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Time Dilation Practice Problems
 Lecture number:
 37
 Pages:
 2
 Type:
 Lecture Note
 School:
 The University of Vermont
 Course:
 Phys 012  Elementary Physics
 Edition:
 1
Documents in this Packet

6 pages

2 pages

Lecture 38 : Length Contraction
1 pages

Lecture 36 : Special Relativity
2 pages

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Lecture 34 : Quantized Electron Orbitals
3 pages

Lecture 33 : WaveParticle Duality of Light and Electrons
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Lecture 32 : Photoelectric and Compton Effects
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Lecture 30 : Particles and Waves
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Lecture 29 : Single Slit Diffraction and Resolving Power
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Lecture 28 : Thin Film Interference and Diffraction
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Lecture 27 : Diffraction and Thin Film Interference
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Lecture 26 : Diffraction and Interference
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Lecture 24 : Total Internal Reflection
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Lecture 23 : Refraction of Light
4 pages

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Lecture 21 : Light Rays and Reflection
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Lecture 20 : In Class Review for Exam 2
2 pages

Lecture 19 : Electromagnetic Spectrum
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Lecture 18 : Electromagnetic Waves
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Lecture 17 : Self Inductance, Transformers, and Circuits Containing Inductors
4 pages

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Lecture 14 : Electromagnetic Induction
4 pages

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Lecture 12 : Currents through Magnetic Fields
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Lecture 11 : Magnetic Fields and Forces
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Lecture 10 : Kirchhoff's Rules and RC Circuits
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Lecture 9 : Resistors and Capacitors.
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Lecture 8 : Electric Currents, Ohm's Law, and
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Lecture 7 : Capacitors and Dielectrics
3 pages

Lecture 6 : Electric Potential Energy and Electric Potential
4 pages

Lecture 5 : Electric Fields and Forces (18.9,19.1)
3 pages

Lecture 4 : Electric Field Lines
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Lecture 1 : Charge and Charge Transfer
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Unformatted text preview:
Lecture 37 Outline of Last Lecture I. Special Relativity a. Newtonian mechanics fails to describe the motion of very fast moving objects (close to the speed of light). b. Event: a physical happening that occurs at a certain place at a certain time i. An observer need three spatial and one temporal dimension (x, y, z, t) c. For special relativity, we need to observe from inertial frames of reference (observational reference frames in which Newton’s Laws of motion are valid). i. Accelerated frame of reference is not inertial. d. Postulates of Special Relativity i. Relativity postulate: the laws of physics are the same in every inertial reference frame ii. Speed of light postulate: the speed of light in a vacuum “c” as measured in any inertial frame of reference always has the same value regardless of how fast the source of light is moving e. Interpretation i. Any inertial reference frame is as good as any other one. There is no absolute velocity. ii. In relativistic mechanics, there is no such thing as absolute length or an absolute time interval. iii. Two events that are observed as simultaneous in one frame of reference are, in general, not simultaneous in another frame moving relative to the first. II. Time Dilation a. Ex) person in a moving train (at velocity v) holding a flashlight jumping up and down to a height of h i. Time for light to go up and down for person on train = proper time = Δtp = 2d/c ii. Time for light to go up and down for stationary person watching train = Δt = (2d)/(c√(1[v2/c2])) = Δtp/√(1[v2/c2]) Outline of Current Lecture III. Time Dilation a. Problem: A pendulum has a period of 3 seconds in the reference frame of the pendulum. What is the period of the pendulum within the reference frame of an observer moving at a constant velocity of 0.95 c? i. γ = 1/√(1[(0.95c)2/c2]) = 1/√(1[0.952]) = 3.2 ii. Δt = Δt0γ = (3)(3.2) = 9.6 seconds Physics 012 1st Edition
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