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PHYSICS 231 INTRODUCTORY PHYSICS I

PHYSICS 231 INTRODUCTORY PHYSICS I. Lecture 20. Q hot. Q hot. engine. fridge. W. W. Q cold. Q cold. Last Lecture. Heat Engine Refrigerator, Heat Pump. Entropy. Measure of Disorder of the system (randomness, ignorance)

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PHYSICS 231 INTRODUCTORY PHYSICS I

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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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