Wolfson Eup3 Ch33 Test Bank

Essential University Physics, 3e (Wolfson)Chapter 33 Relativity

33.1 Conceptual Questions

1) 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 on EarthA) the light will reach the front of the rocket at the same instant that it reaches the back of the rocket.B) the light will reach the front of the rocket before it reaches the back of the rocket.C) the light will reach the front of the rocket after it reaches the back of the rocket.Answer: CVar: 1

2) 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 rocketA) the light will reach the front of the rocket at the same instant that it reaches the back of the rocket.B) the light will reach the front of the rocket before it reaches the back of the rocket.C) the light will reach the front of the rocket after it reaches the back of the rocket.Answer: AVar: 1

3) An astronaut in an inertial reference frame measures a time interval Δt between her heartbeats. What will observers in all other inertial reference frames measure for the time interval between her heartbeats?A) ΔtB) more thanΔtC) less than ΔtD) The answer depends on whether they are moving toward her or away from her.Answer: BVar: 1

4) You are a passenger on a spaceship. As the speed of the spaceship increases, you would observe thatA) the length of your spaceship is getting shorter.B) the length of your spaceship is getting longer.C) the length of your spaceship is not changing.Answer: CVar: 1

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5) 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) 0.90cB) cC) 1.1cD) 1.20cE) 1.9cAnswer: BVar: 1

6) 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.A) the kinetic energyB) the total energyC) the linear momentumD) more than one of theseE) none of theseAnswer: EVar: 1

33.2 Problems

1) Astronaut Spud Nick is space-traveling from planet X to planet Y at a speed of 0.60c relative to the planets, which are at rest relative to each other. When he is precisely halfway between the planets, a distance of 1.0 light-hour from each one as measured in the planet frame, nuclear devices are detonated on each planet. The explosions are simultaneous in the frame of the planets. What is the difference in the time of arrival of the flashes from the explosions as observed by Spud?A) 300 minB) 150 minC) 75 minD) 0 minE) 113 minAnswer: EVar: 1


2) Astronaut Mark Uri is space-traveling from planet X to planet Y at a speed of relative to the planets, which are at rest relative to each other. When he is precisely halfway between the planets, a distance of 1.0 light-hour from each one as measured in the planet frame, nuclear devices are detonated on both planets. The explosions are simultaneous in Mark's frame. What is the difference in the time of arrival of the flashes from the explosions as observed by Mark?A) 0 minB) 180 minC) 90 minD) 360 minE) 113 minAnswer: AVar: 50+

3) As measured in Earth's rest frame, a spaceship traveling at takes to travel between planets. How long does the trip take as measured by someone on the spaceship?A) 2.98 yB) 7.28 yC) 42.1 yD) 30.7 yAnswer: AVar: 50+

4) 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?A) 20.0 yB) 2.81 yC) 4.05 yD) 22.1 yAnswer: AVar: 50+

5) Someone in Earth's rest frame says that a spaceship's trip between two planets took 10.0 y, while an astronaut on the space ship says that the trip took Find the speed of the spaceship in terms of the speed of light.A) 0.779cB) 0.687cC) 0.975cD) 0.384cAnswer: AVar: 50+

6) 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)Answer: 2.3 µsVar: 1


7) 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?Answer: (a) 3.23 y (b) 5.38 yVar: 1

8) A spaceship approaches the earth with a speed 0.50c. A passenger in the spaceship measures his heartbeat as 70 beats per minute. What is his heartbeat rate according to an observer that is at rest relative to the earth?A) 69 beats per minuteB) 73 beats per minuteC) 65 beats per minuteD) 61 beats per minuteE) 80 beats per minuteAnswer: DVar: 1

9) 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?A) 10 yB) 12 yC) 15 yD) 18 yE) 20 yAnswer: DVar: 1

10) Relative to the frame of the observer making the measurement, at what speed parallel to its length is the length of a meterstick 60 cm?A) 0.80cB) 0.60cC) 0.50cD) 0.70cE) 0.90cAnswer: AVar: 1


11) 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?A) 14.4 yB) 22.7 yC) 9.34 yD) 15.0 yE) 4.20 yAnswer: EVar: 1

