Modern Physics for Scientists and Engineers
4th Edition
ISBN: 9781133103721
Author: Stephen T. Thornton, Andrew Rex
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Concept explainers
Question
Chapter 2, Problem 11P
To determine
Equations
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
The positive muon (µ+), an unstable particle, lives on average 2.20 x 10-6 s (measured in its own frame of reference) before decaying. (a) If such a particle is moving, with respect to the laboratory, with a speed of 0.900c, what average lifetime is measured in the laboratory? (b) What average distance, measured in the laboratory, does the particle move before decaying?
(a) Prepare a graph of the relativistic kinetic energy and the classical kinetic energy, both as a function of speed, for an object with a mass of your choice. (b) At what speed does the classical kinetic energy underestimate the experimental value by 1%? (c) By 5%? (d) By 50%?
Calculate the range of speeds for a particle of mass m in which the classical relation for the kinetic energy, (1/2)*m*v^2, is within 0.5 percent of the correct relativistic value. Find the values for an electron and a proton.
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...
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.Similar questions
- Suppose the primed and laboratory observers want to measure the length of a rod that rests on the ground horizontally in the space between the helicopter and the tower (Fig. 39.8B). To derive the length transformation L = L (Eq. 39.5), we had to assume that the positions of the two ends were determined simultaneously. What happens to the length transformation equation if both observers measure the end below the helicopter at one time t1 and the other end at a later time t2?arrow_forwardOne cosmic ray neuron has a velocity of 0.250c relative to the Earth. (a) What is the neutron's total energy in MeV? (b) Find its momentum. (c) Is in this situation? Discuss in terms of the equation given in part (a) of the previous problem.arrow_forwardA Σ+ particle has a mean lifetime of 80.2 ps. A physicist measures that mean lifetime to be 403 ps as the particle moves in his lab. The rest mass of the particle is 2.12 x 10-27 kg. (a) How fast is the particle moving? (b) How far does it travel, as measured in the lab frame, over one mean lifetime? (c) What are its rest, kinetic, and total energies in the lab frame of reference? (d) What are its rest, kinetic, and total energies in the particle’s frame?arrow_forward
- Show that a potential difference of 1.02 x 106 V would be sufficient to give an electron a speed equal to twice the speed of light if Newtonian mechanics remained valid at high speeds. (b) What speed would an electron actually acquire in falling through a potential difference equal to 1.02 x 106 V ?arrow_forwardAs you read this page (on paper or monitor screen), a cosmic ray proton passes along the left–right width of the page with relative speed v and a total energy of 14.24 nJ. According to your measurements, that left–right width is 21.0 cm. (a) What is the width according to the proton’s reference frame? How much time did the passage take according to (b) your frame and (c) the proton’s frame?arrow_forwardAn elementary particle of mass u initially at rest in a frame S completely absorbs a photon that was traveling in the +x direction. After absorbing the photon, the mass of the particle becomes 2µ. (a) What was the energy of the incoming photon? (b) Why is that energy greater than uc??arrow_forward
- A positive K meson (K+) is an unstable subatomic particle that decays into other particles. At rest, its mean lifetime is 1.23 * 10-8 s. (a) What do you measure the mean lifetime of a K+ to be if it is moving at 0.800c relative to you? (b) As measured from the reference frame of this K+, what is the mean lifetime of a second K+ that is at rest relative to you?arrow_forwardAn astronaut wishes to visit the Andromeda galaxy, making a one-way trip that will take 25.3 years in the space-ship's frame of reference. Assume the galaxy is 2.00 million light years away and his speed is constant. (a) How fast must he travel relative to Earth? The following approximation will prove useful: z 1 1 + x for x << 1. 2 - (Complete the equation for your answer.) (1-| C (b) What will be the kinetic energy of his spacecraft, which has mass of 1.08 x 10° kg? (c) What is the cost of this energy if it is purchased at a typical consumer price for electric energy, 13.0 cents per kWh?arrow_forwardIn the 1887 experiment by Michelson and Morley, the length of each arm was 11 m. The experimental limit for the fringe shift was 0.005 fringes. If sodium light was used with the interferometer ( λ=589 nm), what upper limit did the null experiment place on the speed of the Earth through the expected ether?arrow_forward
- Mass of a proton: 1.007825 u; Mass of a neutron: 1.008665 u 1 The lifetime of a free neutron is 887 s. If a neutron moves with a speed 2.9 × 108 m/s relative to an observer in the lab, what does the observer measure the neutron's lifetime to be? What is this an example of? 2. (a) What is the rest energy (in joules) of a subatomic particle whose (rest) mass is 6.7 x 10-3¹ kg? (b) How many MeV's of energy is this? 3. The rest energy of a particular subatomic particle is 1200 MeV. If this particle is traveling at 90% the speed of light, what is its total relativistic energy?arrow_forwardMuons are sub-atomic particles that are similar to electrons (except with much more mass). They are inherently unstable, meaning that after a very short time they decay (fall apart) into an electron and two other particles (called 'neutrinos'). When moving slowly relative to our laboratory reference frame, the lifetime of a muon is only 2.2 μs (2.2 x 10-6 s). How long would a muon last (before decaying) if it is moving at a speed relative to the laboratory frame of 0.987 c (where c is the speed of light in a vacuum = 3.0 x 108 m/s)? Decay time = us (note the units of microseconds) What relative speed of a muon would result in a lifetime of 9.00 us? Express your answer as a fraction of c. Vrel = Carrow_forwardSuppose a particle orbit as a function of time (t) is given in an inertial frame K and the integral dt T = r(t) 1 - B:(1)- B; (t)– B¿ (1)dt is evaluated. Using the invariance of the space-time interval, show that if the same calculation is done in a frame K'moving uniformly with respect to K, then r'=r. In other words, the proper time r along a particle orbit is a Lorentz invariant quantity.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Physics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage Learning
University Physics Volume 3PhysicsISBN:9781938168185Author:William Moebs, Jeff SannyPublisher:OpenStax
Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
Modern PhysicsPhysicsISBN:9781111794378Author:Raymond A. Serway, Clement J. Moses, Curt A. MoyerPublisher:Cengage Learning
Physics for Scientists and Engineers: Foundations...
Physics
ISBN:9781133939146
Author:Katz, Debora M.
Publisher:Cengage Learning
University Physics Volume 3
Physics
ISBN:9781938168185
Author:William Moebs, Jeff Sanny
Publisher:OpenStax
Principles of Physics: A Calculus-Based Text
Physics
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Modern Physics
Physics
ISBN:9781111794378
Author:Raymond A. Serway, Clement J. Moses, Curt A. Moyer
Publisher:Cengage Learning