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Distance between two events w.r.t. two frames

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  1. Jul 13, 2017 #1
    1. The problem statement, all variables and given/known data
    upload_2017-7-13_10-5-2.png

    2. Relevant equations


    3. The attempt at a solution
    Distance between events w.r.t. earth frame,

    De = | (1/2)w(t+Γ)2 - 350 - (1/2)wt2 | = 242 m

    Distance between events w.r.t. train frame,
    Dt =350 m , correct?
    As w.r.t. train frame , the train is not moving.

    But, a person on the train will observe that the train is accelerating.
    But , if the train is not moving, then how will this person observe that the train is accelerating. Here , I am doing some mistake. Please help me.


    W.r.t. earth's frame, the two events occur at (x1,t1) and (x2,t2)
    such that x1 - x2= 242 m
    and t2 - t1 = 60 s

    At t = 0 s, origin of both K's and earth's frames meet each other.
    W.r.t. K's frame, the two events occur at (x'1,t1) and (x'2,t2)
    such that x'1 - x'2= 0 m
    and t2 - t1 = 60 s
    x'1 - x'2= 0 m = x1 - Vt1 - x2 + Vt2

    x1 - x2 = - V( t2 - t1 )

    V = 242/60 = 4.0 m/s
     
  2. jcsd
  3. Jul 13, 2017 #2

    Orodruin

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    No it will not. The train frame is a non-inertial frame.
     
  4. Jul 20, 2017 #3
    How can I,too, reach to this conclusion?
    If a person sitting in an accelerating train wants to measure the acceleration of the train, won't he measure the acceleration to be nonzero?
     
  5. Jul 20, 2017 #4
    How can I,too, reach to this conclusion?
    If a person sitting in an accelerating train wants to measure the acceleration of the train, won't he measure the acceleration to be nonzero?
     
  6. Jul 20, 2017 #5

    Orodruin

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    This depends on what you mean by "measuring the acceleration". An accelerometer will give you a non-zero value, but it will read the same in all frames. By definition of the train frame, the train is stationary in that frame and therefore not accelerating.
     
  7. Jul 20, 2017 #6
    Does "all" imply both inertial and non-inertial frames?
    So, we reach to that conclusion by definition.
     
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