Physics for Scientists and Engineers - Relativity

Physics for Scientists and Engineers Chapter 36 Relativity 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 Earth, A) 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: C 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 rocket, A) 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: A 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) Δt B) more than Δt C) less than Δt D) The answer depends on whether they are moving toward her or away from her. Answer: B 4) You are a passenger on a spaceship. As the speed of the spaceship increases, you would observe that A) 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: C 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) 0.90c B) c C) 1.1c D) 1.20c E) 1.9c Answer: B 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 energy B) the total energy C) the linear momentum D) more than one of these E) none of these Answer: E 36.2 Problems 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 min B) 180 min C) 90 min D) 360 min E) 113 min Answer: A 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 y B) 7.28 y C) 42.1 y ( TIME DILATION ) D) 30.7 y Answer: A 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 y B) 2.81 y C) 4.05 y D) 22.1 y Answer: A 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) 0.779c B) 0.687c C) 0.975c D) 0.384c Answer: A 6) 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 m 7) 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 ? (LORENTZ TRANSFORMATION) A) 380 m B) 340 m C) 360 D) 350 E) 310 Answer: m m m A 8) 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 μs B) -4.9 μs C) 1.7 μs D) 1.3 μs E) 1.5 μs Answer: A 9) 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 Answer: A 10) 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) 0.81c B) 1.0c C) 0.76c D) 0.64c E) 0.96c Answer: A 11) 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) 0.170c B) 0.196c C) 0.911c D) 0.930c E) 0.951c Answer: B 12) 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 kV B) 130 kV C) 180 kV D) 200 kV Answer: A 13) 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/s B) 1.33 × 108 m/s C) 3.24 × 108 m/s D) 3.33 × 108 m/s E) 4.12 × 108 m/s Answer: A 14) 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) 0.25c B) 0.50c C) 0.71c D) 0.75c E) 0.87c Answer: E 15) 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 J B) 9.0 × 1016 J C) 2.7 × 1012 J D) 4.5 × 109 J E) 3.0 × 103 J Answer: B K=(GAMMA-1)MC^2 FIND K.