Exam 28: Special Relativity

An astronomer on earth observes two galaxies moving away from each other along a line that passes through the earth. The astronomer finds that each is moving with a speed of 2.1 × 10⁸ m/s relative to the earth. At what speed are the galaxies moving apart relative to each other?

Which one of the following systems would constitute an inertial reference frame?

The rest energy of a block is E₀. Relative to inertial observer O, the block is moving with speed v so that -Observer O finds that the block takes 12 s to go from A to B. How long would this time interval appear to be to an observer riding on the block?

The temperature of a 5.00-kg lead brick is increased by 525 C°. If the specific heat capacity of lead is 128 J/(kg ^$\circ$ C°), what is the increase in the mass of the lead brick when it has reached its final temperature?

During a baseball game, a batter hits a ball directly back to the pitcher who catches it. An observer flying over the stadium at a speed of 0.75c, measures 0.658 s as the time between the two events (hitting and catching the ball). What is the proper time interval between the two events?

Mars rotates about its axis once every 88 642 s. A spacecraft comes into the solar system and heads directly toward Mars at a speed of 0.800c. What is the rotational period of Mars according to the beings on the spaceship?

At what speed is a particle traveling if its kinetic energy is three times its rest energy?

A bomb is designed to explode 2.00 s after it is armed. The bomb is launched from earth and accelerated to an unknown final speed. After reaching its final speed, however, the bomb is observed by people on earth to explode 2.90 s after it is armed. What is the final speed of the bomb just before it explodes?

Two rockets, A and B, travel toward each other with speeds 0.5c relative to an inertial observer. Determine the speed of rocket A relative to rocket B.

The momentum of an electron is 1.75 times larger than the value computed non-relativistically. What is the speed of the electron?

Two rockets, A and B, approach each other as shown in the figure. A travels to the right at 0.7c while B travels to the left at 0.8c. Both speed measurements are made relative to an inertial observer. -Determine the speed of A relative to B.

At time t = 2.3 s, a 4-kg block that initially moves with a constant speed of 6 m/s undergoes an inelastic collision with another block. Any two inertial observers must agree that

Two rockets, A and B, approach each other as shown in the figure. A travels to the right at 0.7c while B travels to the left at 0.8c. Both speed measurements are made relative to an inertial observer. -Both rockets have a supply of unstable mesons with a mean proper lifetime of 2.6 × 10^-8 s. Which one of the following is a correct observation for the inertial observer?

The figure shows a side view of a galaxy that is 50.0 light years in diameter. This value for the diameter is its proper length. A spaceship enters the galactic plane with speed 0.995c relative to the galaxy. Assume that the galaxy can be treated as an inertial reference frame. Note: A light year is the distance that light travels through vacuum in one year; that is, 1 light year = c × (1 year). -Determine the diameter of the galaxy as perceived by a person in the spaceship.

A subatomic particle X spontaneously decays into two particles, A and B, each of rest energy 1.40 × 10² MeV. The particles fly off in opposite directions, each with speed 0.827c relative to an inertial reference frame S. -Which one of the following statements concerning particle X is true?

The rest energies of three subatomic particles are: Particle X: 107 MeV; Particle Y: 140 MeV; Particle Z: 0.51 MeV. Which one of the following statements is necessarily true concerning these three particles?

Which one of the following statements is a consequence of Special Relativity?

The figure shows a side view of a galaxy that is 50.0 light years in diameter. This value for the diameter is its proper length. A spaceship enters the galactic plane with speed 0.995c relative to the galaxy. Assume that the galaxy can be treated as an inertial reference frame. Note: A light year is the distance that light travels through vacuum in one year; that is, 1 light year = c × (1 year). -How long does it take the spaceship to cross the galaxy according to a clock on board the spaceship?

How much energy is required to accelerate a golf ball of mass 0.046 kg initially at rest to a speed of 0.75c?

Two rockets, A and B, approach each other as shown in the figure. A travels to the right at 0.7c while B travels to the left at 0.8c. Both speed measurements are made relative to an inertial observer. -Determine the ratio of the kinetic energy of rocket B to its rest energy.