Physics (5th Edition)
5th Edition
ISBN: 9780321976444
Author: James S. Walker
Publisher: PEARSON
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Chapter 19.6, Problem 6EYU
Two
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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?
xcom
L
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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 19 Solutions
Physics (5th Edition)
Ch. 19.1 - Enhance Your Understanding (Answers given at the...Ch. 19.2 - Enhance Your Understanding (Answers given at the...Ch. 19.3 - Positive and negative charges of equal magnitude...Ch. 19.4 - Enhance Your Understanding (Answers given at the...Ch. 19.5 - The electric field lines for a system of two...Ch. 19.6 - Two conducting spheres of different radii are...Ch. 19.7 - Four Gaussian surfaces (A, B, C, D) are shown in...Ch. 19 - The fact that the electron has a negative charge...Ch. 19 - Explain why a comb that has been rubbed through...Ch. 19 - Small bits of paper are attracted to an...
Ch. 19 - A charged rod is brought near a suspended object,...Ch. 19 - A charged rod is brought near a suspended object,...Ch. 19 - A point charge +Q is fixed at a height H above the...Ch. 19 - A proton moves in a region of constant electric...Ch. 19 - Describe some of the differences between charging...Ch. 19 - A system consists of two charges of equal...Ch. 19 - The force experienced by charge 1 at point A is...Ch. 19 - Can an electric field exist in a vacuum? Explain.Ch. 19 - Gausss law can tell us how much charge is...Ch. 19 - Predict/Explain An electrically neutral object is...Ch. 19 - (a) Based on the materials listed in Table 19-1,...Ch. 19 - This problem refers to the information given in...Ch. 19 - Find the net charge of a system consisting of (a)...Ch. 19 - Find the total electric charge of 2.5 kg of (a)...Ch. 19 - A container holds a gas consisting of 2.85 moles...Ch. 19 - The Charge on Adhesive Tape When adhesive tape is...Ch. 19 - Four pairs of conducting spheres, all with the...Ch. 19 - A system of 1525 particles, each of which is...Ch. 19 - A charge +q and a charge q are placed at opposite...Ch. 19 - Consider the three electric charges, A, B, and C,...Ch. 19 - Predict/Explain Suppose the charged sphere in...Ch. 19 - At what separation is the electrostatic force...Ch. 19 - How much equal charge should be placed on the...Ch. 19 - Predict/Calculate Two point charges, the first...Ch. 19 - When two identical ions are separated by a...Ch. 19 - Given that q = +18 C and d = 21 cm, find the...Ch. 19 - Five point charges, q1 = +q, q2 = +2q q3 = 3q, q4...Ch. 19 - Three charges, q1 = +q, q2 = q, and q3 = +q, are...Ch. 19 - The attractive electrostatic force between the...Ch. 19 - Prob. 21PCECh. 19 - A sphere of radius 4.22 cm and uniform surface...Ch. 19 - Predict/Calculate Given that q = +12 C and d = 19...Ch. 19 - Suppose the charge q2 in Figure 19-38 can be moved...Ch. 19 - A point charge q = 0.55 nC is fixed at the origin....Ch. 19 - A point charge q = 0.55 nC is fixed at the origin....Ch. 19 - Find the direction and magnitude of the net...Ch. 19 - Predict/Calculate (a) Find the direction and...Ch. 19 - Predict/Calculate Two point charges lie on the x...Ch. 19 - A system consists of two positive point charges,...Ch. 19 - Predict/Calculate The point charges in Figure...Ch. 19 - Referring to the previous problem, suppose that...Ch. 19 - Predict/Calculate (a) If the nucleus in Example...Ch. 19 - Four point charges are located at the corners of a...Ch. 19 - Predict/Calculate Two identical point charges in...Ch. 19 - Two spheres with uniform surface charge density,...Ch. 19 - Point charges, q1 and q2 are placed on the x axis,...Ch. 19 - Two electric charges are separated