Question

[Q2 20 points] A and B devices separated by a distance d- 50 m measured in the reference frame S where they are at rest. The following sequence of events occurs: (K) A sends light signal towards B. (L) As soon as the signal is received by B, B sends a signal back to A. (M) A receives the signal from B The reference frame S', coincides with S at time t = t, 0 and is in motion with respect to S at speed B-u/c-0.6 in the positive x-direction. i Draw the space time diagram (ct, x) showing events K, L and M from the point of view of the reference frame S. Indicate slopes and ct intervals between events on your diagram. [4] ii. From the point of view of S', what is the time interval c Atky between even K and event iv. Using the Lorentz transformation, find the time interval c Atki between K and L, and V. Draw the space time diagram (ct', x') showing events K, L and M from the point of view From the point of view of S', what is the distance separating A and B? (4] M2 14] c AtiM between L and M. [4] of the reference frame S'.[4]

Answer 1

Given that x_2 - x_1 = 50 m = d in s frame p = u/L = 0.6 K - object A sends right to B L - B receives right, sends back to A M - A received right space time diagram ((f), x) of events k, l, m space time diagram [(f), x^� events k, l, m \r\n distance between A and B in s� frame we know that x = x^� + beta ct^�/squareroot 1 - beta^2 x_2 - x_1 = x^1_2 - x^1_1/squareroot 1 - beta^2 + beta c (f^1_2 - f^1_1)/squareroot 1 - beta^2 here we consider f^1_2 = f^1_1 thus x_2 - x_1 = x^1_2 - x_1/squareroot 1 - beta^2 rightdoublearrow 50 m = x^1_2 - x^1_1/0.8 rightdoublearrow x^1_2 - x^1_1 = 40 m time interval between k and m in s^1 frame + 1_km = c . delta t/squareroot 1 - beta^2 (delta x = 0 here because x_k = u_m) c delta f^1 = 1.252 c delta f c delta tf^1k_1