Modern Physics for Scientists and Engineers
4th Edition
ISBN: 9781133103721
Author: Stephen T. Thornton, Andrew Rex
Publisher: Cengage Learning
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Chapter 2, Problem 9P
Prove that the constancy of the
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The crew of an enemy spacecraft attempts to escape from your spacecraft by moving away from you at 0.283 of the
speed of light. But all is not lost! You launch a space torpedo toward the foe at 0.351 of the speed of light with respect to
you.
(a) at what speed in kilometers per second does the enemy crew observe the torpedo approaching its spacecraft?
(b) Is this more or less than the classical limit? Use the Galilean transform to prove this.
(c) What if the torpedo is launched at the speed of light? At what speed in kilometers per second does the enemy crew
observe the torpedo approaching its spacecraft? (Show all work.)
(d) How fast would the second craft have to be going to measure the torpedoes speed as 10% greater than the classical
limit. (Assume the torpedo is launched at the original speed, 0.351 of the speed of light.)
A light source recedes from an observer with a speed υS that is small compared with c. (a) Show that the fractional shift in the measured wavelength is given by the approximate expression Δλ/λ ≈ υS/cThis phenomenon is known as the redshift because the visible light is shifted toward the red. (b) Spectroscopic measurements of light at λ = 397 nm coming from a galaxy in Ursa Major reveal a redshift of 20.0 nm. What is the recessional speed of the galaxy?
To circle Earth in low orbit, a satellite must have a speed of about 2.9 × 10ª km/h. Suppose that two such satellites orbit Earth in
opposite directions. (a) What is their relative speed as they pass, according to the classical Galilean velocity transformation equation?
(b) What fractional error do you make in (a) by not using the (correct) relativistic transformation equation?
(a) Number
Units
(b) Number
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Chapter 2 Solutions
Modern Physics for Scientists and Engineers
Ch. 2 - Michelson used the motion of the Earth around the...Ch. 2 - If you wanted to set out today to find the effects...Ch. 2 - Prob. 3QCh. 2 - Prob. 4QCh. 2 - Prob. 5QCh. 2 - Prob. 6QCh. 2 - Prob. 7QCh. 2 - Prob. 8QCh. 2 - Devise a system for you and three colleagues, at...Ch. 2 - In the experiment to verify time dilation by...
Ch. 2 - Can you think of an experiment to verify length...Ch. 2 - Would it be easier to perform the muon decay...Ch. 2 - On a spacetime diagram, can events above t = 0 but...Ch. 2 - Prob. 14QCh. 2 - What would be a suitable name for events connected...Ch. 2 - Prob. 16QCh. 2 - Prob. 17QCh. 2 - Explain how in the twin paradox, we might arrange...Ch. 2 - In each of the following pairs, which is the more...Ch. 2 - Prob. 20QCh. 2 - Prob. 21QCh. 2 - A salesman driving a very fast car was arrested...Ch. 2 - A salesman driving a very fast car was arrested...Ch. 2 - Show that the form of Newtons second law is...Ch. 2 - Prob. 2PCh. 2 - Prob. 3PCh. 2 - A swimmer wants to swim straight across a river...Ch. 2 - Prob. 5PCh. 2 - Prob. 6PCh. 2 - Prob. 7PCh. 2 - Prob. 8PCh. 2 - Prove that the constancy of the speed of light...Ch. 2 - Prob. 10PCh. 2 - Prob. 11PCh. 2 - Prob. 12PCh. 2 - Two