600 meters 84 meters Change in starship's length when moving at 99% of light's speed when viewed by an observer Starship at rest a. Find lim Ra. b. If you are traveling in a starship at velocities approaching the speed of light, what does the limit in part (a) indicate about your aging rate relative to a friend on Earth? c. Explain why a left-hand limit is used in part (a).
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- One year (yr) is 365.24 days. One light-year (lyr) is 9.467 × 10^15 m. Convertthe speed of light (3.00 × 10^8 m/s) to lyr/yr.In special relativity, we introduced the momentum of a particle in a given Lorentz frame as pu = (E, pi ), where E is the energy of the particle and pi is the relativistic 3-momentum. Explain why, in general relativity, the energy of a particle measured by an observer is given, irrespective of the coordinate system used, by −p · uobs, where pu is the momentum of the particle and uuobs is the velocity of the observer in those coordinates.The speed of light is about 3 x 108 meters per second. The Millennium Falcon is traveling from Earth to Mars at the speed of light. The distance between the Earth and Mars fluctuates between 5.46 x 10¹0 meters and 4,01 x 10¹¹ meters. If the day the Millennium Falcon makes the "Mars Run," the distance is 2.25 x 10¹¹ meters, how long will it take them? Note: distance = rate time, and time = distance/rate Express your answer in scientific notation. Use for the multiplication. seconds Convert your answer to minutes. Include at least 3 decimal places in your answer, which can be expressed in standard notation. minutes Suppose the Millennium Falcon flies for 5 hours at the speed of light. How far will they travel? Express your answer in scientific notation. meters
- The speed of light in free space has been measured to be 2.99792458 x 108-m/s. Express the speed of light to (a) three significant figures, (b) five significant figures, and (c) seven significant figures.a) Suppose you decide to travel to a star 66 light-years away at a speed that tells you the distance is only 24 light-years. How many years would it take you to make the trip? Express your answer using two significant figures. b)In its own reference frame, a box has the shape of a cube 1.5 mm on a side. This box is loaded onto the flat floor of a spaceship and the spaceship then flies past us with a horizontal speed of 0.90 cc.What is the volume (m3 ) of the box as we observe it?As a spaceship is moving toward Earth, an Earthling measures its length to be 403 m, while the captain on board radios that her spaceship's length is 624 m. Calculate the spaceship's speed relative to earth and supply the missing numerical factor below. __)c
- A particle has γ=18,399. a)Calculate c-v in m/s. (I would have asked for 1 - v/c, making the answer dimensionless, but the system doesn't seem to take numbers that small. Gamma is chosen to make the particle extremely close to the speed of light.) If your calculator gives problems, you might want to solve the appropriate equation for c-v or c(1 - v/c) and use an approximation. b) In the previous problem, in a race to the moon, by 3/4ths the distance, light is one or ten meters ahead of the particle. We routinely approximate mass as zero, gamma as infinite, and speed as the speed of light. ("Massless particles" -- gamma and m have to be eliminated from the expressions. Light is a true massless particle.) If a massless particle has momentum 1,739 MeV/c, calculate its energy in MeV.The speed of light in free space has been measured to be 2.99792458 × 108 m/s. (A) 3 Significant Figures (B) 5 Significant Figures (C) 7 Significant FiguresThe speed of light in free space has been measured to be 2.99792458 x 108-m/s.Express the speed of light to (a) three significant figures, (b) five significant figures, and (c) seven significant figures.
- dx 4x 3. In so-called "natural units" (which is just a sneaky way to let us ignore a bunch of constants), the relativistic kinetic energy of a rigid body is given by the formula 1 КЕ — т V1 – v2 where m is the rest mass of the body and v is its relative speed. Alien scientists on a space station are observing an object falling into a black hole. As the object falls, it is disintegrating, losing mass at a rate of 3 (so its mass is changing at a rate of -3). How fast is the kinetic energy of the main part of the object changing when its mass is 20, its velocity is .7, and it is accelerating at a rate of .1 (remember that acceleration is the derivative of velocity with respect to time: a = dt 1Note that this formula does not make sense when v > 1. That is because in natural units, a speed of 1 corresponds to the speed of light, and nothing with positive rest mass can go that fast.For the machine element shown, locate the y coordinate of the center of gravity.How many meters are there in 3.2 light year (s), if the speed of light is 3 x 108 m/s. This number may be very large so do not round or truncate your number. Answer: