Modern Physics
2nd Edition
ISBN: 9780805303087
Author: Randy Harris
Publisher: Addison Wesley
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Question
Chapter 2, Problem 112E
(a)
To determine
To Find: The frame of reference where situations after-collision is simplest and also the invariant in that frame.
(b)
To determine
To Find: The invariant before collision of particle and expression for mass of object.
(c)
To determine
To Find: The momentum and energy of an object in laboratory frame and justify for the mass of object.
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Question 3 of 17
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In the figure above, three uniform thin rods, each of length L, form
an inverted U. The vertical rods each have a mass m; the horizontal
rod has a mass 3m.
NOTE: Express your answer in terms of the variables given.
(a) What is the x coordinate of the system's center of mass?
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(b) What is the y coordinate of the system's center of mass?
Ycom
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Sketch the harmonic on graphing paper.
Exercise 1:
(a) Using the explicit formulae derived in the lectures for the (2j+1) × (2j + 1) repre-
sentation matrices Dm'm, (J/h), derive the 3 × 3 matrices corresponding to the case
j = 1.
(b) Verify that they satisfy the so(3) Lie algebra commutation relation:
[D(Î₁/ħ), D(Î₂/h)]m'm₁ = iƊm'm² (Ĵ3/h).
(c) Prove the identity
3
Dm'm,(β) = Σ (D(Ρ)D(Ρ))m'¡m; ·
i=1
Chapter 2 Solutions
Modern Physics
Ch. 2 - Explain to your friend, who is willing to accept...Ch. 2 - A friend says, “It makes no sense that Anna could...Ch. 2 - The Lorentz transformation equations have x and t...Ch. 2 - You are gliding over Earth’s surface at a high...Ch. 2 - A thin plate has a round hole whose diameter in...Ch. 2 - In the twin paradox situation, a fellow student...Ch. 2 - Does the asymmetric aging of an Earthbound...Ch. 2 - You are floating in space when you notice a flying...Ch. 2 - Prob. 9CQCh. 2 - A relativity enthusiast says, “If E=mc2 and energy...
Ch. 2 - Prob. 11CQCh. 2 - Prob. 12CQCh. 2 - Two objects isolated from the rest of the universe...Ch. 2 - Particles of light have no mass. Does the Sun’s...Ch. 2 - Prob. 15CQCh. 2 - In a television picture tube, a beam of electrons...Ch. 2 - Prob. 17ECh. 2 - Verify that the special case x=vt,x=0 leads to...Ch. 2 - If an object actually occupies less space...Ch. 2 - Through a window in Carl’s spaceship, passing at...Ch. 2 - According to an observer on Earth, a spacecraft...Ch. 2 - According to Bob on Earth, Planet Y (uninhabited)...Ch. 2 - Anna is on a railroad flatcar moving at 0.6c...Ch. 2 - A polevaulter holds a 16 ft. pole. A barn has...Ch. 2 - Anna and Bob are in identical spaceships, each 100...Ch. 2 - Bob is watching Anna fly by in her new highspeed...Ch. 2 - Rob and Bob Jr. stand at open doorways at opposite...Ch. 2 - The diagram shows Bob’s view of the passing of two...Ch. 2 - Refer to Figure 2.18. (a) How long is a spaceship?...Ch. 2 - You are in a bus traveling on a straight road at...Ch. 2 - A spaceship travels at 0.8c. As this spaceship...Ch. 2 - You are on a highspeed train, traveling at a...Ch. 2 - A famous experiment detected 527 muons per hour at...Ch. 2 - In the frame in which they are at rest, the number...Ch. 2 - A supersonic plane travels at 420 m/s. As this...Ch. 2 - Prob. 36ECh. 2 - According to Bob, on Earth, it is 20 ly to Planet...Ch. 2 - A plank, fixed to a sled at rest in frame S, is of...Ch. 2 - Bob in frame S, is observing the moving plank of...Ch. 2 - An experimenter determines that a particle created...Ch. 2 - A muon has a mean lifetime of 2.2s in its rest...Ch. 2 - A pion is an elementary particle that, on averages...Ch. 2 - Anna and Bob have identical spaceships 60 m long....Ch. 2 - Demonstrate that equations (212) and (213) become...Ch. 2 - Planet W is 12 ly from Earth. Anna and Bob are...Ch. 2 - Anna and Bob are both born just as Anna’s...Ch. 2 - Consider Anna, Bob, and Carl in the twin paradox....Ch. 2 - You stand at the center of your 100 m spaceship...Ch. 2 - From a standstill, you begin jogging at 5 m/s...Ch. 2 - A meterstick is glued to the wall with its 100 cm...Ch. 2 - Prob. 51ECh. 2 - By what factor would a star’s characteristic...Ch. 2 - At rest, a light source emits 532 nm light. (a) As...Ch. 2 - The light from galaxy NGC 221 consists of a...Ch. 2 - A space probe has a powerful light beacon that...Ch. 2 - Prob. 56ECh. 2 - Prob. 57ECh. 2 - To catch speeders, a police radar gun detects the...Ch. 2 - Bob is on Earth. Anna is on a spacecraft moving...Ch. 2 - According to Anna, on Earth, Bob is on a spaceship...Ch. 2 - Prove that if v and u are less than c, it is...Ch. 2 - In a particle collider experiment, particle 1 is...Ch. 2 - A light beam moves in the xyplane and has an...Ch. 2 - A light beam moves at an angle ? with the xaxis as...Ch. 2 - You tire a light signal at 60° north of west. (a)...Ch. 2 - At t=0 , a bright beacon at the origin flashes,...Ch. 2 - Prob. 67ECh. 2 - By applying the relativistic velocity...Ch. 2 - Prob. 69ECh. 2 - What are the momentum, energy, and kinetic energy...Ch. 2 - What would be the internal energy, kinetic energy,...Ch. 2 - By how much (in picograms) does the mass of 1 mol...Ch. 2 - Prob. 73ECh. 2 - A typical household uses 500 kWh of energy in 1...Ch. 2 - Prob. 75ECh. 2 - Prob. 76ECh. 2 - Prob. 77ECh. 2 - Show that the relativistic expression for kinetic...Ch. 2 - At Earth’s location, the intensity of sunlight is...Ch. 2 - Prob. 80ECh. 2 - Prob. 81ECh. 2 - Prob. 82ECh. 2 - How fast must an object be moving for its kinetic...Ch. 2 - How much work must be done to accelerate an...Ch. 2 - An electron accelerated from rest through a...Ch. 2 - What is the momentum of a proton accelerated...Ch. 2 - A proton is accelerated from through a potential...Ch. 2 - xzA particle of mass m0 moves the lab at 0.6c....Ch. 2 - 89. The boron14 nucleus (mass: 14.02266 u) “beta...Ch. 2 - A 3.000 u object moving to the right through a...Ch. 2 - A 10 kg object is moving to the right at 0.6c. It...Ch. 2 - Particle 1, of mass m1 , moving at 0.8c relative...Ch. 2 - Consider the collisions of two identical...Ch. 2 - A kaon (denoted K0 ) ¡s an unstable particle mass...Ch. 2 - In the frame of reference shown, a stationary...Ch. 2 - Prob. 96ECh. 2 - Show that E2=p2c2+m2c4 follows from expressions...Ch. 2 - Equation (2-30) is an approximation correct only...Ch. 2 - According to an observer at Earth’s equator, by...Ch. 2 - If it is fundamental to nature that a given mass...Ch. 2 - Prob. 101ECh. 2 - Suppose particles begin moving in one dimension...Ch. 2 - Prob. 103ECh. 2 - From the Lorentz transformation equations, show...Ch. 2 - (a) Determine the Lorentz transformation matrix...Ch. 2 - For the situation given in Exercise 22, find the...Ch. 2 - Show that equation (236) follows from the...Ch. 2 - A 1 kg object moves at 0.8crelative to Earth. (a)...Ch. 2 - From p=umu (i.e., px=umux , py=umuy , and pz=umuz...Ch. 2 - Prob. 110ECh. 2 - An object of mass 3m0 moves to the right at...Ch. 2 - Prob. 112ECh. 2 - Derive the following expressions for the...Ch. 2 - (a) Determine the Lorentz transformation matrix...Ch. 2 - A point charge +q rests halfway between two steady...Ch. 2 - Prob. 116CECh. 2 - Prob. 117CECh. 2 - A rocket maintains a constant thrust F, giving it...Ch. 2 - Exercise 117 gives the speed u of an object...Ch. 2 - In Example 2.5, we noted that Anna could go...
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