An electron goes through 10 revolutions in a betatron with n= 0.6. How many vertical oscillations does it perform in the small displacement approximation? How many radial oscillations does it perform? Because the time-scale is so short for 10 revolutions, you may assume that y is constant.
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- NiloAn 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?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).
- PROBLEMS 8.1. A trip to the grocery store. Tabetha needs to pick up bananas from a grocery store located 1200 feet from her home. She travels there at a speed of V = c. As she starts her journey, her wristwatch, her home's wall clock, and the grocery store's wall clock all read noon. (Tip: It will help to make four sketches: in the Earth's frame, leaving home and arriving at the store; in Tabetha's frame, leaving home and arriving at the store.) a. How much time elapses in the Earth's frame during her journey? b. How much time does Tabetha's wristwatch tick off during this journey? c. In Tabetha's frame, the grocery store moves toward her. How far must it travel to reach her? d. Using your result for part (c) and the definition speed = distance traveled time elapsed find out how much time it takes for the grocery store to reach Tabetha. Compare with your result from part (b).been having some trouble with this problem: Michelson used rotating mirrors, similar to those shown below, to calculate the speed of light. Light is emitted from the light source, reflects from mirror surface X to the plane mirror, and then to the position of surface Z. By the time the light moves from the X to Z position, mirror surface X will have moved to the position of mirror surface Z. The light then continues to the observer. The distances from the light source and the observer to the rotating mirrors are negligible. The distance from the rotating mirrors to the plane mirror is 35.0 km.If the mirrors are rotating at 480 rev/s, the speed of light calculated from the given information isA family brought their grandfather clock from Denver, Colorado to Clarksville, TN when they moved. Shortly afterwards, they discovered that the clock no longer ran accurately due to a change in the local g value. Do you expect the clock runs faster or slower? How do you fix the problem, moving the oscillating piece up or down? The clock runs faster. Moving the oscillating mass up slightly so the rod is shorter. Moving the oscillating mass down the rod slightly so the rod is longer. The clock runs slower. 1. Yes. 2. No.
- Given the time series below. Which of these can be interpreted as a generic chaotic trajectory of some dynamical system? 1) Acos(b sin(t)) 2) A1cos(f1t)+A2sin(f2t) 3) Acos(at2 +b) 4) Atang[at/(1+t)]Events 1 and 2 are exploding firecrackers that each emit light pulses. In the reference frame of the detector, event 1 leaves a char mark at a distance 3.40 m from the detector, and event 2 leaves a similar mark at a distance 2.10 m from the detector. If the two events are simultaneous in the reference frame of the detector and occur at instant t = 0, at what instant of time will each light pulse be detected?