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**PHYSICS 231 INTRODUCTORY PHYSICS I**

Lecture 20

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**Last Lecture Heat Engine Refrigerator, Heat Pump Qhot Qhot W W engine**

Qcold W Qhot fridge Qcold W

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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 greater if molecules spread evenly in both halves.

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**2nd Law of Thermodynamics (version 2)**

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

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**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

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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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**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 ;

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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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**Period and Frequency Amplitude: A Period: T Frequency: f = 1/T**

Angular frequency:

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**Phases Often a phase is included to shift the timing of the peak:**

for peak at Phase of 90-degrees changes cosine to sine

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**Velocity and Acceleration vs. time**

x v T Velocity and Acceleration vs. time 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

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

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**Connection to Circular Motion**

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

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**What is w? Simple Harmonic Motion Circular motion Cons. of E:**

Angular speed: Radius: A => Speed: v=A

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Formula Summary

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**Example13.1 a) 0.153 J b) 0.783 m/s c) 17.5 m/s2**

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) J b) m/s c) 17.5 m/s2

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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) cm b) 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) cm

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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

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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

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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

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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

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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 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,

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