An equilateral triangle with each side of length s is placer! such that one of its sides is on the a axis of a coordinate system with the vertex opposite to this side on the y axis. Compute its interior angles in a frame that moves to the right of S (along the +ve x axis) with speed v. Is the sum of angles still 180° (take v = c/2 for example and confirm)?
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- 4.3 Time dilation for a biological clock. I trim my moustache every 6 weeks. If I were in a rocket ship flying past you at a speed of V=c, then how much time, in your frame, would elapse between my moustache trimmings? 44 Munn lifetime. The lifetime of a stationary muon is 2.2 microseconds. A beam ofConsider a point charge q at rest, situated at the origin of some frame S. Its electric field, according to S is 9 E(,1) = 1 2/21 47€ 12 Of course, its magnetic field is zero. Now, you want to know what will happen to the fields if q moved to the right (positive x direction). Since it is at rest in the S frame, what you can do is go to another frame, S', then boost it to the negative x direction. This way, q moves to the right according to S'. Let the velocity of S'be v = -vi Solve for the magnetic field components as seen in the S' frame. Combine these to write down B'(x, t)Please explain in detail An observer P stands on a train station platform as a high-speed train passes by at u/c = 0.8. The observer P, who measures the platform to be 60 m long, notices that the front and back ends of the train line up exactly with the ends of the platform at the same time. (a) How long does it take the train to pass P as he stands on the platform, as measured by his watch? (b) According to a rider T on the train, how long is the train? (c) According to a rider T on the train, what is the length of the train station platform?
- A rod moving relative to an observer is measured to have its length Lmoving contracted to one-half of its length when measured at rest. Find the value of u/c for the rod's rest frame relative to the observer's frame of reference.2.2. A rod of mass m= 1 kg flies with constant velocity past a mark which is stationary in the K frame. In the K frame, it takes the rod At= 20 ns to fly pass the mark, In the K' frame fixed to the rod, the mark moves past the rod in At' = 25 ns. (a) What is the velocity of the rod in the K frame? (b) What is the proper length of the rod? (c) What is the kinetic energy of the rod in the K frame in units of its total energy? (d) What is momentum of the rod in the K frame?Suppose two angry rhinoceros charge each other. According to a few observers on the ground, the rhinoceros on the left moved to the right at a speed of (1 - ϵ)c while the rhinoceros on the right moved to the left at a speed of (1 - ϵ)c. ϵ is in the range of 0 < ϵ < 1. How fast is the rhinoceros on the right moving in the frame of the rhinoceros on the left? (Show that this speed is less than c, no matter how small ϵ is)
- Problem 3: A mass m is thrown from the origin att = 0 with initial three-momentum po in the y direction. If it is subject to a constant force F, in the x direction, find its velocity v as a function of t, and by integrating v find its trajectory. Check that in the non-relativistic limit the trajectory is the expected parabola. Hint: The relationship F = P is still true in relativistic mechanics, but now p = ymv instead of p = mv. To find the non-relativistic limit, treat c as a very large quantity and use the Taylor approximation (1+ x)" = 1 + nx when a is small.A stationary observer O is standing on a platform of length 65 meters on earth. A rocket passes at a velocity of – 0.80c, parallel to the edge of the platform. The observer O notes that at a particular instant the front and back of the rocket simultaneously line up with the ends of the platform. (a) According to O, what is the time necessary for the whole rocket to pass a particular point on the platform? c = 3 × 10% m/s. (b) What is the rest length of the rocket according to an observer O' on the rocket? (c) According to O', what is the length of the platform? 65 m 0.8c O' Figure 2: Problem 4.