by a finite...Ch. 19 - What is the magnitude of the electric field...Ch. 19 - A +5.0-C charge experiences a 0.64-N force in the...Ch. 19 - Two point charges lie on the x axis. A charge of...Ch. 19 - Two point charges lie on the x axis. A charge of...Ch. 19 - The electric field on the dashed line in Figure...Ch. 19 - An object with a charge of 2.1 C and a mass of...Ch. 19 - Predict/Calculate Figure 19-42 shows a system...Ch. 19 - Two point charges of equal magnitude are 8.3 cm...Ch. 19 - Predict/Calculate A point charge q = +4.7 C is...Ch. 19 - Predict/Calculate Four point charges, each of...Ch. 19 - The electric field at the point x = 5.00 cm and y...Ch. 19 - Predict/Calculate The electric field lines...Ch. 19 - Referring to Figure 19-43, suppose q2 is not...Ch. 19 - The electric field lines surrounding three charges...Ch. 19 - Make a qualitative sketch of the electric field...Ch. 19 - Sketch the electric field lines for the system of...Ch. 19 - Sketch the electric field lines for the system of...Ch. 19 - Suppose the magnitude of the electric field...Ch. 19 - Predict/Explain Gaussian surface 1 has twice the...Ch. 19 - Suppose the conducting shell in Figure 19-33which...Ch. 19 - Rank the Gaussian surfaces shown in Figure 19-45...Ch. 19 - A uniform electric field of magnitude 35,000 N/C...Ch. 19 - Prob. 61PCECh. 19 - A surface encloses the charges q1 = 3.2 C, q2 =...Ch. 19 - BIO Nerve Cells Nerve cells are long, thin...Ch. 19 - The electric flux through each of the six sides of...Ch. 19 - Consider a spherical Gaussian surface and three...Ch. 19 - The surface charge per area on the outside of a...Ch. 19 - Photovoltaic Field Suppose the field in the...Ch. 19 - A thin wire of infinite extent has a charge per...Ch. 19 - CE Predict/Explain An electron and a proton are...Ch. 19 - CE Predict/Explain In Conceptual Example 19-9,...Ch. 19 - CE Under normal conditions, the electric field at...Ch. 19 - A proton is released from rest in a uniform...Ch. 19 - BIO Ventricular Fibrillation If a charge of 0.30 C...Ch. 19 - A point charge at the origin of a coordinate...Ch. 19 - Prob. 76GPCh. 19 - The Balloon and Your Hair Suppose 7.5 1010...Ch. 19 - The Balloon and the Wall When a charged balloon...Ch. 19 - CE Four lightweight, plastic spheres, labeled A,...Ch. 19 - Find (a) the direction and (b) the magnitude of...Ch. 19 - A small object of mass 0.0150 kg and charge 3.1 C...Ch. 19 - The electric field at a radial distance of 47.7 cm...Ch. 19 - Predict/Calculate Three charges are placed at the...Ch. 19 - Predict/Calculate BIO Cell Membranes The cell...Ch. 19 - A square with sides of length L has a point charge...Ch. 19 - Two small plastic balls hang from threads of...Ch. 19 - A small sphere with a charge of +2.44 C is...Ch. 19 - Twelve identical point charges q are equally...Ch. 19 - BIO Nerve Impulses When a nerve impulse propagates...Ch. 19 - Predict/Calculate The Electric Field of the Earth...Ch. 19 - An object of mass m = 2.5 g and charge Q = +42C is...Ch. 19 - Four identical charges, +Q occupy the corners of a...Ch. 19 - Two charges, +q and q, occupy two corners of an...Ch. 19 - Figure 19-52 shows an electron entering a...Ch. 19 - Two identical conducting spheres are separated by...Ch. 19 - Have you ever pulled clothes from a dryer only to...Ch. 19 - Have you ever pulled clothes from a dryer only to...Ch. 19 - The force required to detach a grain of pollen...Ch. 19 - Pollen of the lisianthus plant requires a force 10...Ch. 19 - Predict/Calculate Referring to Example 19-14...Ch. 19 - Predict/Calculate Referring to Example 19-14 In...Ch. 19 - Predict/Calculate Referring to Example 19-16 The...Ch. 19 - Referring to Example 19-16 Suppose the magnitude...
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