Solved: A spaceship moves at one-quarter the speed of

Which of the following statements are fundamental postulates of the special theory of relativity? (a) Light moves through a substance called the ether. (b) The speed of light depends on the inertial reference frame in which it is measured. (c) The laws of physics depend on the inertial reference frame in which they are used. (d) The laws of physics are the same in all inertial reference frames. (e) The speed of light is independent of the inertial reference frame in which it is measured.

A spaceship moves at one-quarter the speed of light relative to Earth in a direction perpendicular to the line of sight of an observer at rest with respect to Earth. If the spaceship has a length L when at rest, which statement is true concerning the moving ships length L9 as measured by the observer? (a) L9 . L (b) L9 , L (c) L9 5 L (d) L9 ,, L (e) L9 .. L

A cars headlights come on, and an observer on the ground measures the speed of the light beam to be c 5 3.00 3 108 m/s. As the driver heads down the highway traveling at a speed v away from the ground observer, which of the following statements are true about the measured speed of the light beam? (a) The ground observer measures the light speed to be c 1 v. (b) The driver measures the light speed to be c. (c) The ground observer measures the light speed to be c. (d) The driver measures the lights speed to be slightly less than c. (e) The ground observer measures the lights speed to be slightly less than c.

An astronaut is traveling in a rocket in outer space in a straight line at a constant speed of 0.5c. Which of the following effects would she experience? (a) She would feel heavier. (b) She would find it harder to breathe. (c) Her heart rate would change. (d) Some of her dimensions would be shorter. (e) None of these effects would occur.

A pendulum in a spaceship traveling through space at a speed of 0.9c relative to Earth has a period P as measured by an astronaut in the spaceship. What is true about the period T as measured by an observer on Earth? (a) P . T (b) P 5 T (c) P , T (d) P , T or P . T, depending on the direction of motion of the spacecraft (e) None of these

A cube measured at rest has volume V. An observer then passes the cube parallel to one of its sides at 0.98c, so g < 5. What is the volume of the cube as measured by the moving observer? (a) V/125 (b) V/25 (c) V/5 (d) V (e) 5V

Suppose a photon, proton, and electron all have the same total energy E. Rank their momenta from smallest to greatest. (a) photon, electron, proton (b) proton, photon, electron (c) electron, photon, proton (d) electron, proton, photon (e) proton, electron, photon

Two identical clocks are set side by side and synchronized. One remains on the Earth. The other is put into orbit around the Earth moving rapidly toward the east. As measured by an observer on the Earth, does the orbiting clock (a) run faster than the Earth-based clock, (b) run at the same rate, or (c) run slower?

A massspring system moving with simple harmonic motion has a period T when measured by a ground observer. If the same system is then placed in an inertial frame of reference that moves past the ground observer at a speed of 0.50c, by what factor should T be multiplied to give the systems period as measured by the ground observer? (a) 0.50 (b) 0.87 (c) 1.00 (d) 1.15 (e) 1.35

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 onethird the rate of an identical clock on the Earth. What does an observer on the spacecraft measure about the Earth-based clocks 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 distant astronomical object (a quasar) is moving away from us at half the speed of light. What is the speed of the light we receive from this quasar? (a) greater than c (b) c (c) between c/2 and c (d) c/2 (e) between 0 and c/2

A proton in a large accelerator has a kinetic energy of 175 GeV. (a) Compare this kinetic energy to the rest energy of the proton, and find an approximate expression for the protons kinetic energy. (b) Find the speed of the proton.

What speed must a particle attain before its kinetic energy is double the value predicted by the nonrelativistic expression KE 5 12 mv2?

Determine the energy required to accelerate an electron from (a) 0.500c to 0.900c and (b) 0.900c to 0.990c.

A spaceship of mass 2.40 3 106 kg is to be accelerated to a speed of 0.700c. (a) What minimum amount of energy does this acceleration require from the spaceships fuel, assuming perfect efficiency? (b) How much fuel would it take to provide this much energy if all the rest energy of the fuel could be transformed to kinetic energy of the spaceship?

An unstable particle with a mass equal to 3.34 3 10227 kg is initially at rest. The particle decays into two fragments that fly off with velocities of 0.987c and 20.868c, respectively. Find the masses of the fragments. Hint: Conserve both massenergy and momentum.

Starting with the definitions of relativistic energy and momentum, show that E 2 5 p2c 2 1 m2c 4 (Eq. 26.10).

Consider the reaction 2 9 3 2 5U 1 0 1n S 1 5 4 7 8La 1 3 8 5 7Br 1 0 1n. (a) Write the conservation of relativistic energy equation symbolically in terms of the rest energy and the kinetic energy, setting the initial total energy to the final total energy. (b) Using values from Appendix B, find the total mass of the initial particles. (c) Using the values given below, find the total mass of the particles after the reaction takes place. (d) Subtract the final particle mass from the initial particle mass. (e) Convert the answer to part (d) to MeV, obtaining the kinetic energy of the daughter particles, neglecting the kinetic energy of the reactants. Note: Lanthanum-148 has atomic mass 147.932 236 u; bromine-87 has atomic mass 86.920 711 19 u.

Consider electrons accelerated to a total energy of 20.0 GeV in the 3.00-km-long Stanford Linear Accelerator. (a) What is the g factor for the electrons? (b) How long does the accelerator appear to the electrons? Electron mass energy: 0.511 MeV.

An electron has a speed of 0.750c. (a) Find the speed of a proton that has the same kinetic energy as the electron. (b) Find the speed of a proton that has the same momentum as the electron.

The rest energy of an electron is 0.511 MeV. The rest energy of a proton is 938 MeV. Assume both particles have kinetic energies of 2.00 MeV. Find the speed of (a) the electron and (b) the proton. (c) By how much does the speed of the electron exceed that of the proton? Note: Perform the calculations in MeV; dont con- vert the energies to joules. The answer is sensitive to rounding.

A spring of force constant k is compressed by a distance x from its equilibrium length. (a) Does the mass of the spring change when the spring is compressed? Explain. (b) Find an expression for the change in mass of the spring in terms of k, x, and c. (c) What is the change in mass if the force constant is 2.0 3 102 N/m and x 5 15 cm?

A star is 5.00 ly from the Earth. At what speed must a spacecraft travel on its journey to the star such that the Earthstar distance measured in the frame of the spacecraft is 2.00 ly?

An electron has a total energy equal to five times its rest energy. (a) What is its momentum? (b) Repeat for a proton.

An astronaut wishes to visit the Andromeda galaxy, making a one-way trip that will take 30.0 years in the spaceships 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 3 106 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: 1 "1 1 x < 1 2 x 2 for x ,, 1

An alarm clock is set to sound in 10 h. At t 5 0, the clock is placed in a spaceship moving with a speed of 0.75c (relative to Earth). What distance, as determined by an Earth observer, does the spaceship travel before the alarm clock sounds?

Owen and Dina are at rest in frame S9, which is moving with a speed of 0.600c with respect to frame S. They play a game of catch while Ed, at rest in frame S, watches the action (Fig. P26.39). Owen throws the ball to Dina with a speed of 0.800c (according to Owen) and their separation (measured in S9) is equal to 1.80 3 1012 m. (a) According to Dina, how fast is the ball moving? (b) According to Dina, what time interval is required for the ball to reach her? According to Ed, (c) how far apart are Owen and Dina, and (d) how fast is the ball moving?