Essential University Physics
4th Edition
ISBN: 9780134988566
Author: Wolfson, Richard
Publisher: Pearson Education,
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Chapter 33, Problem 46P
Derive the Lorentz transformations for time from the transformations for space.
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Essential University Physics
Ch. 33.2 - Prob. 33.1GICh. 33.4 - Triplets A and B board spaceships and head away...Ch. 33.5 - A comet plunges into the planet Jupiter. At the...Ch. 33.7 - The rest energy of a proton is 938 MeV. Without...Ch. 33 - Prob. 1FTDCh. 33 - Does relativity require that the speed of sound be...Ch. 33 - Time dilation is sometimes described by saying...Ch. 33 - If youre in a spaceship moving at 0.95c relative...Ch. 33 - The Andromeda Galaxy is 2 million light years from...Ch. 33 - Prob. 6FTD
Ch. 33 - Prob. 7FTDCh. 33 - The rest energy of an electron is 511 keV. Whats...Ch. 33 - An atom in an excited state emits a burst of...Ch. 33 - The quantity EB is invariant. What does this say...Ch. 33 - An airplane makes a round trip between two points...Ch. 33 - Consider a Michelson-Morley experiment with 11-m...Ch. 33 - Two stars are 50 ly apart, measured in their...Ch. 33 - How long would it take a spacecraft traveling at...Ch. 33 - A spaceship passes by you at half the speed of...Ch. 33 - An extraterrestrial spacecraft whizzes through the...Ch. 33 - How fast would you have to move relative to a...Ch. 33 - A hospitals linear accelerator produces electron...Ch. 33 - Prob. 19ECh. 33 - At what speed will the momentum of a proton (mass...Ch. 33 - Prob. 21ECh. 33 - A particle is moving at 0.90c. If its speed...Ch. 33 - Find (a) the total energy and (b) the kinetic...Ch. 33 - At what speed will the relativistic and Newtonian...Ch. 33 - Example 33.1: A spaceship departs on a trip to...Ch. 33 - Prob. 26ECh. 33 - Prob. 27ECh. 33 - Prob. 28ECh. 33 - Prob. 29ECh. 33 - Prob. 30ECh. 33 - Prob. 31ECh. 33 - Prob. 32ECh. 33 - Show that the time of Equation 33.2 is longer than...Ch. 33 - Youre designing a Michelson interferometer in...Ch. 33 - Earth and Sun are 8.3 light minutes apart, as...Ch. 33 - Youre the communications officer on a fast...Ch. 33 - You wish to travel to a star N light years from...Ch. 33 - Prob. 38ECh. 33 - Twins A and B live on Earth. On their 20th...Ch. 33 - Radioactive oxygen-15 decays at such a rate that...Ch. 33 - Two distant galaxies are receding from Earth at...Ch. 33 - Two spaceships are racing. The slower one passes...Ch. 33 - Use relativistic velocity addition to show that if...Ch. 33 - Earth and Sun arc 8.33 light minutes apart. Event...Ch. 33 - The Curiosity rover touched down on Mars when...Ch. 33 - Derive the Lorentz transformations for time from...Ch. 33 - In the light box of Fig. 33.6, let event A be the...Ch. 33 - Prob. 48PCh. 33 - How fast would you have to go to reach a star 240...Ch. 33 - An advanced civilization has developed a spaceship...Ch. 33 - A spaceship travels at 0.80c from Earth to a star...Ch. 33 - Use Equation 33.6 to calculate the square of the...Ch. 33 - A light beam is emitted at event A and arrives at...Ch. 33 - Compare the momentum changes needed to boost a...Ch. 33 - Event A occurs at x = 0 and t = 0 in reference...Ch. 33 - When a particle's speed doubles, its momentum...Ch. 33 - Find (a) the speed and (b) the momentum of a...Ch. 33 - Prob. 58PCh. 33 - A large city consumes electrical energy at the...Ch. 33 - In a nuclear-fusion reaction, two deuterium nuclei...Ch. 33 - Use the binomial approximation (Appendix A) to...Ch. 33 - Prob. 62PCh. 33 - At what speed are a particle’s kinetic and rest...Ch. 33 - Use the Lorentz transformations to show that if...Ch. 33 - A source emitting light with frequency f moves...Ch. 33 - You’d like to travel to a star a distance d from...Ch. 33 - A large spaceship is passing Earth at 0.75c....Ch. 33 - Prob. 68PCh. 33 - The highest energy cosmic rays observed are...Ch. 33 - Consider a line of positive charge with line...Ch. 33 - Prob. 71PCh. 33 - Youve been named captain of NASAs first...Ch. 33 - Youve been named captain of NASAs first...Ch. 33 - Youve been named captain of NASAs first...Ch. 33 - Youve been named captain of NASAs first...
