Physics for Scientists and Engineers: Foundations and Connections
1st Edition
ISBN: 9781133939146
Author: Katz, Debora M.
Publisher: Cengage Learning
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Chapter 5, Problem 11PQ
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Find the unknown force
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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
2
(b) What is the y coordinate of the system's center of mass?
Ycom
45
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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 5 Solutions
Physics for Scientists and Engineers: Foundations and Connections
Ch. 5.2 - Because Newtons first law is counterintuitive, it...Ch. 5.2 - Train Collision and Newtons First Law A group of...Ch. 5.3 - Shown in Figure 5.4 are four situations in which a...Ch. 5.3 - A person stands on a spring scale in an elevator...Ch. 5.4 - Prob. 5.5CECh. 5.5 - Prob. 5.6CECh. 5.6 - a. Take a moment to be sure that you understand...Ch. 5.7 - Imagine weighing the same bunch of bananas with...Ch. 5.7 - For all three situations, find the magnitude and...Ch. 5.9 - Prob. 5.10CE
Ch. 5.9 - A child jumping off the monkey bars at a...Ch. 5.9 - Prob. 5.12CECh. 5 - Why is it easier to lift a very large beach ball...Ch. 5 - Prob. 2PQCh. 5 - Imagine pushing two blocks on ice. The light block...Ch. 5 - When Julia Child would cook an omelet, she would...Ch. 5 - Prob. 5PQCh. 5 - Prob. 6PQCh. 5 - Prob. 7PQCh. 5 - Prob. 8PQCh. 5 - Prob. 9PQCh. 5 - Prob. 10PQCh. 5 - Prob. 11PQCh. 5 - You blow a small piece of paper through the air....Ch. 5 - Prob. 13PQCh. 5 - Prob. 14PQCh. 5 - Prob. 15PQCh. 5 - Prob. 16PQCh. 5 - Prob. 17PQCh. 5 - A ball hanging from a light string or rod can be...Ch. 5 - Prob. 19PQCh. 5 - You are riding a luxury bus. In front of you is a...Ch. 5 - Prob. 21PQCh. 5 - A particle with mass m = 4.00 kg accelerates...Ch. 5 - The x and y coordinates of a 4.00-kg particle...Ch. 5 - In the movie Garden State, one of the characters...Ch. 5 - The starship Enterprise has its tractor beam...Ch. 5 - A race car is moving around a circular track at a...Ch. 5 - A particle of mass m1 accelerates at 4.25 m/s2...Ch. 5 - Prob. 28PQCh. 5 - Two forces F1=(62.98i15.80j) N and...Ch. 5 - Three forces F1=(62.98i15.80j) N,...Ch. 5 - A hockey stick pushes a 0.160-kg puck with...Ch. 5 - If the vector components of the position of a...Ch. 5 - If the vector components of the position of a...Ch. 5 - A 15.0-kg object is in free fall near the surface...Ch. 5 - A black widow spider hangs motionless from a web...Ch. 5 - Determine whether each of the following statements...Ch. 5 - You place tomatoes in the pan of a hanging spring...Ch. 5 - Kinetic friction is proportional to the normal...Ch. 5 - A student takes the elevator up to the fourth...Ch. 5 - A sleigh is being pulled horizontally by a train...Ch. 5 - Two blocks are connected by a rope that passes...Ch. 5 - Find an expression for the carts acceleration in...Ch. 5 - A woman uses a rope to pull a block of mass m...Ch. 5 - A student working on a school project modeled a...Ch. 5 - One great form of athletic competition for...Ch. 5 - A heavy crate of mass 50.0 kg is pulled at...Ch. 5 - A block with mass m1 hangs from a rope that is...Ch. 5 - To get in shape, you head to the local gym to...Ch. 5 - A block with mass m1 hangs from a rope that is...Ch. 5 - FIGURE P5.49 Problems 49 and 50. Suppose the...Ch. 5 - Two objects, m1 = 3.00 kg and m2 = 8.50 kg, are...Ch. 5 - A runaway piano starts from rest and slides down a...Ch. 5 - Does the ground need to exert a force on you for...Ch. 5 - A boxer breaks his hand by punching another boxers...Ch. 5 - Prob. 55PQCh. 5 - A textbook rests on a movable wooden plank that is...Ch. 5 - Prob. 57PQCh. 5 - Prob. 58PQCh. 5 - Prob. 59PQCh. 5 - A worker is attempting to lift a 55.0-kg palette...Ch. 5 - Prob. 61PQCh. 5 - A concept map is a visual representation of...Ch. 5 - A 75.0-g arrow, fired at a speed of 110 m/s to the...Ch. 5 - Prob. 64PQCh. 5 - A box with mass m1 = 6.00 kg sliding on a rough...Ch. 5 - Prob. 66PQCh. 5 - A cosmic ray muon with mass m = 1.88 1028 kg...Ch. 5 - Prob. 68PQCh. 5 - Prob. 69PQCh. 5 - A 1.50-kg particle initially at rest and at the...Ch. 5 - A block of ice (m = 15.0 kg) with an attached rope...Ch. 5 - A block of ice (m = 15.0 kg) with an attached rope...Ch. 5 - Prob. 73PQCh. 5 - Starting from rest, a rectangular toy block with...Ch. 5 - When a 1.50-kg dress hangs midway from a taut...Ch. 5 - Jamal and Dayo are lifting a large chest, weighing...Ch. 5 - A heavy chandelier with mass 125 kg is hung by...Ch. 5 - Two children, Raffi and John, sitting on sleds...Ch. 5 - Two boxes with masses m1 = 4.00 kg and m2 = 10.0...Ch. 5 - Two blocks of mass m1 = 1.50 kg and m2 = 5.00 kg...Ch. 5 - An aerial demonstration aircraft dives at an angle...Ch. 5 - A painter sits on a scaffold that is connected to...Ch. 5 - Three crates with masses m1 = 5.45 kg, m2 = 7.88...Ch. 5 - A small block with mass m is set on the top of an...
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