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5) (4 marks) Consider two simultaneous events (i.e., t = tb) separated by Az = {B-T...
Two time-like separated events in spacetime have coordinates in the lab frame S given by (ch,...
Two time-like separated events in spacetime have coordinates in the lab frame S given by (ch, x) = (1,1) and (a) How fast must S' be moving so that events 1 and 2 happen at the same point in space (i.e, their x coordi- (b) If S' is moving at speed u = 0.9c, how far separated in time (equivalently the coordinate cr) are the two (c) How fast must S be moving so that events 1 and 2 are...
Keilah, in reference frame S, measures two events to be simultaneous. Event A occurs at the...
Keilah, in reference frame S, measures two events to be simultaneous. Event A occurs at the point (55.0 m, 0, 0) at the instant 9:00:00 Universal time on January 15, 2013. Event B occurs at the point (115 m, 0, 0) at the same moment. Torrey, moving past with a velocity of 0.810cî, also observes the two events. 1. In her reference frame S', which event occurred first? A.) event A B.) event B 2. What time interval elapsed between...
3. In an inertial frame S two events A and B take place at different locations...
3. In an inertial frame S two events A and B take place at different locations and at different times such that A (XA, ta) and B (Xa, to). Consider a second inertial frame S' moving at a constant speed u along the x axis with respect to S. Can the observer in S' observe these two events to be simultaneous and occurring at the same location i.e. (x'A=x'® and t's=t')? Make necessary calculations to justify your answer.
131 Consider two observers: O at rest in space (inertial reference frame S), and O' in...
131 Consider two observers: O at rest in space (inertial reference frame S), and O' in a noninertial rotating frame, S. S' is rotating relative to S with a time-dependent angular velocity w = 2t î - { +(2+ + 4) Ê. (a) In the rotating frame, a particle has position vector given by r' (t) = (t? + 1)î -- 6th + 4th. Find the true velocity v(t) in reference frame S and the apparent velocity v'(t) in frame...
According to observer O, two events occur separated by a time interval Δt=0.48 μs and at...
According to observer O, two events occur separated by a time interval Δt=0.48 μs and at locations separated by Δx=47.8 m. (a) According to observer O', who is in motion relative to O at a speed of u=0.950c in the positive x direction, what is the time interval between the two events? Answer: 1.052 μs (b)What is the spatial separation between the two events, according to O'? m
Question 5 [12 10 22 marks] (a) In a given inertial reference frame, S', consider a...
Question 5 [12 10 22 marks] (a) In a given inertial reference frame, S', consider a region of space where there is a uniform and constant electric field, E', and zero magnetic field, i.e. B' = 0. The frame S' moves with respect to an observer, in another frame S, with velocity v. Write an expression for the electric field, E, observed in S? Clearly explain any notation (i) and new quantities introduced Write an expression for the magnetic field,...
[Q2 20 points] A and B devices separated by a distance d- 50 m measured in...
[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...
Problem 4. Given a curve C, the vectors T(t), N(t), and B(t) form a special coordinate...
Problem 4. Given a curve C, the vectors T(t), N(t), and B(t) form a special coordinate system (called an orthonormal reference frame) that lets us discuss velocity and acceleration of a moving object from the perspective of the object itself. (Consider, for example, looking only at the motion of an airplane to study its stability without worrying about its position relative to its starting point.) (a) Use the fact that v uT, where u(t)-|r(t)l is the speed of the particle,...
2. (25points) Now consider the following space time coordinates, or 4 vectors, of 2 other events:...
2. (25points) Now consider the following space time coordinates, or 4 vectors, of 2 other events: Event A: (ctA, xA, yA, zA) = (0.9m ,0.4m, 0.7m, 0m), Event B: (ctB, xB, yB, zB) = (1.2m, 0.4m, 0.6m, 0m) Remember what you learned about the invariant interval I in class and discussion and answer the following questions: (a) Are the two events A and B potentially causally connected ? (b) Does a reference frame exist in which the two events are...
Two spaceships leave the Earth at time t-0 in opposite directions with velocities v1 and v2...
Two spaceships leave the Earth at time t-0 in opposite directions with velocities v1 and v2 (V1 > v2). At a subsequent time ts two light signals are sent from the Earth to both of the spaceships. E, and E2 are the events of the light signal reached at spaceship 1 and spaceship 2 respectively. (a) Find ty and xt of E, and the spatial coordinates of E, and E2 as viewed from (30 marks) (b) Obtain the ratio between...
Two time-like separated events in spacetime have coordinates in the lab frame S given by (ch, x) = (1,1) and (a) How fast must S' be moving so that events 1 and 2 happen at the same point in space (i.e, their x coordi- (b) If S' is moving at speed u = 0.9c, how far separated in time (equivalently the coordinate cr) are the two (c) How fast must S be moving so that events 1 and 2 are...
3. In an inertial frame S two events A and B take place at different locations and at different times such that A (XA, ta) and B (Xa, to). Consider a second inertial frame S' moving at a constant speed u along the x axis with respect to S. Can the observer in S' observe these two events to be simultaneous and occurring at the same location i.e. (x'A=x'® and t's=t')? Make necessary calculations to justify your answer.
131 Consider two observers: O at rest in space (inertial reference frame S), and O' in a noninertial rotating frame, S. S' is rotating relative to S with a time-dependent angular velocity w = 2t î - { +(2+ + 4) Ê. (a) In the rotating frame, a particle has position vector given by r' (t) = (t? + 1)î -- 6th + 4th. Find the true velocity v(t) in reference frame S and the apparent velocity v'(t) in frame...
Question 5 [12 10 22 marks] (a) In a given inertial reference frame, S', consider a region of space where there is a uniform and constant electric field, E', and zero magnetic field, i.e. B' = 0. The frame S' moves with respect to an observer, in another frame S, with velocity v. Write an expression for the electric field, E, observed in S? Clearly explain any notation (i) and new quantities introduced Write an expression for the magnetic field,...
[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...
Problem 4. Given a curve C, the vectors T(t), N(t), and B(t) form a special coordinate system (called an orthonormal reference frame) that lets us discuss velocity and acceleration of a moving object from the perspective of the object itself. (Consider, for example, looking only at the motion of an airplane to study its stability without worrying about its position relative to its starting point.) (a) Use the fact that v uT, where u(t)-|r(t)l is the speed of the particle,...
Two spaceships leave the Earth at time t-0 in opposite directions with velocities v1 and v2 (V1 > v2). At a subsequent time ts two light signals are sent from the Earth to both of the spaceships. E, and E2 are the events of the light signal reached at spaceship 1 and spaceship 2 respectively. (a) Find ty and xt of E, and the spatial coordinates of E, and E2 as viewed from (30 marks) (b) Obtain the ratio between...
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