Please derive the attatched velocity transformations by using the Lorentz transformation for the velocity four vector (uμ). (hint: two of the Lorentz transformation equations are needed to solve this)
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Please derive the attatched velocity transformations by using the Lorentz transformation for the velocity four vector (uμ). (hint: two of the Lorentz transformation equations are needed to solve this)
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- When parked, your car is 5 m long. Unfortunately, your garage is only 4.0 m long. In order to solve for how fast would your car have to be moving for an observer on the ground to find your car shorter than your garage, complete the following given information: a) Who would get the O frame? The observer outside or the observer in the car? b) Who would calculate the proper length of the garage? ______________ In order to solve for, when you are driving at this speed, how long is your garage, measured in the car's frame of reference, complete the following given as information: c) Who would get the O frame? The observer in the car or an observer in the garage? d) Without solving quantitatively, would the car fit according to the observer in the car's frame of reference?b) A stationary observer at r = 7M in Schwarzschild geometry observes two particles travelling radially inward from infinity. If one body initially starts with a conserved energy per unit mass of 2 and the other of 3, determine the ratio of the speeds as they pass by the observer's position.Solve the following problem using Lorentz transformations: Two ships A and B are moving in the same direction. From the ground, spacecraft A is moving at 0.8c and B at 0.9c. How fast is ship B traveling from ship A?
- Question 32 and 33 pleaseShow that the defi nition of linear momentum, p' = mv' , has the same form p mv under a Galilean transformationChoose the option that makes the following statement cor- rect. Two events at a single location define a time interval. The proper time interval At, is measured by an observer [(a) at rest; (b) moving] relative to the location where the two events Occur.
- A light source G is moving, with respect to an observer O, at an angle θ=�=154∘∘ between the direction of relative motion and the line of sight from O to G. The redshift of the light emitted by G and measured by O is z=0�=0. Find the speed of G with respect to O in units of c�, the speed of light. Enter your answer to 3 decimal places.(a) Find the value of γ for the following situation. An astronaut measures the length of her spaceship to be 25.0 m, while an Earth-bound observer measures it to be 100 m. (b) What is unreasonable about this result? (c) Which assumptions are unreasonable or inconsistent?Show that the following form of Newton's second law satisfies the Lorentz transformation. Assume the force is parallel to the velocity. dv 1 F = m dt [1 – (v²/c²)]³/2
- An astronaut wishes to visit the Andromeda galaxy, making a one-way trip that will take 25.3 years in the space-ship's frame of reference. Assume the galaxy is 2.00 million light years away and his speed is constant. (a) How fast must he travel relative to Earth? The following approximation will prove useful: z 1 1 + x for x << 1. 2 - (Complete the equation for your answer.) (1-| C (b) What will be the kinetic energy of his spacecraft, which has mass of 1.08 x 10° kg? (c) What is the cost of this energy if it is purchased at a typical consumer price for electric energy, 13.0 cents per kWh?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.The Lorentz coordinate transformation assumes that t = t′ at x = x′ = 0. At what other values of x and x′ does t = t′?