Concept explainers
(a)
How much time would light, moving at speed c, need to travel from the partially silvered plate to one mirror and back again, suppose that the distance in the Michelson-Morley experiment from the partially silvered plate to either mirror is 20,000 m?
Explanation of Solution
Given info:
Formula used:
Calculation:
The Michelson−Morley experiment attempted to measure a difference between light travel times in two perpendicular legs of an interferometer: One leg was situated parallel to the ether wind and the other perpendicular to the ether wind. For the "parallel leg" of the interferometer, we need to calculate the speed of the light traveling with the wind and against the wind; the round-trip time on this leg is equal to the sum of the times of each one-way trip. For the "perpendicular leg," we need to calculate the component of the
Parallel time:
Perpendicular time:
Time difference between legs:
Speed:
Gamma:
Time difference between legs:
Conclusion:
Time difference between legs
(b)
How much additional time would be required if the ether existed, if the Galilean velocity transformation were valid, and if Earth moved relative to the ether along the direction from the partially silvered plate to this mirror at speed at 0.01c?
Explanation of Solution
Given info:
Formula used:
Calculation:
Gamma:
Time difference between legs:
Conclusion:
Time difference between legs
(c)
How much additional time would be required if the ether existed, if the Galilean velocity transformation were valid, and if Earth moved relative to the ether along the direction from the partially silvered plate to this mirror at speed at 0.1c?
Explanation of Solution
Given info:
Formula used:
Calculation:
Gamma:
Time difference between legs:
Conclusion:
Time difference between legs
(d)
How much additional time would be required if the ether existed, if the Galilean velocity transformation were valid, and if Earth moved relative to the ether along the direction from the partially silvered plate to this mirror at speed at 0.5c?
Explanation of Solution
Given info:
Formula used:
Calculation:
Gamma:
Time difference between legs:
Conclusion:
Time difference between legs
(e)
How much additional time would be required if the ether existed, if the Galilean velocity transformation were valid, and if Earth moved relative to the ether along the direction from the partially silvered plate to this mirror at speed at 0.9c?
Explanation of Solution
Given info:
Formula used:
Calculation:
Gamma:
Time difference between legs:
Conclusion:
Time difference between legs
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Chapter 25 Solutions
COLLEGE PHYSICS,VOLUME 1
- Our solar system orbits the center of the Milky Way Galaxy. Assuming a circular orbit 30,000 ly in radius and an orbital speed of 250 km/s, how many years does it take for one revolution? Note that this is approximate, assuming constant speed and circular orbit, but it is representative of the time for our system and local stars to make one revolution around the galaxy.arrow_forwardConstruct Your Own Problem Consider an astronaut traveling to another star at a relativistic velocity. Construct a problem in which you calculate the time for the trip as observed on the Earth and as observed by the astronaut. Also calculate the amount of mass that must be converted to energy to get the astronaut and ship to the velocity travelled. Among the things to be considered are the distance to the star, the velocity, and the mass of the astronaut and ship. Unless your instructor directs you otherwise, do not include any energy given to other masses, such as rocket propellants.arrow_forwardAn Earth satellite used in the Global Positioning System moves in a circular orbit with period 11 h 58 min. (a) Determine the radius of its orbit. (b) Determine its speed. (c) The satellite contains an oscillator producing the principal nonmilitary GPS signal. Its frequency is 1 575.42 MHz in the reference frame of the satellite. When it is received on the Earths surface, what is the fractional change in this frequency due to time dilation, as described by special relativity? (d) The gravitational blueshift of the frequency according to general relativity is a separate effect. The magnitude of that fractional change is given by ff=Ugmc2 where Ug/m is the change in gravitational potential energy per unit mass between the two points at which the signal is observed. Calculate this fractional change in frequency. (e) What is the overall fractional change in frequency? Superposed on both of these relativistic effects is a Doppler shift that is generally much larger. It can be a redshift or a blueshift, depending on the motion of a particular satellite relative to a GPS receiver (Fig. P1.39).arrow_forward
- An interstellar space probe is launched from Earth. After a brief period of acceleration, it moves with a constant velocity, 70.0% of the speed of light. Its nuclear-powered batteries supply the energy to keep its data transmitter active continuously. The batteries have a lifetime of 15.0 years as measured in a rest frame. (a) How long do the batteries on the space probe last as measured by mission control on Earth? (b) How far is the probe from Earth when its batteries fail as measured by mission control? (c) How far is the probe from Earth as measured by its built-in trip odometer when its batteries fail? (d) For what total time after launch are data received from the probe by mission control? Note dial radio waves travel at the speed of light and fill the space between the probe and Earth at the time the battery fails.arrow_forwardAn alien spaceship traveling 0.600c toward Earth launches a landing craft with an advance guard of purchasing agents. The lander travels in the same direction with a velocity 0.800c relative to the spaceship. As observed on Earth, the spaceship is 0.200 light-years from Earth when the lander is launched. (a) With what velocity is the lander observed to be approaching by observers on Earth? (b) What is the distance to Earth at the time of landcr launch, as observed by the aliens on the mother ship? (c) How long does it take the lander to reach Earth as observed by the aliens on the mother ship? (d) If the lander has a mass of 4.00 105 kg, what is its kinetic energy as observed in Earths reference frame?arrow_forwardSuppose youre an astronaut being paid according to the time you spend traveling in space. You take a long voyage traveling at a speed near that of light. Upon your return to Earth, youre asked how youd like to be paid: according to the time elapsed on a clock on Earth or according to your ships clock. To maximize your paycheck, which should you choose? (a) The Earth clock (b) The ship's clock (c) Either clock because it doesnt make a differencearrow_forward
- If relativistic effects are to be less than 3%, then must be less than 1.03. At what relative velocity is =1.03 ?arrow_forwardA physics professor on the Earth gives an exam to her students, who are in a spacecraft traveling at speed v relative to the Earth. The moment the craft passes the professor, she signals the start of the exam. She wishes her students to have a time interval T0 (spacecraft time) to complete the exam. Show that she should wait a time interval (Earth time) of T=T01/c1+/c before sending a light signal telling them to stop. (Suggestion: Remember that it takes some time for the second light signal to travel from the professor to the students.)arrow_forwardA 100-m-long train is heading for an 80-m-long tunnel. If the train moves sufficiently fast, is it possible, according to experimenters on the ground, for the entire train to be inside the tunnel at one instant of time? Explain.arrow_forward
- Does time exist in no energy? Explain?arrow_forwardA pair of computer-interfaced photogates can be used to accurately measure the time interval for an object to break the beam of one photogate to another. If you wanted to know the speed of the object, what additional information would you need? Explain.arrow_forwardHi can you please complete the question fully, Struggling with it at the moment thanks.arrow_forward
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