Exam 26: The Special Theory of Relativity

A satellite with a rest mass of 200 kg and a speed of 0.800c and a second satellite with a rest mass of 100 kg and a speed of 0.600c are traveling toward each other in deep space. The satellites collide And somehow manage to stick together. What is the speed of the combined object after the Collision?

If a particle has a total energy that is $5.00$ times its rest energy, the speed of the particle is closest to which one of the following values?

If you were in a spaceship traveling close to the speed of light with respect to Earth, you would notice that

A spaceship traveling at 0.50c away from Earth launches a secondary rocket in the forward direction at 0.50c relative to the spaceship. As measured by Earthlings, how fast is the secondary Rocket moving away from Earth?

Observer A sees a pendulum oscillating back and forth in a relativistic rocket and measures its period to be TA. Observer B moves along with the rocket and measures the period of the Pendulum to be TB. What is true about these two time measurements?

Astronaut Rob leaves Earth in a spaceship at a speed of $0.960 \mathrm { c }$ relative to an observer on Earth. Rob's destination is a star system $14.4$ light-years away (one light-year is the distance light travels in one year). Relative to a frame of reference that is fixed with respect to Earth, how long does it take Rob to complete the trip?

Two spaceships are approaching one another, each at a speed of 0.31c relative to a stationary observer on Earth. What speed, in terms of the speed of light, does an observer on one spaceship record for the other approaching spaceship?

An astronaut is resting on a bed inclined at an angle above the floor of a spaceship, as shown in the figure. From the point of view of an observer who sees the spaceship moving near the speed of light parallel to the floor, the angle the bed makes with the floor

You are a passenger on a spaceship. As the speed of the spaceship increases, you will observe

During a reaction, $170 \mu \mathrm { J }$ of energy is released. What change of mass would accompany this release? $\left( c = 3.0 \times 10 ^ { 8 } \mathrm {~m} / \mathrm { s } \right)$

Two spaceships approach Earth from the same direction. One has a speed of 0.21c and the other a speed of 0.34c, both relative to Earth. What is the speed of one spaceship relative to the other?

A spaceship is moving in a straight line away from Earth at 0.80c, measured relative to Earth. It launches a missile that moves away from the spaceship in the forward direction at 0.60c, relative to The ship. Relative to Earth, what is the speed of this missile?

If the kinetic energy of a proton is 80% of its total energy, what is the speed of the proton?

Someone in Earth's rest frame says that a spaceship's trip between two planets took $10.0 \mathrm { y }$ , while an astronaut on the space ship says that the trip took $5.78 \mathrm { y }$ . What is the speed of the spaceship, assuming the planets are at essentially at rest?

How much energy would be released if $2.0 \mathrm {~kg}$ of material was lost during a reaction? $\left( c = 3.0 \times 10 ^ { 8 } \right.$ $\mathrm { m } / \mathrm { s }$ )

In a certain chemical reaction, $8.1 \times 10 ^ { - 19 } \mathrm {~J}$ of energy is released per molecule formed. What is the difference in mass per molecule between the sum of the masses of the molecules of the reagents before the reaction and the mass of the molecules produced by the reaction? $\left( c = 3.0 \times 10 ^ { 8 } \mathrm {~m} / \mathrm { s } \right)$

A satellite, initially at rest in deep space, separates into two pieces, which move away from each other. One piece has a rest mass of $190 \mathrm {~kg}$ and moves away with a speed $0.500 c$ , and the second piece has a rest mass of $250 \mathrm {~kg}$ and moves in the opposite direction. What is the speed of the second piece?

From the Earth, the Earthlings see the Enterprise approaching from the west at 0.800c and the Klingons approaching from the east at 0.900c. What speed, in terms of the speed of light, does the crew of the Enterprise measure for the Klingon ship?

Two satellites with equal rest masses of 100 kg are traveling toward each other in deep space. One is traveling at 0.650c and the other at 0.850c. The satellites collide and somehow manage to stick Together. What is the rest mass of the combined object after the collision?

A spaceship with a constant speed of 0.800c relative to Earth travels to a star that is 4.30 light-years from Earth. How much time for this trip would elapse on a clock on Earth?