Explanation Write the expression for the particle travelling at speed v in time interval Δ t 1 . v Δ t 1 = L + u Δ t 1 (1) Here, v is the speed of emitted particle, L contracted length, u is speed to travel the additional distance. Rearrange equation (1) to get the expression for Δ t 1 . Δ t 1 = L v − u (2) Write the expression for the particle travelling at speed c in time interval Δ t 2 . c Δ t 2 = L − u Δ t 2 (3) Here, c is the speed of light and Δ t 2 is the time interval. Rearrange equation (3) to get the expression for Δ t 2 . Δ t 2 = L c + u (4) Write the expression for the time dilation. Δ t = Δ t 0 1 − u 2 c 2 (5) Here, Δ t is the total time dilation. Write the expression for the total time dilation. Δ t = Δ t 1 + Δ t 2 (6) Substitute L v − u for Δ t 1 and L c + u for Δ t 2 in equation (6). Δ t = L v − u + L c + u = L c + L u + L v − L u ( v − u ) ( c + u ) = L ( c + v ) ( v − u ) ( c + u ) Substitute L ( c + v ) ( v − u ) ( c + u ) for Δ t in equation (5). L ( c + v ) ( v − u ) ( c + u ) = Δ t 0 1 − u 2 c 2 Δ t 0 = L ( c + v ) ( v − u ) ( c + u ) 1 − u 2 c 2 (7) Write the expression for the particle to travel a distance at speed c and v ′ . Δ t 0 = L 0 v ′ + L 0 c Substitute L 0 v ′ + L 0 c for Δ t 0 in equation (7). L 0 v ′ + L 0 c = L ( c + v ) ( v − c ) ( c + u ) 1 − u 2 c 2 L 0 ( c + v ′ ) c v ′ = L ( c + v ) ( v − c ) ( c + u ) 1 − u 2 c 2 (8) Write the expression for the contracted length

4th Edition

ISBN: 9781119495550

Author: Krane

Publisher: WILEY

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Chapter 2, Problem 9P

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The derivation for equation v=v′+u1+v′uc2

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Chapter 2, Problem 8P

Chapter 2, Problem 10P

Chapter 2 Solutions

MODERN PHYSICS (LOOSELEAF)

Ch. 2 - Prob. 1Q Ch. 2 - Prob. 2Q Ch. 2 - Describe the situation of Figure 2.4 as it would...Ch. 2 - Does the Michelson–Morley experiment show that the...Ch. 2 - Suppose we made a pair of shears in which the...Ch. 2 - Light travels through water at a speed of about...Ch. 2 - Is it possible to have particles that travel at...Ch. 2 - How does relativity combine space and time...Ch. 2 - Einstein developed the relativity theory after...Ch. 2 - Explain in your own words the terms time dilation...

Ch. 2 - Does the Moon’s disk appear to be a different size...Ch. 2 - According to the time dilation effect, would the...Ch. 2 - Criticize the following argument. “Here is a way...Ch. 2 - Is it possible to synchronize clocks that are in...Ch. 2 - Suppose event A causes event B. To one observer,...Ch. 2 - Is mass a conserved quantity in classical physics?...Ch. 2 - “In special relativity, mass and energy are...Ch. 2 - Which is more massive, an object at low...Ch. 2 - Prob. 19Q Ch. 2 - Prob. 20Q Ch. 2 - You are piloting a small airplane in which you...Ch. 2 - A moving sidewalk 95 m in length carries...Ch. 2 - Prob. 3P Ch. 2 - Prob. 4P Ch. 2 - Prob. 5P Ch. 2 - An astronaut must journey to a distant planet,...Ch. 2 - The proper lifetime of a certain particle is 120.0...Ch. 2 - High-energy particles are observed in laboratories...Ch. 2 - Prob. 9P Ch. 2 - Two spaceships approach the Earth from opposite...Ch. 2 - Rocket A leaves a space station with a speed of...Ch. 2 - One of the strongest emission lines observed from...Ch. 2 - Prob. 13P Ch. 2 - Three rods are joined to form a 45–45–90 triangle,...Ch. 2 - In the Relativistic Heavy Ion Collider (an...Ch. 2 - Derive the Lorentz velocity transformations for ...Ch. 2 - Observer O fires a light beam in the y direction...Ch. 2 - A light bulb at point x in the frame of reference...Ch. 2 - A neutral K meson at rest decays into two π...Ch. 2 - A rod in the reference frame of observer O makes...Ch. 2 - Two events occur at locations separated by a...Ch. 2 - According to observer O, a blue flash occurs at xb...Ch. 2 - Suppose the speed of light were 1000 mi/h. You are...Ch. 2 - Suppose rocket traveler Amelia has a clock made on...Ch. 2 - Suppose Amelia traveled at a speed of 0.80c to a...Ch. 2 - Make a drawing similar to Figure 2.20 showing the...Ch. 2 - Two twins make a round-trip journey from Earth to...Ch. 2 - Agnes makes a round trip at a constant speed to a...Ch. 2 - (a) Using the relativistically correct final...Ch. 2 - Find the momentum, kinetic energy, and total...Ch. 2 - An electron is moving with a kinetic energy of...Ch. 2 - Prob. 32P Ch. 2 - Prob. 33P Ch. 2 - Prob. 34P Ch. 2 - Use Equations 2.32 and 2.36 to derive Equation...Ch. 2 - By carrying the binomial expansion one term...Ch. 2 - (a) According to observer O, a certain particle...Ch. 2 - An electron is moving at a speed of 0.85c. By how...Ch. 2 - Prob. 39P Ch. 2 - Find the kinetic energy of an electron moving at a...Ch. 2 - An electron and a proton are each accelerated...Ch. 2 - Prob. 42P Ch. 2 - A π meson of rest energy 139.6 MeV moving at a...Ch. 2 - An electron and a positron (an antielectron) make...Ch. 2 - It is desired to create a particle of mass 9460...Ch. 2 - A particle of rest energy mc2 is moving with speed...Ch. 2 - Let’s consider a different approach to Example...Ch. 2 - In the muon decay experiment discussed in Section...Ch. 2 - Derive the relativistic expression p2/2K = m +...Ch. 2 - Suppose we want to send an astronaut on a round...Ch. 2 - Prob. 52P Ch. 2 - Observer O sees a red flash of light at the origin...Ch. 2 - Several spacecraft leave a space station at the...Ch. 2 - Observer O sees a light turn on at x = 524 m when...Ch. 2 - Suppose an observer O measures a particle of mass...Ch. 2 - Prob. 59P Ch. 2 - A beam of 2.14 × 1011 electrons/s moving at a...Ch. 2 - An electron moving at a speed of vi = 0.960c in...Ch. 2 - A pion has a rest energy of 135 MeV. It decays...Ch. 2 - Prob. 63P

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