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Understanding Thermodynamics and Harmonic Motion

Discover the concepts of entropy, heat engines, Carnot cycles, and harmonic motion in introductory physics. Explore Hooke's Law, sinusoidal oscillations, angular speed, and energy conservation. Solving example problems included.

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Understanding Thermodynamics and Harmonic Motion

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  1. PHYSICS 231INTRODUCTORY PHYSICS I Lecture 20

  2. Qhot Qhot engine fridge W W Qcold Qcold Last Lecture Heat Engine Refrigerator, Heat Pump

  3. Entropy • Measure of Disorder of the system(randomness, ignorance) • Entropy: S = kBlog(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 greaterif molecules spread evenly in both halves.

  4. 2nd Law of Thermodynamics(version 2) On a macroscopic level, one finds that adding heat raises entropy: The Total Entropy of the Universe can never decrease. (but entropy of system can increase or decrease) Temperature in Kelvin!

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

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

  7. Chapter 13 Vibrations and Waves

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

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

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

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

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

  13. x v a Velocity and Acceleration vs. time T • 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 T T

  14. v and a vs. t Find vmax with E conservation Find amax using F=ma

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

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

  17. Formula Summary

  18. 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/s2

  19. 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

  20. 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

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

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

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

  24. Example 13.4d An object undergoing simple harmonic motion follows the expression, Here, x will be in cm if t is in seconds 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

  25. Example 13.4e An object undergoing simple harmonic motion follows the expression, Here, x will be in cm if t is in seconds The object will pass through the equilibrium positionat 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,

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