A train is moving on its track at a speed of v = 0.9c. We will define by the index 'R' (like tR) all quantities expressed in the rest frame, and without index those expressed in the train frame. Draw a schema of the problem, and define all axes you may need to solve the problem Express the Lorentz transformation for this train An observer measures in the rest frame the length of the train, as it is passing in front of him. He is obtaining a value of R = L. What would be the length of the train if it was still? Someone is standing in front of the train, at distance. In order to warn for the presence of the train in such a case, the constructors have placed a beacon on the train, which emits light at 480nm of wavelength. Knowing that the eyes can see light with a wavelength located within the range 400-800 nm, is this beacon useful? What should be the minimal wavelength of the beacon light in order for the train to be visible to someone sitting in front of the moving train?

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.

A ball of mass m traveling at a speed of 0.80c has a perfectly inelastic collision with an identical ball at rest. If Newtonian physics were correct for these speeds, momentum conservation would tell us that a ball of mass 2m departs the collision with a speed of 0.40c. Let's do a relativistic collision analysis to determine the mass and speed of the ball after the collision. Part C What is the initial total energy? Give your answer as a fraction times mc². Don't forget that there are two balls. Express your answer in terms of c and m. IVD ΑΣΦ E= Submit Part D Uf = Request Answer Because energy can be transformed into mass, and vice versa, you cannot assume that the final mass is 2m. Instead, let the final state of the system be an unknown mass M traveling at the unknown speed uf. You have two conservation laws. Find uf. Express your answer in terms of c and m. Submit IVE ΑΣΦ ? Request Answer ?

At relativistic speeds near that of light, the half-life of an unstable particle moving at high speed is longer than when it is at rest. O an object is longer when moving than when it is stationary. O light emitted by a moving source moves at the same speed with the same frequency. lengths and times only appear different, they are really just the same. O effects precede causes in some inertial frames.

View Policies Current Attempt in Progress (Come) back to the future. Suppose that a father is 20.00 y older than his daughter. He wants to travel outward from Earth for 2.000 y and then back to Earth for another 2.000 y (both intervals as he measures them) such that he is then 20.00 y younger than his daughter What constant speed parameter 3 (relative to Earth) is required for the trip?

Please specify the reference frames and draw diagrams to illustrate the problem. show complete solution too

A train, which is 200 m long, approaches a tunnel, which is 120 m long. The train is moving at a velocity of 0.89 c. a. What is the length of the train as seen be someone standing at the entrance to the tunnel? m b. Is the train ever entirely inside the tunnel as seen be the observer at the entrance to the tunnel? ONLY 1 ATTEMPT IS ALLOWED FOR THIS PART. ---Select--- v c. What is the length of the tunnel as seen be a passenger on the train? m d. Is the train ever entirely inside the tunnel as seen by the passenger on the train? ONLY 1 ATTEMPT IS ALLOWED FOR THIS PART. ---Select--- v

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Problem 2 In terms of the xs, ŷ, 2s coordinates of a fixed space frame {s}, frame {a} has its x-axis pointing in the direction (0, 0, 1) and its ŷ₂-axis pointing in the direction (-1,0, 0), and frame {b} has its x-axis pointing in the direction (1, 0, 0) and its y-axis pointing in the direction (0, 0, -1). The origin of {a} is at (3, 0, 0) in {s} and the origin of {b} is at (0, 2, 0) in {s}. (a) Draw by hand a diagram showing {a} and {b} relative to {s}. (b) Write down the rotation matrices Rsa and Rsb and the transformation matrices Tsa and Tsb. (c Calculate the matrix exponential corresponding to the exponential coordi- nates of rigid-body motion S0 = (0, 1, 2, 3, 0, 0). Draw the corresponding frame relative to {s}, as well as the screw axis S.

Example 6 Bob, who is stationary, measures the length of a moving relativistic train and finds out 50 m. The train passes through a tunnel of length 25 m at a speed 0.5c. Place on a space-time (Minkowski) diagram the following events: (a) Event A: the front of train at the exit of the tunnel. (b) Event B: the front of the train at the entrance of the tunnel. (c) Event C: the rear of the train at the exit of the tunnel. (d) Event D: the rear of the train at the entrance of the tunnel.