tutorial: tutorial examples will be posted at least a day before the tutorial so you can think about...
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Tutorial:
Tutorial examples will be posted at least a day before the tutorial so you can think about them to benefit most from the tutorial
Regular Quizzes (every 2-3 weeks, 15-20 min each) during tutorial
Relativity and QuantaPHYS 242Fall 2013
Lecture:
Lecture notes available ahead of time - READ and answer Pre-Lecture Quiz (Moodle)Tell me your questions via Moodle (or in class) – that’s what we’ll discuss
Assignments:
Will be posted Fridays, are due Monday, 10 days later, during the tutorial.
Exam:
Final exam in December (3 h)
Marking scheme:
Lecture Quizzes: 10 %Tutorial Quizzes: 15 %Assignments: 25 %Exam (final): 50 %
concepts, ideas, some derivations of fundamental formulae
application of the concepts, examples (help for assignments)
examples: experience in applying concepts to actual problems, feedback on learning success, practice for exam (assessment)
Motivator for learning, assessment
W. Rau
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Books
Relativity and QuantaCustom version of: Serway, Moses, Moyer: Modern Physics ; Brooks/Cole -- Thomson Learning (available at Campus Book Store)
A.P. French: Special Relativity W.W.Norton & Company Inc. New York
R. Eisberg, R. Resnick: QUANTUM PHYSICS of Atoms, Molecules, Solids, Nuclei and Particles John Wiley & Sons, New York, London, Sydney, Toronto
Course Web page:
http://www.physics.queensu.ca/~phys242/ :Lecture Notes, Assignments, Tutorial Questions, Solutions
Moodle: Pre-Lecture Quizzes, YOUR Questions, Grades
Relativity and QuantaPHYS 242Fall 2013
W. Rau
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Newton’s laws:1. Inertia: Any object moves with constant velocity as long as no net force acts upon it2. Action: Any object experiences acceleration in presence of a net force: F = ma3. Reaction: If force F acts upon an object, –F acts upon the object where the force originates.
Classical mechanics
Inertial system: Reference frame where Newton’s 1. law applies.
any reference frame that moves with a constant velocity relative to a given inertial system, is also an inertial system and vice versa (any inertial system moves with constant velocity relative to any other inertial system)
Relativity Principle: The evaluation of an observation leads to the same conclusions about the laws of physics in any inertial system
W. Rau
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S S '
V
Coordinate transformation:x = x' + Vt' y = y' z = z ' t = t'
Velocity transformation:vx = vx' + V vy = vy' vz = vz'
x = x ' + R
x ' = ( ) x ''
x = ( ) x '' + R
t = t' + Dt
→ → →
cos a sin a-sin a cos a
→ →
cos a sin a-sin a cos a
→ → →
Coordinate Transformation
v = –– = ––––––– = –– + ––– = v ' + V dx d(x '+ R ) dx ' dRdt d(t' + Dt) dt' dt
→→ →
→→→→ →
Choose: x = x‘ = 0 for t = t‘ = 0, V ║ x
Galilean law for the addition of velocities:
v = v ' + V
(V: velocity of S ' w.r.t. S )
→ → →
→
St1
x1
y1
x1''
y1''
S'' t1''
αx1'
y1'
S'
t1'
R = (∆x,∆y)⃑x⃑
x'⃑
W. Rau
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Boat
Fog
Fog Reference frame of the boat
W. Rau
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Fog
Fog
Wood
Reference frame of the wood
W. Rau
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Wood
Fog
Boat
Fog
Reference frame of the wood(but observer on the boat)
W. Rau
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vx = 0vy = 0
v0
vx,ball = 0vy,ball = v0 - gt
S
S'
Reference frame of the boat
W. Rau
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S''v0
vx,bqll = vvy,ball = v0 - gt
vvx = vvy = 0
S
S'
Reference frame of the wood
W. Rau
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vx,ball = vvy,ball = - gt
v
v0
v
S''
vx = vvy = – v0
S
S'
Reference frame of the elevator
W. Rau
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How to Produce Spacetime diagrams
W. Rau
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How to produce spacetime diagrams (II)
W. Rau
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Spacetime diagram Boat(at rest)
Wood(moving)
Space
Tim
e
W. Rau
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Boat
W. Rau
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W. Rau
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Spacetime diagrams
Boat (center)
Passenger (front)
Passenger (back)
Ball 1
Wood
Ball 2
Boat(center)
Passenger (front)
Passenger (back)
Ball 2
Wood
Ball 1
vB1 = v ; vB2 = – v
vB1 = vB1' + V vB1' = vB1 – V = v – V
vB2 = vB2' + V vB2' = vB2 – V = – v – V
W. Rau
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Boat
Reference frame of boat and water
W. Rau
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Source at rest with respect to medium
W. Rau
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Source moving with respect to medium, frame of medium
W. Rau
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Source moving with respect to medium, frame of source
W. Rau
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Boat
Reference frame of the boat; water moving
W. Rau
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Wood
Reference frame of the wood; boat moving with water
W. Rau
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Source at rest with respect to medium;both are moving relative to reference frame
W. Rau
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vc
Xs
v
X
Case A:Source and Receiver
at rest
Case B:Source moving with
velocity v
Case C:Receiver moving with velocity – v
W. Rau
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SourceReceiver SourceReceiver
Case B
Rest frame of source(and water)
Rest frame of receiver(and water)
Case A Case C
DtR,C
x = v Dt x = 0
t = Dt
t = 0
t1
W. Rau
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SourceReceiver
Case B
Rest frame of receiver(and water)
SourceReceiver
Case B
Rest frame of source
Case C
DtR,B
Rest frame of source(and water)
W. Rau
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Summary
Newton’s Laws1. Inertia: v constant for F = 02. Action: F = ma3. Reaction: each force is balanced
by counter force
Reference Frames, Coordinate SystemsReference frame: “point of view”Coordinate system / transformation: Specify position / time in different frames
S S '
V
x = x' = 0 for t = t' = 0, V = Vx = const.:x = x' + Vt ; vx = vx' + V ; a = a‘
Inertial frame Reference frame where N.’s 1. law applies
Spacetime DiagramsA way to keep track of the position of objects in time
Propagation of Waves, Doppler Effect- Waves propagate with constant vc relative to medium- Observed frequency n depends on velocity of source
vs and receiver vr relative to medium:Moving source: nr = ns / (1 – v/vc)Moving receiver: nr = ns (1 + v/vc)
- Wavelength depends only on vs
Boat (center)
Passenger (front)
Passenger (back)
Ball 1
Wood
Ball 2
t
x
Galilean velocity transformationv= v'+V
W. Rau