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Chapter 12

Chapter 12. Section 1 & 2. Terms to Know. 1)Periodic motion simple harmonic motion: The motion that results when an object that is not at equilibrium (F net = 0) tries to return to its equilibrium. 2)period (T): the time taken for a cycle 3) frequency ( f ) = # of cycles per second = 1/T

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Chapter 12

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  1. Chapter 12 Section 1 & 2

  2. Terms to Know 1)Periodic motion • simple harmonic motion: The motion that results when an object that is not at equilibrium (Fnet = 0) tries to return to its equilibrium

  3. 2)period (T): the time taken for a cycle 3) frequency (f) = # of cycles per second = 1/T 4)amplitude (A) = the max distance from equilibrium

  4. Introduction to Hooke’s Law • khanacademy - Hooke's Law

  5. Hooke’s Law • F = Restoring force (N) • x = displacement (m) • k = spring constant (N∙m-1) • F = -kx (F and x are in opposite directions)

  6. Determining k

  7. 1 dyne = 1 g·cm/s² = 10−5 kg·m/s² = 10−5 N k =? (2) How much work is done by the spring when it is stretched to 10cm?

  8. Limitation in Hooke’s Law

  9. PE in a Spring

  10. KE and PE in Spring

  11. Example 12A, Pg 440 If a mass of 0.55 kg attached to a vertical spring stretches the spring 2.0 cm from its equilibrium (= unstretched) position, what is the spring constant?

  12. Example A spring stretches by 18 cm when a bag of potatoes weighing 56 N is suspended from its end. • Determine the spring constant. • How much elastic potential energy is stored in the spring when it is stretched this far?

  13. Harmonic Motion in Pendulum • Pendulum Motion • acceleration and velocity • http://www.cabrillo.edu/~jmccullough/Applets/Flash/Mechanics/PendulumForces.swf • tension, weight, and net force

  14. Looking at a, v, forces on a pendulum again

  15. Forces acting on a Pendulum

  16. KE and PE in Pendulum

  17. KE + PE = ME

  18. Period of a Pendulum • T = 1/f • For the period derivation • The mass and amplitude do not change the period!

  19. Foucault Pendulum

  20. Sample Problem 12B, Pg 448 You need to know the height of a tower, but darkness obscures the ceiling. You note that a pendulum extending from the ceiling almost touches the floor and that its period is 12 s. How tall is the tower?

  21. Example A pendulum with a length of 36.9 cm has a period of 1.22 s. What is the acceleration due to gravity?

  22. Period of a Spring

  23. Sample Problem 12C, Pg 450 The body of a 1275 kg car is supported by four springs, each of which as a spring constant of 2.0×104 N/m. Two people riding in the car have a combined mass of 153 kg. Find the period of vibration of the car when it is driven over a pothole in the road.

  24. Resonance

  25. Wave Properties • Wave: one of two ways to carry energy • Matter is the other way • Mechanical waves: require a medium through which waves propagates • Medium = rope, water, spring, air • Two types: transverse and longitudinal *Play RealPlayer on two types of waves

  26. More Wave Animation • http://paws.kettering.edu/~drussell/Demos/waves/wavemotion.html

  27. Describing a Wave • amplitude, A • wavelength, λ (lambda) • period, T (sec) • frequency, f (cycles per sec = sec-1 = Hz) • speed, v • phase • crest, compression • trough, rarefaction

  28. T, f, & v

  29. Example A sound wave has a frequency of 192 Hz and travels the length of a football field, 91.4 m, in 0.271 s. • the speed? • the wavelength? • the period? • If the frequency was changed to 442 Hz, new wavelength? New period?

  30. Terms to Know • incident wave • transmitted wave • reflected wave

  31. Wave Behavior • At a free end • At a fixed boundary • At the boundary with another medium • interference • constructive • destructive • Standing waves • Refraction

  32. Wave at a free end • Reflection of a Pulse at a Free End

  33. Waves at a fixed boundary • Reflection of a Pulse at a Fixed End

  34. Waves through different medium • Characteristics of a Transmitted Pulse

  35. Interference • How two or more waves are interacting • Each wave affect the medium independently • Waves algebraically combine to form a new wave - Principle of superposition • Constructive interference • Destructive interference (Show Realplayer)

  36. Constructive Interference(Waves are in phase)

  37. Destructive Interference(Waves are out of phase) • B • A+B A

  38. Standing Wave • (Show RealPlayer)

  39. Refraction • A profound effect of light waves • Bending the light waves when entering a different medium, results in the change of speed.

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