(a) What is the equivalence principle? (b) Describe an early experiment which confirmed the general theory of relativity.
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(a) What is the equivalence principle? (b) Describe an early experiment which confirmed the general theory of relativity.
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- The crew of an enemy spacecraft attempts to escape from your spacecraft by moving away from you at 0.283 of the speed of light. But all is not lost! You launch a space torpedo toward the foe at 0.351 of the speed of light with respect to you. (a) at what speed in kilometers per second does the enemy crew observe the torpedo approaching its spacecraft? (b) Is this more or less than the classical limit? Use the Galilean transform to prove this. (c) What if the torpedo is launched at the speed of light? At what speed in kilometers per second does the enemy crew observe the torpedo approaching its spacecraft? (Show all work.) (d) How fast would the second craft have to be going to measure the torpedoes speed as 10% greater than the classical limit. (Assume the torpedo is launched at the original speed, 0.351 of the speed of light.)Explain the fact the special theory of relativity defines the limits for the validity of Newtonian mechanics.Length contraction, time dilation, and Lorentz velocity transforms; why don't any of these effects show up when I drive down the highway at 70mph? These effects caused problems in the early days of police trying to regulate traffic. In 1953, a device that offset these effects was required in all new cars made worldwide. It is possible to see these effects in cars from before this time, but is illegal to drive them on the road without these devices. They do show up. The fact that the speed is such a small fraction of the speed of light means the effects are far, far too small for us to notice. These effects only work in space. The effects will show up on spaceships, but not on Earth. These effects are valid for atomic size objects only. Anything large enough to be seen without a microscope does not experience these effects.
- The average lifetime of a pi meson in its own frame of reference (i.e., the proper lifetime) is 2.6 10-8 s. (a) If the meson moves with a speed of 0.94c, what is its mean lifetime as measured by an observer on Earth? (b) What is the average distance it travels before decaying, as measured by an observer on Earth? (c) What distance would it travel if time dilation did not occur?A way to measure the length of an object moving at known(relativistic) speed is to measure the interval between the passage of referencepoints past an observer. By considering the times at which the leading and trailling ends of a moving rod pass an observer, and applying Lorentz transformations,show that the same expression for length contraction as : L=yo-1L' is obtained,draw a spacetime diagram if neededName: Hubble Distances Redshift z parameter The relativistic redshift is parametrized by z and given by Δ In terms of the scale factor, 2= X do - de de 1+z= ao a (2) Problem 01. Find the redshift z for a Hydrogen spectral line originally at 656 nm which has been observed at a wavelength of 1.64 μm. Astro 001 Fall 2022 Problem 02. How much smaller was the universe when this light was emitted? U₁ = DHO Using the redshift to measure the velocity, we find D~ (1) 0.1 Hubble's Law Hubble's Law states that the recession velocity of a redshifted galaxy is given by the product of the distance and the Hubble constant. (3) ZC Ho where c = 3 x 108 m/s and Ho = 2.3 x 10-18 s in standard units. The standard measurement of the Hubble constant is Ho = 71 (km/s)/Mpc. Problem 03. What is the distance in Mpc and ly to the galaxy measured in problem 01? 1 pc = 3.26 ly.
- A particle's dynamics are considered "relativistic" when its velocity is a significant fraction of the speed of light. For example, the mass of a moving particle seen by a stationary observer increases in proportion to the square root of 1/(1 - (v/c)2). For typical speeds in the everyday world it is not noticeable, but take a fast moving fundamental particle and you may have apparent mass increases or changes in its lifetime as a consequence of time dilation. Look at this factor for the electron you measured at 100 V in the glass globe. Pick the best answer. The effect is less than 0.1 %. The effect is around 1%. The effect is around 10%. The effect is a factor of 2 change in mass.A car is moving relative to a pedestrian with a Lorentz factor of 1.45. With the length of the car being 5.7m according to the pedestrian, what's the length according to the driver of the car (he's moving at the same speed of the car) ?