Question

According to an observer standing next to the railroad tracks, one electron is moving left- to-right on the tracks at a speed of 0.8c and another electron is moving right-to-left on the tracks at the same speed (0.8c, but in the opposite direction). A boxcar (without a front or a back so the electrons can move through it) is moving toward the right at 0.6c. A passenger in the boxcar records how long it takes each electron to pass from one end of the boxcar to the other end. According to the passenger, which took longer? A. the electron going from back to front B. the electron going from front to back C. they both took the same time D. since nothing can go faster than light, an electron cannot move toward the left with a speed of 0.8c through a boxcar moving toward the right with a speed of 0.6c OA OB OC OD

          According to an observer standing next to the railroad tracks, one electron is moving left-
to-right on the tracks at a speed of 0.8c and another electron is moving right-to-left on the
tracks at the same speed (0.8c, but in the opposite direction). A boxcar (without a front or a
back so the electrons can move through it) is moving toward the right at 0.6c. A passenger
in the boxcar records how long it takes each electron to pass from one end of the boxcar to
the other end. According to the passenger, which took longer?
A. the electron going from back to front
B. the electron going from front to back
C. they both took the same time
D. since nothing can go faster than light, an electron cannot move toward the left with a
speed of 0.8c through a boxcar moving toward the right with a speed of 0.6c
OA
OB
OC
OD

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according to an observer standing next to the railroad tracks one electron is moving left to right on the tracks at a speed of 08c and another electron is moving right to left on the tracks 79064

Added by Oscar M.

University Physics with Modern Physics

Hugh D. Young 14th Edition

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Solved by Expert Sam Stansfield

11/10/2024

Step 1

The boxcar is moving to the right at 0.6c. One electron is moving left-to-right at 0.8c, and the other is moving right-to-left at 0.8c. Show more…

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According to an observer standing next to the railroad tracks, one electron is moving left- to-right on the tracks at a speed of 0.8c and another electron is moving right-to-left on the tracks at the same speed (0.8c, but in the opposite direction). A boxcar (without a front or a back so the electrons can move through it) is moving toward the right at 0.6c. A passenger in the boxcar records how long it takes each electron to pass from one end of the boxcar to the other end. According to the passenger, which took longer? A. the electron going from back to front B. the electron going from front to back C. they both took the same time D. since nothing can go faster than light, an electron cannot move toward the left with a speed of 0.8c through a boxcar moving toward the right with a speed of 0.6c OA OB OC OD

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Transcript

00:01 Okay, so we have this rocket ship that's traveling over here.

00:05 It's got a clock that's putting out ticks every one and a half second.

00:12 To the clock, the delta x is zero because to anyone on the ship, it feels like they're at rest.

00:19 And they're just seeing this clock going tick, tick, tick.

00:23 So their delta x is zero.

00:27 So then we have our lorenz transformation.

00:30 So we got this.

00:31 Then our delta x is zero.

00:40 So delta t prime is gamma delta t.

00:45 Here's delta x prime.

01:11 So our answer to part a.

01:23 So part b is length contraction.

01:32 And the formula for that looks like this.

01:40 So the reason for this, you actually have to derive this.

01:45 You have to think carefully because the events for measuring the length of the spaceship in the unprime frame, there's actually two events.

02:00 They have to look at both ends of it at the same time and say, gee, what's the length in between? but those two events occur at different times in the prime frame.

02:13 And you have to take that into account.

02:16 So that's how there's a one over gamma here.

02:18 You can look at any physics book, any relativity text, and it'll tell you about how to do that.

02:28 So our l is 100 divided by our gamma...

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