Lect08 - PHYS 172 Modern Mechanics Fall 2009 Lecture 9...

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Fall 2009 PHYS 172: Modern Mechanics Lecture 9 – Harmonic Oscillators, Sound, Circular Motion Read 4.14 – 4.20
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Today’s Lecture •The Harmonic Oscillator • Speed of Sound in Solids • Circular Motion
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CLICKER QUESTION #1 Reading Question (Sections 4.14 – 4.20) (This is a closed-book quiz, no consulting with neighbors, etc.) In our spring-mass model of solids, we can make a reasonable guess as to the speed of sound, V s . We find that V s depends on: A. the atomic mass and the spring constant. B. The angular frequency and distance between atoms. C. the amplitude of each atom’s harmonic motion. D. the frequency of oscillation
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A Mechanism For Contact Forces: Tension The heavier the ball, the more the wire has to pull upwards. How does the wire “know” how to do this? The more you stretch a spring, the harder it pulls back!
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T F L strain = ; stress = L A ! ( ) ( ) 2 s k / ; atomic version Y = / s T s d k F L Y A L s d d ! = = Young’s modulus can be expressed in terms of the atomic spring constant: Young’s Modulus
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What is the distance between atoms in a simple solid? Assume you have 1cubic cm ( 1 cm 3 ) of aluminum (Al, atomic mass = 27 amu). Density of aluminum is ρ = 2.7 gm/cm 3 . How many Al atoms are there in 1 cc of Al? Since aluminum has an atomic mass of 27, that means that 1 mole of Al atoms has a mass of 27 grams, and one mole corresponds to 6.0 x 10 23 atoms. One cm 3 has a mass of 2.7 gms, which is 0.10 moles, or N=6.02 x 10 22 atoms.
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