events occur in an inertial system K as...Ch. 2 - Is there a frame K in which the two events...Ch. 2 - Prob. 15PCh. 2 - An event occurs in system K at x = 2 m, y = 3.5 m,...Ch. 2 - Prob. 17PCh. 2 - Prob. 18PCh. 2 - A rocket ship carrying passengers blasts off to go...Ch. 2 - Prob. 20PCh. 2 - Particle physicists use particle track detectors...Ch. 2 - The Apollo astronauts returned from the moon under...Ch. 2 - A clock in a spaceship is observed to run at a...Ch. 2 - A spaceship of length 40 m at rest is observed to...Ch. 2 - Prob. 25PCh. 2 - A mechanism on Earth used to shoot down...Ch. 2 - Prob. 27PCh. 2 - Imagine that in another universe the speed of...Ch. 2 - Prob. 29PCh. 2 - Prob. 30PCh. 2 - Prob. 31PCh. 2 - A proton and an antiproton are moving toward each...Ch. 2 - Imagine the speed of light in another universe to...Ch. 2 - Prob. 34PCh. 2 - Three galaxies are aligned along an axis in the...Ch. 2 - Prob. 36PCh. 2 - Prob. 37PCh. 2 - Consider a reference system placed at the U.S....Ch. 2 - Prob. 39PCh. 2 - Prob. 40PCh. 2 - Use the Lorentz transformation to prove that s2 =...Ch. 2 - Prob. 42PCh. 2 - Prove that for a spacelike interval, two events...Ch. 2 - Given two events, (x1, t1) and (x2, t2), use a...Ch. 2 - Prob. 45PCh. 2 - Consider a fixed and a moving system with their...Ch. 2 - Prob. 47PCh. 2 - An astronaut is said to have tried to get out of a...Ch. 2 - Prob. 49PCh. 2 - Do the complete derivation for Equation (2.33)...Ch. 2 - A spacecraft traveling out of the solar system at...Ch. 2 - Prob. 52PCh. 2 - Prob. 53PCh. 2 - Prob. 54PCh. 2 - Newtons second law is given by F=dp/dt. If the...Ch. 2 - Use the result of the previous problem to show...Ch. 2 - Prob. 57PCh. 2 - Prob. 58PCh. 2 - A particle having a speed of 0.92c has a momentum...Ch. 2 - A particle initially has a speed of 0.5c. At what...Ch. 2 - Prob. 61PCh. 2 - Prob. 62PCh. 2 - Prob. 63PCh. 2 - Prob. 64PCh. 2 - Prob. 65PCh. 2 - Prob. 66PCh. 2 - Prob. 67PCh. 2 - Prob. 68PCh. 2 - Prob. 69PCh. 2 - Prob. 70PCh. 2 - What is the speed of an electron when its kinetic...Ch. 2 - Prob. 72PCh. 2 - Prob. 73PCh. 2 - Prob. 74PCh. 2 - Prob. 75PCh. 2 - Calculate the energy needed to accelerate a...Ch. 2 - Prob. 77PCh. 2 - Prob. 78PCh. 2 - Prob. 79PCh. 2 - Prob. 80PCh. 2 - The Large Hadron Collider at Europes CERN facility...Ch. 2 - What is the kinetic energy of (a) an electron...Ch. 2 - A muon has a mass of 106 MeV/c2. Calculate the...Ch. 2 - Prob. 84PCh. 2 - The reaction 2H + 3H → n + 4He is one of the...Ch. 2 - Instead of one positive charge outside a...Ch. 2 - Prob. 87PCh. 2 - Show that the following form of Newton’s second...Ch. 2 - Prob. 89PCh. 2 - For the twins Frank and Mary described in Section...Ch. 2 - Frank and Mary are twins. Mary jumps on a...Ch. 2 - A police radar gun operates at a frequency of 10.5...Ch. 2 - Prob. 93PCh. 2 - Prob. 94PCh. 2 - A proton moves with a speed of 0.90c. Find the...Ch. 2 - A high-speed K0 meson is traveling at a speed of...Ch. 2 - Prob. 97PCh. 2 - The International Space Federation constructs a...Ch. 2 - Prob. 99PCh. 2 - Prob. 100PCh. 2 - A spaceship is coming directly toward you while...Ch. 2 - Quasars are among the most distant objects in the...Ch. 2 - One possible decay mode of the neutral kaon is K0...Ch. 2 - Prob. 104PCh. 2 - Prob. 105PCh. 2 - Small differences in the wavelengths in the sun’s...
