
Matter and Interactions
4th Edition
ISBN: 9781118875865
Author: Ruth W. Chabay, Bruce A. Sherwood
Publisher: WILEY
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Chapter 2.3, Problem 3CP
(a)
To determine
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(b)
To determine
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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
Matter and Interactions
Ch. 2.1 - (1) Two external forces. 〈40, −70, 0〉 N and 〈20,...Ch. 2.2 - (a) In the colliding students example, how was Δt,...Ch. 2.3 - (1) You drop a piece of paper, and observe that it...Ch. 2.4 - (1) For the third time step in the iterative...Ch. 2.5 - A ball is kicked on Earth from a location 〈9.0,...Ch. 2.6 - 6 (1) You push on a spring whose stiffness is 11...Ch. 2.6 - Prob. 7CPCh. 2.6 - Prob. 8CPCh. 2.7 - Jupiter goes around the Sun in 4333 Earth days....Ch. 2.7 - Some code would need to be added in front of each...
Ch. 2 - Prob. 1QCh. 2 - An object is moving in the +y direction. Which, if...Ch. 2 - You observe three carts moving to the left. Cart A...Ch. 2 - In order to pull a sled across a level field at...Ch. 2 - Prob. 5QCh. 2 - A comet passes near the Sun. When the comet is...Ch. 2 - A ball moves in the direction of the arrow labeled...Ch. 2 - A system is acted upon by two forces, 〈18, 47,...Ch. 2 - A truck driver slams on the brakes and the...Ch. 2 - At a certain instant a particle is moving in the...Ch. 2 - At t = 16.0 s an object with mass 4 kg was...Ch. 2 - A proton (mass 1.7 × 10−27 kg) interacts...Ch. 2 - A Ping-Pong ball is acted upon by the Earth, air...Ch. 2 - In outer space a rock of mass 5 kg is acted on by...Ch. 2 - A steel safe with mass 2200 kg falls onto...Ch. 2 - In a crash test, a truck with mass 2500 kg...Ch. 2 - A tennis ball has a mass of 0.057 kg. A...Ch. 2 - An object is on a collision course with the Earth...Ch. 2 - Prob. 20PCh. 2 - You throw a metal block of mass 0.25 kg into the...Ch. 2 - A small space probe, of mass 240 kg, is launched...Ch. 2 - A soccer ball of mass 0.43 kg is rolling with...Ch. 2 - As your spaceship coasts toward Mars, you need to...Ch. 2 - A runner starts from rest and in 3 s reaches a...Ch. 2 - The driver of a car traveling at a speed of 18 m/s...Ch. 2 - On a straight road with the +x axis chosen to...Ch. 2 - A ball of mass 0.4 kg flies through the air at low...Ch. 2 - For each graph of vx vs. t numbered 1–6 in Figure...Ch. 2 - A cart rolls with low friction on a track. A fan...Ch. 2 - Consider the three experiments described in...Ch. 2 - Consider the three experiments described in...Ch. 2 - You are a detective investigating why someone was...Ch. 2 - Prob. 34PCh. 2 - A ball is kicked from a location 〈9, 0, −6〉 (on...Ch. 2 - Prob. 37PCh. 2 - Prob. 38PCh. 2 - The performance of two different cars, car 1 and...Ch. 2 - A driver starts from rest on a straight test track...Ch. 2 - The stiffness of a particular spring is 40 N/m....Ch. 2 - A spring with a relaxed length of 25 cm and a...Ch. 2 - Prob. 43PCh. 2 - Prob. 44PCh. 2 - Prob. 46PCh. 2 - Prob. 47P
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