conserved Esys = Kb + U s mv + ksx = constant 2 2 When this is the case the amplitude of the block s oscillation back and forth through its equilibrium position remains constant. If we measure carefully enough or observe the system for long enough, however, that is not the case. The oscillation amplitude gradually decreases which means that the system energy defined above, the macroscopic kinetic energy of the block plus the spring potential energy, gradually decreases. In such cases we say that the system s initial energy is dissipated into microscopic kinetic and potential energies of the system and its surroundings, the block and floor getter warmer, for example.

3 Air Resistance A small metal ball from our hand to the ground when we let go as if the constant gravitational force exerted on it by the Earth is the only force acting on it. A coffee filter released in the same way falls differently. It reaches a nearly constant terminal velocity

4 Approximate Air-Drag Formula Observations about air resistance: 1. F air increases with speed. 2. Increases with area. 3. Depends on density of air. 4. Depends on object s shape (not mass) 5. Opposes direction of motion. The force due to air resistance can be approximated as: F air mg v 1 v 2 F air 1 2 Cρ Av2 ˆv F air mg ρ = density of air A = area of object v = speed of object C = shape-dependent parameter

5 Application: Fuel Efficiency of a Car F air 1 2 Cρ Av2 ˆv air_drag_507.html Daihatsu UFE III: C = 0.16 Toyota Prius: C = 0.26 Toyota Tacoma: C = 0.44

6 Q1. A single falling coffee filter quickly reaches a constant terminal speed of 1 m/s. At this speed, what do we know about the air resistance force? 1) Fair > Fgrav 2) Fair = Fgrav 3) Fair < Fgrav 4) not enough information v filter Q2. Three nested coffee filters fall, quickly reaching a terminal speed of ~ 1.7 m/s. If the Magnitude of the air resistance force on a single falling coffee filter was F 1, how large is the air resistance force on the three falling filters? 1) F 1 2) 3F 1 3) (1/3)F 1 4) not enough information to know Q3. If the cross-sectional area of a coffee filter were doubled, how would you expect the air resistance force to change? 1) Its magnitude would be larger 2) Its magnitude would stay the same 3) Its magnitude would be smaller

7 Where does the energy go? The hand exerts a constant force which keeps the stretch of the spring constant and the block moving at constant velocity. Apply the Energy Principle: System = Block The block s kinetic energy is constant, but work is done by the force exerted by the of spring on the block. Where does the energy go? The block and table-top get warmer. Macroscopically, we say that their thermal energies increase. Microscopically, we say that the kinetic and potential energies of the block s and table-top s atoms increase.

8 Driven Harmonic Oscillations Oscillations damped by some viscous fluid: guess sinusoidal motion s = the stretch A = ω 2 2 ( ) 2 F 2 c ωf ωd ωd m 2 D With an interesting amplitude

9 Resonance A = ω 2 F c ωf ωd ωd m ( ) 2 D D=driving motor amplitude A=amplitude of object ω F =free oscillation (natural) frequency ω D =driving frequency c=friction constant Want a big response? Drive it at the Resonant Frequency. Don t want a big response? Stay away from the Resonant Frequency!

10 Energy Quantization Our study of energy to this point makes it seem that a system can possess any amount of energy and that its energy will vary continuously as it interacts with its surroundings. It turns out that this is not the case and that this is most obvious for atomic and other microscopic systems. In this class we will not be able to predict the specific energies that a microscopic system can possess (you will study quantum mechanics later to learn how we make such predictions), however, we can use the fact of energy quantization to understand important phenomena that are easily observed. In chapter 8 we focus on the implications of energy quantization for the emission and absorption of light energy by atoms and other microscopic systems. Later, we will use it to better understand the microscopic physics underlying thermal phenomena.

11 Spectroscopy Spectrum of white light is essentially continuous. Spectrum of hydrogen gas is clearly discrete. What s going on here?

12 Light and Energy cooler hotter Different colors of light = different photon energies h E photon = p photonc = c λ photon the wavelength λ determines color of light

13 Energy Quantization in Atoms Consider a hydrogen atom (1 proton and 1 electron) It turns out that the electron seems only to be able to execute certain orbits. Then U + K electron takes only certain values. N=1 N=2 N=3 NOTE: A satellite seems able to orbit the Earth at any height and, so, U + K satellite can take on any value whatsoever.

14 Energy Quantization in Atoms 1 ev = 1.6 x J E K + U = N e e N = 1, 2,3, etc 13.6 ev 2 N electronic energy levels of hydrogen atom (no other atom has these specific levels!)

15 Emission and Absorption of Photons emitted photon absorbed photon