RELATIVITY REVIEW -- physics 2
1) Would it be appropriate, from the perspective of special relativity, to add the velocity of light relative to the sun to the velocity of the sun relative to the earth in order to obtain the velocity of light relative to the earth? Explain.
No, the speed of light is constant (3.0 x 108 m/s) in ALL frames of reference.
2) At the end of the 19th century, significant efforts were made to experimentally prove that the earth was moving through a substance known as the luminiferous ether. These experiments consistently failed. Which of Einstein's postulates deals most directly with this failure? Explain.
3) A chess game taking place on earth is observed by observer A, who is passing by in a spaceship. Observer B is standing on earth looking over the shoulder of the players. Which of these two observers measures the longer time for the time between moves in the game? Explain.
Observer A measures the longer time for a move because he is moving relative to the game, and events that are moving are observed to slow-down for him compared to Observer B, who is at rest relative to the game.
4) A radioactive isotope with a certain half-life is moving with a high speed in a particle accelerator. Does an observer at rest in the lab measure the proper time for the half-life of this isotope? Explain.
No…an observer who is moving along with the isotope would measure the proper (non-dilated) time.
5) A spaceship is moving with a large velocity past observer A, who is standing on earth. Observer B is a mission specialist aboard the spaceship. Which of these observers measures the longer length for the length of the spaceship? Explain.
Observer B measures the greater length, since B is at rest relative to the ship. Observer A observes the ship length to contract, since the ship is moving relative to his F-O-R.
6) Referring to the last question: how would their measurements of the other two dimensions of the ship compare?
Both observers would note that the other dimensions of the ship are unchanged.
7) Is Newton's 2nd law, written in the form ∑F = ma, valid for objects traveling at velocities near the velocity of light? Explain.
No, as speed increases, an object’s mass increases (as measured from a moving F-O-R). The 2nd Law equation would need to be modified to include the mass-increase formula.
8) If we compress a spring and lock it into its newly compressed configuration, have we changed the mass of the spring? Explain.
Yes, the mass of the spring increases slightly. This is due to the equivalence of mass and energy—E = mc2.
9) One of the many obstacles to long-term spaceflight is the idea that astronauts’ muscles would atrophy in the absence of gravity for these extended periods. One proposed solution is to have the entire spaceship spin as it moves. Why would that work?
Astronauts would be in a non-inertial (accelerating) F-O-R, which is equivalent to a gravitational field in every way.
10) What is spacetime?
It is the 4-dimensional fabric of the universe; contains x, y, z, and t coordinates.
11) Explain how gravity can affect the path of a light beam.
Since gravity is just a warping of space-time, a light beam just follows the curvature, causing its path to bend.
12) Describe the phenomenon of gravitational lensing.
It is the shifting/blurring of the image of a distant object (i.e. a star) due to light following curved space time in the vicinity of a massive object.
13) Is it possible for a father to have aged less than his child, if they observe each other to be at rest? Explain.
Yes, if the father is in a strong gravitational field (and the child is not), time runs slower for him than for his child.
14) Is a black hole just a hole in space that contains no mass? Explain.
No, it is an extremely massive object that distorts space time to the point that there is no bottom to the distortion.
15) What is a gravity wave? How is it made?
A fluctuation of space time, caused by an accelerating mass.
16) Is it possible for an astronaut to leave on a space trip and return before his twin brother was born? Explain.
No, traveling backward in time is not possible according to Relativity Theory.
17) An astronaut aims a flashlight towards the tail of her spaceship that is traveling with a velocity of 0.5c relative to the earth. What is the velocity of the light beam relative to the earth?
3.0 x 108 m/s
18) An astronaut cooks a three-minute egg in his spaceship, which is whizzing past earth at a speed of 0.90c. How long has the egg cooked as measured by an observer on earth?
6.88 minutes
19) An observer on earth notes that an astronaut on a spaceship puts in a 4.0-hr shift at the controls, while the astronaut measures the shift to be 3.5 hr long. How fast is the spaceship traveling relative to the earth?
0.48c
20) A spaceship that is 40.0 m long as measured by its occupants is traveling at a speed of 0.100c relative to the earth. How long is the spaceship as measured by mission control in Houston?
39.8 m
21) A spaceship is traveling with a velocity of 0.900c relative to the earth. What is the momentum of the spaceship if its mass is 2.00 x 103 kg?
1.24 x 1012 kg m/s (m = 4588 kg)
21) What is the mass equivalence of 750,000 Joules of energy?
8.3 x 10-12 kg