12) In their common rest frame, two stars are 90.0 light-years (ly) apart. If they are 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) 0.991cB) 0.986cC) 0.980cD) 0.972cAnswer: AVar: 50+

13) A particle in a 453 m-long linear particle accelerator is moving at How long does the particle accelerator appear to the particle?A) 219 mB) 589 mC) 104 mD) 936 mAnswer: AVar: 50+

14) A spaceship is moving between two distant stars at 0.932c. To someone in the ship, the distance between the two stars appears to be What is the distance between the stars in the rest frame of the stars?A) 74.2 lyB) 9.75 lyC) 21.5 lyD) 56.5 lyAnswer: AVar: 50+


15) 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)A) 97 msB) 220 msC) 510 msD) 58 msE) 39 msAnswer: AVar: 1

16) 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)Answer: 64 mVar: 1

17) System has a velocity u = +0.45c 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 = 600 m and at time t = 1.9 μs, as measured by an observer in S. What is the -coordinate of the event, measured by an observer in ?

A) 380 mB) 340 mC) 360 mD) 350 mE) 310 mAnswer: AVar: 1


18) 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) 1.8 μsB) -4.9 μsC) 1.7 μsD) 1.3 μsE) 1.5 μsAnswer: AVar: 1

19) 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) 0.866cB) 1.091cC) 0.883cD) 0.788cAnswer: AVar: 50+

20) A spaceship approaching an asteroid at a speed of 0.60c launches a rocket forward with a speed of 0.40c relative to the spaceship. At what speed is the rocket approaching the asteroid as measured by an astronaut on the asteroid?A) 0.81cB) 1.0cC) 0.76cD) 0.64cE) 0.96cAnswer: AVar: 1


21) 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?

A) 0.37cB) 0.24cC) 0.34cD) 0.30cE) 0.27cAnswer: AVar: 1

22) Three spaceships A, B, and C are in motion, as shown in the figure. The commander on ship B observes ship C approaching with a relative velocity of 0.78c. The commander also observes ship A, advancing in the rear, with a relative velocity of 0.31c. What is the velocity of ship C, relative to an observer on ship A?



23) Three spaceships A, B, and C are in motion as shown in the figure. The commander on ship B observes ship C approaching with a relative velocity of 0.83c. The commander also observes ship A, advancing in the rear, with a relative velocity of 0.48c. As measured by commander on ship B, at what speed is ship A approaching ship C?


24) Consider three galaxies, Alpha, Beta and Gamma. An observer in Beta sees the other two galaxies each moving away from him in opposite directions at speed 0.70c. At what speed would an observer in Alpha see the galaxy Beta moving?A) 0.82cB) 0.70cC) 0.94cD) 0.35cE) 0.57cAnswer: BVar: 1

25) 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?Answer: 0.52cVar: 50+

26) 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?Answer: (a) 0.93c (b) 0.50cVar: 1


27) 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) 0.944cB) 0.922cC) 0.981cD) 0.592cAnswer: AVar: 50+

28) 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). A) 34%B) 28%C) 38%D) 43%Answer: AVar: 46

29) In the lab, a relativistic proton has a momentum of 1.00 × 10-19 kg ∙ m/s and a rest energy of 0.150 nJ. What is the speed of the proton in the lab? (c = 3.00 × 108 m/s, mproton = 1.67 × 10-27

kg)A) 0.170cB) 0.196cC) 0.911cD) 0.930cE) 0.951cAnswer: BVar: 1

30) An electron has a speed of 0.643c. Through what potential difference would the electron need to be accelerated (starting from rest) in order to reach this speed? (c = 3.00 × 108 m/s, e = 1.60 × 10-19 C, mel = 9.11 × 10-31 kg)A) 160 kVB) 130 kVC) 180 kVD) 200 kVAnswer: AVar: 50+


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

A) 1.24 × 108 m/sB) 1.33 × 108 m/sC) 3.24 × 108 m/sD) 3.33 × 108 m/sE) 4.12 × 108 m/sAnswer: AVar: 1