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- Under what condition would the Lorentz transformation reduce to the Galilean transformation? For a body moving along the x-axis at the speed of light, x = ct. Use the Lorentz transformation to show that x′ = ct′, i.e. the body moves at the speed of light in the moving frame as well.arrow_forwardTwo objects are moving at the same speed of v= 2.25 × 108 m/s but in directions perpendicular to each other.Derive the relative speed between the two objects:a) based on the classical, Galilean, velocity transformation formulas; andb) based on the velocity transformation formulas of special relativityarrow_forwardA train moves at a constant speed. A stone on the train is released from rest.(a) Using the principle of relativity, describe the motion of the stone as seen by observers on the train.(b) Using the Galilean transformation, describe the motion of the stone as seen by observers on the ground. Draw a sketch.arrow_forward
- An important idea in relativity is to know when you can use classical mechanics and when you should use relativity. The relativistic and classical formulas for kinetic energy are: T_relativistic = E - moc² and T_classical = 1/2mov² = 1/2moc²beta². At what fraction of the rest energy is the classical formula valid to within 2%? Express your answer as: T/m0c^2 = 1/aarrow_forwardA light source G is moving, with respect to an observer O, at an angle θ=�=154∘∘ between the direction of relative motion and the line of sight from O to G. The redshift of the light emitted by G and measured by O is z=0�=0. Find the speed of G with respect to O in units of c�, the speed of light. Enter your answer to 3 decimal places.arrow_forwardImagine an astronaut on a trip to Sirius, which lies 8 light - years from Earth. Upon arrival at Sirius, the astronaut finds that the trip lasted 6 years. If the trip was made at a constant speed of 0.8c, how can the 8 - light - year distance be reconciled with the 6 - year duration?arrow_forward
- The star Epsilon Eridani is 10.4 light-years from Earth. Imagine a spaceship that travels from Earth to Epsilon Eridani at a constant speed of 0.921c. On Earth, we would measure the time it takes for the ship to reach the star to be (10.4ly/0.921c)= 11.2 years. (a) How much time (in years) would it take the ship to travel from the Earth to the star as measured by a passenger aboard the ship? years (b) What is the distance to the star (in light years) as measured by a passenger aboard the ship?arrow_forwardSuppose an astronaut travels to a star 10 lightyears away at a significant fraction of the speed of light (for example, v=0.99c) and returns. Assume negligible amount of time is spent at the destination. Does this round-trip journey take less than, equal to, or more than 20 years as observed by an Earth-based observer? Does this round-trip journey take less than, equal to, or more than 20 years as observed by the astronaut?arrow_forwardThe Milky Way has a diameter (proper length) of about 1.2 x 105 light-years. As far as an astronaut is concerned, how long (in years) would it take to cross the Milky Way, if the speed of the spacecraft is 0.99999 c?arrow_forward
- An astronaut takes a trip to Sirius, which is located a distance of 8 light-years from the Earth. The astronaut measures the time of the one-way journey to be 6 years. If the spaceship moves at a constant speed of 0.8c, how can the 8-ly distance be reconciled with the 6-year trip time measured by the astronaut?arrow_forwardProblem 1: Show that the spacetime coordinates of an event seen in two reference frames moving at a velocity v relative to each other in the z-direction are related by the Lorentz transformation x' y' = y z' = y(z – vt) %3D - ť = y(t – vz/c²) where 1 VI- (v/c)² * 1 – |arrow_forwardA ship is heading off to Bernard's star at 0.700c. As it passes a space station (at rest with respect to the Earth) a few days out from Earth, the ship fires a "photon torpedo" in the forward direction and another in the reverse direction. the torpedoes have a speed relative to the ship of 0.700c. On a space-time diagram, determine the direction and speed of each torpedo as seen by the station. Check your answers using the relativistic addition of velocities formula.arrow_forward
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