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Exam 36: Relativity

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Question 1

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In an "atom smasher," two particles collide head on at relativistic speeds.If the velocity of the first particle is 0.741c to the left,and the velocity of the second particle is to the right (both of these speeds are measured in Earth's rest frame) ,how fast are the particles moving with respect to each other?

A) 0.866c
B) 1.091c
C) 0.883c
D) 0.788c

E) A) and C)
F) B) and D)

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Question 2

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In their common rest frame,two stars are 90.0 light-years (ly) apart.If they are 12.0 ly apart as measured by the navigator in a spaceship traveling between them,how fast is the spaceship moving? Express your answer in terms of c.

A) 0.991c
B) 0.986c
C) 0.980c
D) 0.972c

E) A) and B)
F) A) and C)

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Question 3

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Two space stations are at rest relative to each other and are 6.0 × 10⁷ m apart,as measured by observers on the stations.A spaceship traveling from one station to the other at 0.90c relative to the stations passes both of them,one after the other.As measured by an observer in the spaceship,how long does it take to travel from one station to the other? (c = 3.00 × 10⁸ m/s)

An astronaut leaves Earth in a spaceship at a speed of 0.960c relative to an observer on Earth.The astronaut's destination is a star system 14.4 light-years away.(One light-year is the distance light travels in one year.) According to the astronaut,how long does the trip take?

How much work must be done to accelerate a particle of mass from a speed of to a speed of

A star is moving towards the earth with a speed at 90% the speed of light.It emits light,which moves away from the star at the speed of light.Relative to us on earth,what is the speed of the light moving toward us from the star?

A rocket is moving at 1/4 the speed of light relative to Earth.At the center of this rocket,a light suddenly flashes.To an observer at rest in the rocket,

A particle is moving at 0.75c relative to a lab on Earth.By what percentage is the Newtonian expression for its momentum in error? (The percentage error is the difference between the erroneous and correct values,divided by the correct one) .

An astronaut on a spaceship moving at 0.927c says that the trip between two stationary stars took How long does this journey take as measured by someone at rest relative to the two stars?

At what speed relative to the lab will a 0.272-kg object have the same momentum as a 1.30-kg object that is moving at 0.515c relative to the lab?

A spacecraft is measured by an observer on the ground to have a length of 53 m as it flies toward the earth with a speed 1.7 × 10⁸ m/s.The spacecraft then lands and its length is again measured by the observer on the ground,this time while the spacecraft is at rest on the launchpad.What result does he now get for the length? (c = 3.00 × 10⁸ m/s)

The closest known star to our solar system is Alpha Centauri,which is approximately 4.30 light years away.A spaceship with a constant speed of 0.800c relative to the earth travels from Earth to this star. (a)How much time would elapse during the trip on a clock on board the spaceship? (b)How much time would elapse during the trip on a clock on Earth?

A spaceship is moving away from the earth with a constant speed of 0.80c.The spaceship fires a 28-kg missile with a speed of 0.50c relative to the spaceship.What is the speed of the missile measured by observers on the earth if the missile is fired (a)away from the earth? (b)toward the earth?

The special theory of relativity predicts that there is an upper limit to the speed of a particle.It therefore follows that there is also an upper limit on the following properties of a particle.

Two spaceships are approaching one another,each at a speed of 0.28c relative to a stationary observer on Earth.What speed does an observer on one spaceship record for the other approaching spaceship?

An electron is accelerated from rest through a potential difference of 50.0 kV.What is the TOTAL energy of the electron? (c = 3.00 × 10⁸ m/s,e = 1.60 × 10^-19 C,m_el = 9.11 × 10^-31 kg)

System has a velocity u = +0.56c relative to system S,as shown in the figure.The clocks of S and are synchronized at t = = 0 when the origins O and coincide.An event is observed in both systems.The event takes place at x = 800 m and at time t = 3.0 μs as measured by an observer in S.What is the time of the event,measured by an observer in ?

A set of twins,Andrea and Courtney,are initially 10 years old.While Courtney remains on Earth,Andrea rides on a spaceship which travels away from Earth at a speed of 0.60c for five years (as measured by Courtney) ,then immediately turns around and comes back at 0.60c.When Andrea returns,Courtney is 20 years old.How old is Andrea upon her return?

The captain of spaceship A observes enemy spaceship E escaping with a relative velocity of 0.48c,as shown in the figure.A missile M is fired from ship A,with a velocity of 0.72c relative to ship A.What is the relative velocity of approach of missile M,observed by the crew on ship E?

An unstable particle is moving at a speed of 2.6 × 10⁸ m/s relative to a laboratory.Its lifetime is measured by a stationary observer in the laboratory to be 4.7 × 10^-6 seconds.What is the lifetime of the particle,measured in the rest frame of the particle? (c = 3.00 × 10⁸ m/s)