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PHYSICS 231 INTRODUCTORY PHYSICS I Lecture 20

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Heat Engine Refrigerator, Heat Pump Last Lecture Q hot engine Q cold W Q hot fridge Q cold W

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Entropy Measure of Disorder of the system (randomness, ignorance) Entropy: S = k B log(N) N = # of possible arrangements for fixed E and Q Number of ways for 12 molecules to arrange themselves in two halves of container. S is greater if molecules spread evenly in both halves.

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On a macroscopic level, one finds that adding heat raises entropy: Temperature in Kelvin! 2 nd Law of Thermodynamics (version 2) The Total Entropy of the Universe can never decrease. (but entropy of system can increase or decrease)

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Why does Q flow from hot to cold? Consider two systems, one with T A and one with T B Allow Q > 0 to flow from T A to T B Entropy changes by: S = Q/T B - Q/T A This can only occur if S > 0, requiring T A > T B. System will achieve more randomness by exchanging heat until T B = T A

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Carnot Engine Carnot cycle is most efficient possible, because the total entropy change is zero. It is a “reversible process”. For real engines:

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Chapter 13 Vibrations and Waves

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When x is positive, F is negative ; When at equilibrium (x=0), F = 0 ; When x is negative, F is positive ; Hooke’s Law Reviewed

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Sinusoidal Oscillation If we extend the mass, and let go, the pen traces a sine wave.

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Graphing x vs. t A : amplitude (length, m)T : period (time, s) A T

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Amplitude: A Period: T Frequency: f = 1/T Angular frequency: A T Period and Frequency

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Phases Often a phase is included to shift the timing of the peak: Phase of 90-degrees changes cosine to sine for peak at

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a x v Velocity is 90 “out of phase” with x: When x is at max, v is at min.... Acceleration is 180° “out of phase” with x a = F/m = - (k/m) x Velocity and Acceleration vs. time T T T

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v and a vs. t Find v max with E conservation Find a max using F=ma

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Connection to Circular Motion circular motion with constant angular velocity Simple Harmonic Motion Projection on axis

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What is ? Circular motion Angular speed: Radius: A => Speed: v=A Simple Harmonic Motion Cons. of E:

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Formula Summary

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Example13.1 An block-spring system oscillates with an amplitude of 3.5 cm. If the spring constant is 250 N/m and the block has a mass of 0.50 kg, determine (a) the mechanical energy of the system (b) the maximum speed of the block (c) the maximum acceleration. a) 0.153 J b) 0.783 m/s c) 17.5 m/s 2

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Example 13.2 A 36-kg block is attached to a spring of constant k=600 N/m. The block is pulled 3.5 cm away from its equilibrium positions and released from rest at t=0. At t=0.75 seconds, a) what is the position of the block? b) what is the velocity of the block? a) -3.489 cm b) -1.138 cm/s

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Example 13.3 A 36-kg block is attached to a spring of constant k=600 N/m. The block is pulled 3.5 cm away from its equilibrium position and is pushed so that is has an initial velocity of 5.0 cm/s at t=0. a) What is the position of the block at t=0.75 seconds? a) -3.39 cm

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Example 13.4a An object undergoing simple harmonic motion follows the expression, The amplitude of the motion is: a) 1 cm b) 2 cm c) 3 cm d) 4 cm e) -4 cm Where x will be in cm if t is in seconds

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Example 13.4b An object undergoing simple harmonic motion follows the expression, The period of the motion is: a) 1/3 s b) 1/2 s c) 1 s d) 2 s e) 2/ s Here, x will be in cm if t is in seconds

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Example 13.4c An object undergoing simple harmonic motion follows the expression, The frequency of the motion is: a) 1/3 Hz b) 1/2 Hz c) 1 Hz d) 2 Hz e) Hz Here, x will be in cm if t is in seconds

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Example 13.4d An object undergoing simple harmonic motion follows the expression, The angular frequency of the motion is: a) 1/3 rad/s b) 1/2 rad/s c) 1 rad/s d) 2 rad/s e) rad/s Here, x will be in cm if t is in seconds

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Example 13.4e An object undergoing simple harmonic motion follows the expression, The object will pass through the equilibrium position at the times, t = _____ seconds a) …, -2, -1, 0, 1, 2 … b) …, -1.5, -0.5, 0.5, 1.5, 2.5, … c) …, -1.5, -1, -0.5, 0, 0.5, 1.0, 1.5, … d) …, -4, -2, 0, 2, 4, … e) …, -2.5, -0.5, 1.5, 3.5, Here, x will be in cm if t is in seconds

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