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Explain the concept of Time Dilation and Length Contraction.
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Consider the equation for kinetic energy: KE = 1/2mv^2 = 1/2 * m * v^2. If I ask you to take the derivative of kinetic energy, you should ask "the derivative with respect to what?" a) Suppose mass m is constant. Compute the derivative of KE with respect to v, (d(KE)/dv). b) Who takes derivatives with respect to velocity? No one. Except you, just now. Sorry. The rate of change of energy with respect to time is more important: it is the Power. Now, consider velocity v to be a function of time, v(t). We will rewrite KE showing this time dependance: KE= 1/2 * m * v(t)^2. Show that (d(KE)/dt) = F(t)v(t). Hint: use Newton's second law, F = ma, to simplify. c) In the computation above, we assumed m was constant, and v was changing in time. Think of a physical situation in which both m and v are varying in time. d) Compute the Power when both mass and velocity are changing in time. (First rewrite KE(t) showing time dependence, then compute (d(KE)/dt).
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Please specify the reference frames and draw diagrams to illustrate the problem. show complete solution too
Define the concepts of Time Dilation and Length Contraction. Use equations and/or examples to support your answer.
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
1. Some jets emitted by galaxies, for astronomical distances large enough, can appear to travel faster than the speed of light c, through our line of sight. Suppose that a distant galaxy, AB15, is moving with speed v at an angle e with respect to the earth and it emits two light rays separated by a time At in its local time. show that a) The time interval on earth in which the two light rays are emitted is given by Atr = At(1– B cos 0) b) The apparent speed of AB15 measured by an observer on earth is ArT VA = Att B sin e 1-B cos 0 %3D c) For B = 0.75, calculate the value of 0 for which Va =c
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