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- Two powerless rockets are on a collision course. The rockets are moving with speeds of 0.800c and 0.600c and are initially 2.52 × 1012 m apart as measured by Liz, an Earth observer, as shown in Figure P1.34. Both rockets are 50.0 m in length as measured by Liz. (a) What are their respective proper lengths? (b) What is the length of each rocket as measured by an observer in the other rocket? (c) According to Liz, how long before the rockets collide? (d) According to rocket 1, how long before they collide? (e) According to rocket 2, how long before they collide? (f) If both rocket crews are capable of total evacuation within 90 min (their own time), will there be any casualties? Figure P1.34arrow_forwardShow that the equation is invariant under a Lorentz transformation but not under a Galilean transformation. (This is the wave equation that describes the propagation of light waves in free space.)arrow_forwardA yet-to-be-built spacecraft starts from Earth moving at constant speed to the yet-to-be-discovered planet Retah, which is 20 lighthours away from Earth. It takes 25 h (according to an Earth observer) for a spacecraft to reach this planet. Assuming that the clocks are synchronized at the beginning of the journey, compare the time elapsed in the spacecraft’s frame for this one-way journey with the time elapsed as measured by an Earth-based clock.arrow_forward
- It is said that Einstein, in his teenage years, asked the question, What would I see in a mirror if I carried it in my hands and ran at the speed of light? How would you answer this question?arrow_forwardYou are driving on a freeway at a relativistic speed. Straight ahead of you, a technician standing on the ground turns on a searchlight and a beam of light moves exactly vertically upward, as seen by the technician. As you observe the beam of light, you measure the magnitude of the vertical component of its velocity as (a) equal to c, (b) greater than c, or (c) less than c. If the technician aims the searchlight directly at you instead of upward, you measure the magnitude of the horizontal component of its velocity as (d) equal to c, (e) greater than c, or (f) less than c.arrow_forwardA spacecraft moves at a speed of 0.900c. If its length is L as measured by an observer on the spacecraft, what is the length measured by a ground observer?arrow_forward
- Given the fact that light travels at c, can it have mass? Explain.arrow_forwardAn astronaut moves away from Earth at a speed close to the speed of light. If an observer on Earth could make measurements of the astronauts size and pulse rate, what changes (if any) would he or she measure? Would the astronaut measure any changes?arrow_forwardIf a spaceship is approaching the Earth at 0.100c and a message capsule is sent toward it at 0.100c relative to Earth, what is the speed of the capsule relative to the ship?arrow_forward
- You have been hired as an expert witness in the future by an attorney representing the driver of a spacecraft. The driver is accused of exceeding the galactic speed limit of 0.700c relative to the Earth while being chased by a galactic police spacecraft. The driver claims he is innocent, that his speed was well below that limit. You have been provided with the following data: the police spacecraft was traveling at 0.600c while chasing the driver and a technician on the police spacecraft measured the suspected spacecraft as traveling at 0.300c relative to the police spacecraft. What advice should you give the attorney?arrow_forwardOwen and Dina are at rest in frame S, which is moving at 0.600c with respect to frame S. They play a game of catch while Ed, at rest in frame S, watches the action (Fig. P9.63). Owen throws the ball to Dina at 0.800c (according to Owen), and their separation (measured in S) is equal to 1.80 1012 m. (a) According to Dina, how fast is the ball moving? (b) According to Dina, what time interval is required for the ball to reach her? According to Ed, (c) how far apart are Owen and Dina, (d) how fast is the ball moving, and (e) what time interval is required for the ball to reach Dina? Figure P9.63arrow_forwardShow that for a particle is invariant under Lorentz transformations.arrow_forward
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Length contraction: the real explanation; Author: Fermilab;https://www.youtube.com/watch?v=-Poz_95_0RA;License: Standard YouTube License, CC-BY