Cheryl is sitting exactly in the middle of a railway carriage as it travels alon

Question

Cheryl is sitting exactly in the middle of a railway carriage as it travels along a straight track. There are mirrors on the inside end walls of the carriage: mirror A is at the front of the carriage and mirror B at the back. Cheryl measures both mirrors to be a distance do 15 meters away from her, and the length of the carriage to be 30 meter Tom is a train spotter, who is standing by the side of the track at a railway station, observes that the through train is travelling extremely fast, at c/2. where c is the speed of light. He V also notes that, at the very instant Cheryl passes him, she starts to light a match. This question refers to the first spark from this match. Both Cheryl and Tom have set their watches so that this t corresponds to time zero. Some light from the spark initially even travels in the direction of the train's motion, is reflected from mirror A and returns to Cheryl other light from the same spark initially travels in the opposite direction, is reflected fr mirror Band also returns to Cheryl. You are required to answer the following parts (a) to (e (a) According to Cheryl, find the following time i) when light from the spark reaches mirror A 110 when light from the spark reaches mirror B (iii) when light from the spark returns to Cheryl from mirror A: and Civ) when light from the spark returns to Cheryl from mirror B (b) Similarly, find the times according to Tom, when the same four events take place. One answering this question is to start from Cheryl's space and time coordinates of way of the four events and then apply the Lorentz transformation equations. In applying these equations note that it is permissible to choose Cheryl's frame on the moving train as the unprimed frame and Tom's frame on the ground as the primed frame his choice has some advantages in simplifying the algebra, but you will need to take care in allocating signs to physical quantities Use your answers in parts (a) and (b to answer the following (c) Do Tom and Cheryl agree that light from the spark reaches mirror A at the same time as mirror B Do they agree that the light returning from mirror A reaches Cheryl at the same time as the light returning from mirror B Comment on your answers, drawing out general principles about the relativi of simultaneity in special relativity. ty (d) Do Tom and Cheryl agree that the time taken for light to travel from the spark to mirror A is the same as the time taken for light to travel from nirror B to Cheryl? Give a simple argument explaining why such agreement or disagreement is reasonable (e) Use two of the time s calculated in parts (a) and (b) to illustrate what is meant by time dilation in special relativity.

Explanation / Answer

A...FOR CHERYL...CHERYL MOVES WITH THE TRAIN(WITH CONSTANT VELOCITY:this is as good as rest))...SO FOR HER THE TIME IS SAME for all....THUS

Let length be 'd and lenght till mirror=d0'...v is velocity of train and t is time required..

ANSWERS..1,2,3,4=T=d/2c=5*10^-8 SEC

b...according to TOM...let total length be 'd' and lenght till mirror=d0...v is velocity of train and t is time required..

1..the time taken by light from cheryl to A

eqn:c*t=d/2-v*t

=d/2(c-C/2)=d/c=10*10^(-80sec

2..for B the train moves forward thus less time will be needed

eqn:c*t=d/2+v*t

=d/c+c/2=d/3c=3.33*10^(-8)sec

3...by similar logic...from a to cheryl less time is required

=d/3c=3.33*10^(-8)SEC

4....d/c=10*10^(-8)sec

C....NO...CHERYL AND TOM DON'T AGREE ON ANY ASPECT...CHERYL WILL SAY YES..TOM WILL SAY NO...THIS IS DUE TO USE OF FRAME

D...NO..SAME AS C

E,...TIME DILATION IS THE DIFFERENCE IN TIME OBSERVED BY TWO INERTIAL FRAMES AS SEEN IN OUR PROBLEM...BY TOM AND CHERYL...BOTH OF THEM ARE CORRECT

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