Exam 26: Special Relativity

A spaceship with a constant velocity of 0.800c relative to Earth travels to the star that is 4.30 light-years from Earth.What distance does the space ship travel as measured by a passenger on the ship?

Two stars are at rest relative to each other.A spaceship is moving between these two stars at 0.932c relative to each star.To someone in the ship,the distance between the two stars appears to be $\text { 26.4 light-years. }$ What is the distance between the stars in their own rest frame?

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?

A tracking station on Earth observes a rocket move away at 0.370c.This rocket is designed to launch a projectile at 0.505c relative to the rocket.What speed (in terms of the speed of light)does the tracking station measure for the projectile if it is fired (a)straight ahead of the rocket or (b)backward from the rocket?

A really high-speed train moves in a direction parallel to its length with a speed that approaches the speed of light.The length of the train,as measured by a stationary observer on the ground,

How much energy would be released if 2.0 kg of material was lost during a reaction? (c = 3.0 × 10⁸ m/s)

A space barge pushes on a spaceship with a rest mass of 15,000 kg and accelerates it from a speed of 0.600c to a speed of 0.700c.How much work does the barge have to do to accomplish this? (c = 3.00 × 10⁸ m/s)

Two spaceships approach each other along a straight line at a constant relative velocity of 0.9880c as measured by the captain of one of the ships.An observer on Earth is able to measure the speed of only one of the ships as 0.9000c.From the point of view of the observer on Earth,what is the speed of the other ship in terms of the speed of light?

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 board the spaceship?

The figure shows a right-angled construction frame ABC.When measured at rest,it has dimensions as follows: AB = 26.0 m,AC = 10.0 m,and BC = 24.0 m.This frame is now given a new velocity of 0.760c,relative to Earth,in a direction parallel to AC.How long is part AC of this frame with the new velocity as measured by Earth-based engineers?

During a reaction,a reactant loses 4.8 × 10^-28 kg of mass.How many joules of energy are released? (c = 3.0 × 10⁸ m/s)

According to the equation E = mc²,an object turns into energy when it reaches the speed of light.

How fast must a meter stick move,relative to the frame of the observer making the measurement,so its length will be measured to be 0.60 m?

A spaceship,traveling at 0.100c away from a stationary space platform,launches a secondary rocket towards the station,with a speed of 0.560c relative to the spaceship.What is the speed of the secondary rocket relative to the space platform?

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 kg and moves away with a speed 0.280c,and the second piece moves in the opposite direction with a speed 0.600c.What is the rest mass of the second piece?

Two satellites with equal rest masses are traveling toward each other in deep space.One is traveling at 0.550c and the other at 0.750c.The satellites collide and somehow manage to stick together.What is the speed of the combined object after the collision?

How much work must be done to accelerate a particle of mass $3.5 \times 10 ^{- 14} \mathrm {~kg}$ from a speed of $1.2 \times 10 ^ { 8 } \mathrm {~m} / \mathrm { s }$ to a speed of $1.9 \times 10 ^ { 8 } \mathrm {~m} / \mathrm { s } ?$ (c = 3.0 × 10⁸ m/s)

When a proton is traveling at 0.80c,what is the ratio of its kinetic energy to its rest energy?

Two spaceships are traveling through space at speeds of 0.600c and 0.900c,respectively,with respect to Earth.If they are headed directly toward each other,what is their approach speed (in terms of the speed of light)as measured by the captain of either ship?

A spaceship enters the solar system moving toward the sun at a constant speed relative to the sun.By its own clock,the time elapsed between the time it crosses the orbit of Jupiter and the time it crosses the orbit of Mars is 50.0 minutes.As measured in the coordinate system of the sun,how long did it take for the spaceship to travel that distance? The radius of the orbit of Jupiter is 778 × 10⁹ m,and that of the orbit of Mars is 228 × 10⁹ m.