The Physical Universe
15th Edition
ISBN: 9780073513928
Author: Konrad Krauskopf, Arthur Beiser
Publisher: MCGRAW-HILL HIGHER EDUCATION
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Chapter 6, Problem 27MC
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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 6 Solutions
The Physical Universe
Ch. 6 - The charge on an electron a. is 1 C b. depends on...Ch. 6 - A positive electric charge a. attracts other...Ch. 6 - A positively charged rod is brought near an...Ch. 6 - Protons and electrons have different masses. When...Ch. 6 - Coulombs law for the force between electric...Ch. 6 - The electric force between a proton and an...Ch. 6 - An atom consists of a a. uniform distribution of...Ch. 6 - Prob. 8MCCh. 6 - An object has a positive electric charge whenever...Ch. 6 - A solid conductor is one a. whose electrons are...
Ch. 6 - Prob. 11MCCh. 6 - Match each of the electrical qualities listed...Ch. 6 - Electric power is equal to a. (current)(voltage)...Ch. 6 - The electric energy lost when a current passes...Ch. 6 - When a magnetized bar of iron is strongly heated,...Ch. 6 - All magnetic fields originate in a. iron atoms b....Ch. 6 - The force on an electron that moves in a curved...Ch. 6 - Magnetic field lines provide a convenient way to...Ch. 6 - In a drawing of magnetic field lines, the weaker...Ch. 6 - Prob. 20MCCh. 6 - Prob. 21MCCh. 6 - Prob. 22MCCh. 6 - Prob. 23MCCh. 6 - Prob. 24MCCh. 6 - Prob. 25MCCh. 6 - Prob. 26MCCh. 6 - Prob. 27MCCh. 6 - A generator is said to generate electricity. What...Ch. 6 - Prob. 29MCCh. 6 - Prob. 30MCCh. 6 - If 105 electrons are added to a neutral object,...Ch. 6 - A positive and a negative charge are initially 4...Ch. 6 - The force between two charges of 3 109 C that are...Ch. 6 - Five joules of work are needed to shift 10 C of...Ch. 6 - When the voltage across a certain resistance is V,...Ch. 6 - The voltage needed to produce a current of 5 A in...Ch. 6 - The resistance of a lightbulb that draws a current...Ch. 6 - The current in a 40-W, 120-V electric lightbulb is...Ch. 6 - A cars storage battery is being charged at a rate...Ch. 6 - A 120-V, 1-kW electric heater is mistakenly...Ch. 6 - A 240-V, 1-kW electric heater is mistakenly...Ch. 6 - Prob. 42MCCh. 6 - What reasons might there be for the universal...Ch. 6 - Electricity was once thought to be a weightless...Ch. 6 - A plastic ball has a charge of +1012 C. (a) Does...Ch. 6 - Why does the production of electricity by friction...Ch. 6 - Prob. 5ECh. 6 - Compare the basic characters of electric and...Ch. 6 - Find the total charge of 1 g of protons.Ch. 6 - Is there any distance at which the gravitational...Ch. 6 - When two objects attract each other electrically,...Ch. 6 - How do we know that the force holding the earth in...Ch. 6 - A hydrogen molecule consists of two hydrogen atoms...Ch. 6 - A charge of +2 107 C is 10 cm from a charge of 6 ...Ch. 6 - A charge of +3 109 C is 50 cm from a charge of 5 ...Ch. 6 - Two charges repel each other with a force of 0.1 N...Ch. 6 - Two charges originally 80 mm apart are brought...Ch. 6 - Two small spheres are given identical positive...Ch. 6 - (a) A metal sphere with a charge of +1 105 C is...Ch. 6 - Suppose the force between the earth and the moon...Ch. 6 - How far apart are two charges of +1 108 C that...Ch. 6 - How is the movement of electricity through air...Ch. 6 - One terminal of a battery is connected to a...Ch. 6 - Why do you think bending a wire does not affect...Ch. 6 - What basic aspect of superconductivity has...Ch. 6 - Sensitive instruments can detect the passage of as...Ch. 6 - (a) The capacity of a battery is usually quoted in...Ch. 6 - The energy stored in a certain 12-V battery is 3...Ch. 6 - The potential difference between a cloud and the...Ch. 6 - (a) A person can be electrocuted while taking a...Ch. 6 - How much current is drawn by a 240-V water heater...Ch. 6 - Prob. 30ECh. 6 - Prob. 31ECh. 6 - A fuse prevents more than a certain amount of...Ch. 6 - Should a fuse be connected in series or in...Ch. 6 - Heavy users of electric power, such as large...Ch. 6 - How are the terminals of a set of batteries...Ch. 6 - Prob. 36ECh. 6 - (a) If a 75-W lightbulb is connected to a 120-V...Ch. 6 - Prob. 38ECh. 6 - Prob. 39ECh. 6 - Prob. 40ECh. 6 - Prob. 41ECh. 6 - Prob. 42ECh. 6 - Prob. 43ECh. 6 - Prob. 44ECh. 6 - A 1.35-V mercury cell with a capacity of 1.5 A h...Ch. 6 - Prob. 46ECh. 6 - Prob. 47ECh. 6 - Prob. 48ECh. 6 - Prob. 49ECh. 6 - A current flows west through a power line. Find...Ch. 6 - Prob. 51ECh. 6 - Prob. 52ECh. 6 - Two parallel wires carry currents in the same...Ch. 6 - Prob. 54ECh. 6 - A current-carrying wire is in a magnetic field....Ch. 6 - Prob. 56ECh. 6 - Prob. 57ECh. 6 - Prob. 58ECh. 6 - Prob. 59ECh. 6 - Prob. 60ECh. 6 - Prob. 61ECh. 6 - Prob. 62ECh. 6 - Prob. 63ECh. 6 - Given a coil of wire and a small lightbulb, how...Ch. 6 - Prob. 65ECh. 6 - Prob. 66ECh. 6 - A transformer rated at a maximum power of 10 kW is...Ch. 6 - An electric welding machine uses a current of 400...
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