As the velocity of an inertial frame of reference increases with respect to a stationary observer, Einstein's theory of special relativity predicts that the length of an object, measured in the dimension parallel to the motion of the reference frame, will A. decrease. B. remain unchanged. C. increase. D. increase at first but start to decrease when the speed of the reference frame equals half the speed of light. E. decrease at first but start to increase when the speed of the reference frame equals half the speed of light.

As the velocity of an inertial frame of reference increases with respect to a stationary observer, Einstein's theory of special relativity predicts that the length of an object, measured in the dimension parallel to the motion of the reference frame, will A. decrease. B. remain unchanged. C. increase. D. increase at first but start to decrease when the speed of the reference frame equals half the speed of light. E. decrease at first but start to increase when the speed of the reference frame equals half the speed of light.

College Physics

10th Edition

ISBN:9781285737027

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter26: Relativity

Section: Chapter Questions

Problem 26P: A pulsar is a stellar object that emits light in short bursts. Suppose a pulsar with a speed of...

See similar textbooks

Similar questions

A pulsar is a stellar object that emits light in short bursts. Suppose a pulsar with a speed of 0.950c approaches Earth, and a rocket with a speed of 0.995c heads toward the pulsar. (Both speeds are measured in Earth's frame of reference.) If the pulsar emits 10.0 pulses per second in its own frame of reference, at what rate are the pulses emitted in the rockets frame of reference?
(a) Suppose the speed of light were only 3000 m/s. A jet fighter moving toward a target on the ground at 800 m/s shoots bullets, each having a muzzle velocity of 1000 m/s. What are the bullets' velocity relative to the target? (b) If the speed of light was this small, would you observe relativistic effects in everyday life? Discuss.
An astronaut wishes to visit the Andromeda galaxy, making a one-way trip that will take 30.0 years in the space-ships frame of reference. Assume the galaxy is 2.00 million light-years away and his speed is constant. (a) How fast must he travel relative to Earth? (b) What will be the kinetic energy of his spacecraft, which has mass of 1.00 106 kg? (c) What is the cost of this energy if it is purchased at a typical consumer price for electric energy, 13.0 cents per kWh? The following approximation will prove useful: 11+x1x2forx1
Review. A global positioning system (GPS) satellite moves in a circular orbit with period 11 h 58 min. (a) Determine the radius of its orbit. (b) Determine its speed. (c) The nonmilitary GPS signal is broadcast at a frequency of 1 575.42 MHz in the reference frame of the satellite. When it is received on the Earths surface by a GPS receiver (Fig. P38.41), 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. It is called a blueshift to indicate a change to a higher frequency. The magnitude of that fractional change is given by ff=Ugmc2 where Ug is the change in gravitational potential energy of an objectEarth system when the object of mass m is moved between the two points where the signal is observed. Calculate this fractional change in frequency due to the change in position of the satellite from the Earths surface to its orbital position. (e) What is the overall fractional change in frequency due to both time dilation and gravitational blueshift? Figure P38.41
A spacecraft zooms past the Earth with a constant velocity. An observer on the Earth measures that an undamaged clock on the spacecraft is ticking at one-third the rate of an identical clock on the Earth. What does an observer on the spacecraft measure about the Earth-based clock's ticking rate? (a) It runs more than three times faster than his own clock. (b) It runs three times faster than his own. (c) It runs at the same rate as his own. (d) It runs at one-third the rate of his own. (e) It runs at less than one-third the rate of his own.
(a) Calculate the relativistic kinetic energy of a 1000-kg car moving at 30.0 m/s if the speed of light were only 45.0 m/s. (b) Find the ratio of the relativistic kinetic energy to classical.
Suppose an astronaut is moving relative to the Earth at a significant fraction of the speed of light. (a) Does he observe the rate of his clocks to have slowed? (b) What change in the rate of Earth-bound clocks does he see? (c) Does his ship seem to him to shorten? (d) What about the distance between stars that lie on lines parallel to his motion? (e) Do he and an Earth-bound observer agree on his velocity relative to the Earth?
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.
An 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?
Construct 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.
(a) All but the closest galaxies are receding from our own Milky Way Galaxy. If a galaxy 12.0109ly ly away is receding from us at 0. 0.900c, at what velocity relative to us must we send an exploratory probe to approach the other galaxy at 0.990c, as measured from that galaxy? (b) How long will it take the probe to reach the other galaxy as measured from the Earth? You may assume that the velocity of the other galaxy remains constant. (c) How long will it then take for a radio signal to be beamed back? (All of this is possible in principle, but not practical.)
An observer in a coasting spacecraft moves toward a mirror at speed v relative to the reference frame labeled by S in Figure P26.46. The mirror is stationary with respect to S. A light pulse emitted by the spacecraft travels toward the mirror and is reflected back to the spacecraft. The spacecraft is a distance d from the mirror (as measured by observers in S) at the moment the light pulse leaves the spacecraft. What is the total travel time of the pulse as measured by observers in (a) the S frame and (b) the spacecraft? Figure P26.46