1. PHYSICS 231 INTRODUCTORY PHYSICS I
Lecture 20

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

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 greater if molecules spread evenly in both halves.

4. 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!

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

11. Period and Frequency 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. Velocity and Acceleration vs. timex 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

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 Circular motion Cons. of E:
Angular speed: 
Radius: A
=> Speed: v=A

17. Formula Summary

18. 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

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) cm
b) 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) 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 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,