32) In a certain particle accelerator, a proton has a kinetic energy that is equal to its rest energy. What is the speed of the proton relative to the accelerator?A) 0.25cB) 0.50cC) 0.71cD) 0.75cE) 0.87cAnswer: EVar: 1

33) How many joules of energy are required to accelerate a 1.0-kg mass from rest to a speed of 86.6% the speed of light? (c = 3.00 × 108 m/s)A) 1.8 × 1017 JB) 9.0 × 1016 JC) 2.7 × 1012 JD) 4.5 × 109 JE) 3.0 × 103 JAnswer: BVar: 1

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

of to a speed of

Answer: 1200 JVar: 50+

35) Assume that a certain city consumes electrical energy at an average rate of 2.0 × 109 W. What would be the mass change in producing enough energy to keep this city running for 21 weeks? (c = 3.00 × 108 m/s) A) 0.28 kgB) 0.32 kgC) 0.39 kgD) 0.48 kgAnswer: AVar: 17


36) During a nuclear reaction, the particles involved lose 4.8 × 10-28 kg of mass. How many joules of energy are released by this reaction? (c = 3.00 × 108 m/s)A) 4.3 × 10-11 JB) 1.4 × 10-19 JC) 1.6 × 10-36 JD) 2.1 × 10-40 JE) 5.3 × 10-45 JAnswer: AVar: 1

37) During a nuclear reaction, 1.7 × 10-4 J of energy is released. What is the resulting change in mass of the particles involved? (c = 3.00 × 108 m/s)A) 5.1 × 10-4 kgB) 4.3 × 10-11 kgC) 1.5 × 10-13 kgD) 4.8 × 10-18 kgE) 1.9 × 10-21 kgAnswer: EVar: 1

38) 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, mel = 9.11 × 10-31 kg)

A) 8.00 × 10-15 JB) 16.2 × 10-15 JC) 8.20 × 10-14 JD) 9.00 × 10-14 JE) 16.2 × 10-14 JAnswer: DVar: 1

39) A relativistic proton has a momentum of 1.0 × 10-17 kg ∙ m/s and a rest energy of 0.15 nJ. What is the kinetic energy of this proton? (c = 3.00 × 108 m/s, mproton = 1.67 × 10-27 kg)A) 1.3 pJB) 1.6 pJC) 3.0 pJD) 2.2 pJE) 2.5 pJAnswer: CVar: 1


40) A proton in a certain particle accelerator has a kinetic energy that is equal to its rest energy. What is the TOTAL energy of the proton as measured by a physicist working with the accelerator? (c = 3.00 × 108 m/s, mproton = 1.67 × 10-27 kg)

A) 5.69 × 10-11 JB) 1.50 × 10-10 JC) 2.07 × 10-10 JD) 3.01 × 10-10 JE) 8.77 × 10-10 JAnswer: DVar: 1

41) A proton in a certain particle accelerator has a kinetic energy that is equal to its rest energy. What is the momentum of the proton as measured by a physicist working with the accelerator? (c = 3.00 × 108 m/s, mproton = 1.67 × 10-27 kg)

A) 2.51 × 10-19 kg ∙ m/sB) 2.89 × 10-19 kg ∙ m/sC) 4.34 × 10-19 kg ∙ m/sD) 5.01 × 10-19 kg ∙ m/sE) 8.68 × 10-19 kg ∙ m/sAnswer: EVar: 1

42) How fast must a proton move so that its kinetic energy is 80% of its total energy?A) 0.020cB) 0.87cC) 0.92cD) 0.98cE) 0.80cAnswer: DVar: 1

43) As a spaceship is moving toward Earth, an Earthling measures its length to be 325 m, while the captain on board radios that her spaceship's length is 1150 m. (c = 3.00 × 108 m/s)(a) How fast is the rocket moving relative to Earth?(b) What is the TOTAL energy of a 75.0-kg crewman as measured by (i) the captain in the rocket and (ii) the Earthling?Answer: (a) 0.959c = 2.88 × 108 m/s (b) (i) 6.75 × 1018 J (ii) 2.39 × 1019 JVar: 1


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Wolfson Eup3 Ch33 Test Bank