An observer on the ground has a coordinate system (S) with x axis extended from west to east. On the x axis in S, a switch at x = -500 m is connected to a light bulb at x = operator at x = -500 m flips the switch at time t = 0 and sees the light from the bulb reaches 1000 m. An him at t = 15.0 μs (or 15.0 × 10-6 s). Note that the light takes 5.00 μs to get to the operator, therefore the signal travels from the switch to the bulb in 10.0 μs. A relativistic train is zooming by at the speed of 0.900c from east toward west with attached S' coordinate system and x' axis from west to east direction. As usual, t = t' = 0 when the coordinates of S and S' coinside. a) Find the spacetime coordinates (x, t) of the switch flipping, and (x2, t2) of the light bulb turning on as observed in S'. b) Calculate the distance Ax' = x2 - x₁ and time interval At' = t₁₂ – t₁ for the two events as observed in S'. c) Calculate the speed of the signal directly using v' = Ax' /At' in S'. d) Use the relativistic addition of velocities to find v', the speed of the signal in S'. e) According to length contraction, the observer in S' should see the distance between 1500 654 m. Also, according to time the switch and the light bulb as Ax' Ax = Y 2.294 = dilation, we should have At' = yAt = 22.94 s. Explain why these do not work here.
An observer on the ground has a coordinate system (S) with x axis extended from west to east. On the x axis in S, a switch at x = -500 m is connected to a light bulb at x = operator at x = -500 m flips the switch at time t = 0 and sees the light from the bulb reaches 1000 m. An him at t = 15.0 μs (or 15.0 × 10-6 s). Note that the light takes 5.00 μs to get to the operator, therefore the signal travels from the switch to the bulb in 10.0 μs. A relativistic train is zooming by at the speed of 0.900c from east toward west with attached S' coordinate system and x' axis from west to east direction. As usual, t = t' = 0 when the coordinates of S and S' coinside. a) Find the spacetime coordinates (x, t) of the switch flipping, and (x2, t2) of the light bulb turning on as observed in S'. b) Calculate the distance Ax' = x2 - x₁ and time interval At' = t₁₂ – t₁ for the two events as observed in S'. c) Calculate the speed of the signal directly using v' = Ax' /At' in S'. d) Use the relativistic addition of velocities to find v', the speed of the signal in S'. e) According to length contraction, the observer in S' should see the distance between 1500 654 m. Also, according to time the switch and the light bulb as Ax' Ax = Y 2.294 = dilation, we should have At' = yAt = 22.94 s. Explain why these do not work here.
Physics for Scientists and Engineers
10th Edition
ISBN:9781337553278
Author:Raymond A. Serway, John W. Jewett
Publisher:Raymond A. Serway, John W. Jewett
Chapter38: Relativity
Section: Chapter Questions
Problem 18P: A rod moving with a speed v along the horizontal direction is observed to have length and to make...
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Transcribed Image Text:An observer on the ground has a coordinate system (S) with x axis extended from west to east.
On the x axis in S, a switch at x = -500 m is connected to a light bulb at x =
operator at x = -500 m flips the switch at time t = 0 and sees the light from the bulb reaches
1000 m. An
him at t = 15.0 μs (or 15.0 × 10-6 s). Note that the light takes 5.00 μs to get to the operator,
therefore the signal travels from the switch to the bulb in 10.0 μs.
A relativistic train is zooming by at the speed of 0.900c from east toward west with attached S'
coordinate system and x' axis from west to east direction. As usual, t = t' = 0 when the
coordinates of S and S' coinside.
a) Find the spacetime coordinates (x, t) of the switch flipping, and (x2, t2) of the
light bulb turning on as observed in S'.
b) Calculate the distance Ax' = x2 - x₁ and time interval At' = t₁₂ – t₁ for the two
events as observed in S'.
c) Calculate the speed of the signal directly using v' = Ax' /At' in S'.
d) Use the relativistic addition of velocities to find v', the speed of the signal in S'.
e) According to length contraction, the observer in S' should see the distance between
1500 654 m. Also, according to time
the switch and the light bulb as Ax'
Ax
=
Y
2.294
=
dilation, we should have At' = yAt = 22.94 s. Explain why these do not work here.
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