Observer O fires a light beam in the y direction (v, = c). Use the Lorentz velocity transformation to find v and v and show that Ở also measures the value c for the speed of light. Assume that Ở moves relative to O with velocity u in the x direction.
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- Derive an expression for E using the attached equation (Lorentz Force Law), and calculate a predicted value for E in N/C if a particle had v = 40 m/s, q = -0.001 C, m = 0.3 ⨉ 10 -3 kg, and B = 0.6 T.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.a) Find the value of y for the following situation. An astronaut measures the length of his spaceship to be 100 m, while an earthbound observer measures it to be 25 m. b) What is the speed of the spaceship relative to Earth?
- Please answer D A spaceship from another galaxy passes over the solar system directly above a radial line from the sun to the Earth. (We measure the distance between the Earth and the Sun to be 1.496 x 1011 m.) An observer standing on the Earth measures that the spaceship is approaching at 0.800c. The Earth-based observer also measures that it takes the spaceship 625 seconds to travel from the sun to Earth. Ignore the relative motion of the Sun and Earth in this problem – their relative speed is only 0.001c, negligibly small compared to 0.800c. a) According to a scientist in the spaceship, the Earth-Sun distance is: 8.976 x 1010m b) According to a scientist in the spaceship, the time it takes her to travel the Earth-Sun distance is: 357s c) What is the ratio of the kinetic energy to rest energy of the spaceship? KE/ER = 0.667 d) As the spaceship passed over the Sun, the alien scientist launched a probe toward Earth, traveling at 0.200c relative to the spaceship. What would the…The proper length of one spaceship is three times that of another. The two spaceships are traveling in the same direction and, while both are passing overhead, an Earth observer measures the two spaceships to have the same length. If the slower spaceship has a speed of 0.354c with respect to Earth, determine the speed of the faster spaceship. (Give your answer to at least 3 significant figures.) |cAn 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.
- Determine an expression for the total travel time of the light pulse, as measured by the following: A) an observer in the S frame (Use the following as necessary: c, d, and v.) B) an observer on the spacecraft (Use the following as necessary: c, d, and v.) What If? If the transmitted light beam has a wavelength λT, determine an expression for the shift in the wavelength of the light beam, as measured by the following C) an observer in the S frame (Use the following as necessary: c, v, and λT.) D) an observer on the spacecraft (Use the following as necessary: c, v, and λT.)A car is moving relative to a pedestrian with a Lorentz factor of 1.45. With the length of the car being 5.7m according to the pedestrian, what's the length according to the driver of the car (he's moving at the same speed of the car) ?Einstein concluded that the speed of light is the same in all inertial frames. Prove that the analysis of the Michelson-Morley experiment (see attached image) is in error.