lecture_3

lecture_3 - Simultaneous Events L v E2 c L c v Tr Tf T L D...

Info iconThis preview shows pages 1–12. Sign up to view the full content.

View Full Document Right Arrow Icon
1 Simultaneous Events L v c c v E 2 c v E 1 L L T r T f T cT r = L 2 - vT r cT f = L 2 + vT f T = T f - T r cT = v ( T f + T r ) D D = c ( T r + T f ) T = Dv c 2
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
2 If events E 1 and E 2 are simultaneous in one frame of reference, then in a second frame that moves with speed v in the direction pointing from E 1 to E 2 , the event E 2 happens at a time Dv/c 2 earlier than event E 1 , where D is the distance between the events in the second frame.
Background image of page 2
3 If two clocks are synchronized and separated by a distance D in their proper frame, then in a frame in which the clocks move along the line joining them with speed v , the reading of the clock in front is behind the reading of the clock in the rear by Dv/c 2 .
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
4 0 0 v 0 T B v v 0 0 0 0 T B T B T A -T A L A L B L B D B D B D A Train Frame (Alice’s) Track Frame (Bob’s) T A = L A v c 2 T B = D B v c 2 "slowing-down factor": T A T B = 1 - v 2 c 2 "shrinking factor": L B L A = D A D B = 1 - v 2 c 2
Background image of page 4
5 L A = D A T A T B = D A D B = L B L A = s L B = sL A D B = L B + vT B = L B + v 2 D B c 2 L B = s 2 D B s = 1 - v 2 c 2 T A = L A v c 2 T B = D B v c 2 "slowing-down factor": T A T B = 1 - v 2 c 2 "shrinking factor": L B L A = D A D B = 1 - v 2 c 2
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
6 A stick and a clock, in relative motion 0 0 T T L L Stick Frame Clock Frame sL sL v v v v
Background image of page 6
7 The proper lifetime of a certain particle is 100.0 ns. a) How long does it live in the laboratory if it moves at v =0.96c? b) How far does it travel in the laboratory during that time? c) How far does it travel in its own frame of reference?
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
8 2.7: Experimental Verification Time Dilation and Muon Decay Figure 2.18: The number of muons detected with speeds near 0.98 c is much different (a) on top of a mountain than (b) at sea level, because of the muon’s decay. The experimental result agrees with our time dilation equation.
Background image of page 8
9 Newtonian Principle of Relativity If Newton’s laws are valid in one reference frame, then they are also valid in another reference frame moving at a uniform velocity relative to the first system. This is referred to as the Newtonian principle of relativity or Galilean invariance.
Background image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
10 K is at rest and K’ is moving with velocity Axes are parallel K and K’ are said to be INERTIAL COORDINATE SYSTEMS Inertial Frames K and K’
Background image of page 10
11 The Galilean Transformation For a point P In system K: P = ( x , y , z , t ) In system K’: P = ( x ’, y ’, z ’, t ’) x K P K’ x’-axis x-axis r V P ' = r V P - r v
Background image of page 11

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 12
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 25

lecture_3 - Simultaneous Events L v E2 c L c v Tr Tf T L D...

This preview shows document pages 1 - 12. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online