Apply the special theory of relativity to prove that the length L in the moving reference frame S′ appears to be smaller by a factor √1 − v^2/c^2 to the observer in the stationary frame S.
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reference frame S′ appears to be smaller by a factor √1 − v^2/c^2 to the observer in the stationary frame S.
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- The origins of two frames coincide at t = t' = 0 and the relative speed is 0.961c. Two micrometeorites collide at coordinates x = 129 km and t = 192 μs according to an observer in frame S. What are the (a) spatial and (b) temporal coordinate of the collision according to an observer in frame S'?The origins of two frames coincide at t = t' = 0 and the relative speed is 0.968c. Two micrometeorites collide at coordinates x = 139 km and t = 234 μs according to an observer in frame S. What are the (a) spatial and (b) temporal coordinate of the collision according to an observer in frame S'?cordinates in M
- At the Stanford Linear Accelerator Center (SLAC; see Fig. 33.9), subatomic particles are accelerated to high energies over a straight path whose length, in Earth's reference frame, is 3.2 km. For an electron traveling at 0.9999995c, how long does the trip take as measured (a)in Earth's frame and (b) in the electrons' frame?An observer moving at a speed of 0.995c relative to a rod (see figure below) measures its length to be x = 2.20 m and sees its length to be oriented at 0 = 33.0° with respect to its direction of motion. x Ꮎ Motion of observer (a) What is the proper length of the rod? m (b) What is the orientation angle in a reference frame moving with the rod? OThe origins of two frames coincide at t = ť = 0 and the relative speed is 0.976c. Two micrometeorites collide at coordinates x = 85.2 km and t= 260 us according to an observer in frame S. What are the (a) spatial and (b) temporal coordinate of the collision according to an observer in frame 5? (a) Number i Units (b) Number i Units
- My question is about special relativity. Three interconnected rods form a 90-45-45 triangle that reside on the plane x′y ′ of frame O. The chord of this triangle is in the direction of the x-axis. The frame O in the x direction moves away from the frame O at a speed of 0.6c. What are the angles of this triangle from the observer O's point of view (in degrees)?An astronaut is traveling at a constant velocity of 0.8 times the speed of light (c = 3 x 10^8 m/s) away from a space station. If the astronaut's clock is ticking normally, but the space station observes their clock to be running slower due to time dilation, calculate the time interval experienced by the astronaut during a 1-hour period according to their own clock.In frame S, event B occurs 2 ms after event A and at Dx = 1.5 km from event A. (a) How fast must an observer be moving along the +x axis so that events A and B occur simultaneously? (b) Is it possible for event B to precede event A for some observer?(c) Draw a spacetime diagram that illustrates your answers to (a) and (b). (d) Compute the spacetime interval and proper distance between the events.
- An object is moving with ordinary speed 0.5c in S reference frame along a direction making an angle (tan 9 = 2) with respect to the positive x - axis. Find the zeroth component of the proper velocity.The measured mean lifetime of an elementary particle when it is at rest in the lab is measured to be 2.6x10-8 s. If the particle is observed while traveling at a speed v=0.9 c with respect to the lab. What will be the value of the measured mean lifetime while the particle is moving?In the Marvel comics universe, Quicksilver is awfully fast. Let's say he can run at a velocity of 0.56c. He measures a trip as having a distance of 4.60e+05 m. How much time does Quicksilver measure this trip as taking? 2.73e-3 S Does Quicksilver measure the proper or dilated time? 2 proper time v Quicksilver's sister, Wanda Maximoff, is standing stationary near where he is running. How much time does Wanda measure this trip as taking? 3 3.29e-3 S What distance does Wanda measure for Quicksilver's trip? 4 Xm