COSMIC PERSPECTIVE
COSMIC PERSPECTIVE
9th Edition
ISBN: 9780135729458
Author: Bennett
Publisher: PEARSON
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Chapter 2, Problem 1EAP
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A planar double pendulum consists of two point masses \[m_1 = 1.00~\mathrm{kg}, \qquad m_2 = 1.00~\mathrm{kg}\]connected by massless, rigid rods of lengths \[L_1 = 1.00~\mathrm{m}, \qquad L_2 = 1.20~\mathrm{m}.\]The upper rod is hinged to a fixed pivot; gravity acts vertically downward with\[g = 9.81~\mathrm{m\,s^{-2}}.\]Define the generalized coordinates \(\theta_1,\theta_2\) as the angles each rod makes with thedownward vertical (positive anticlockwise, measured in radians unless stated otherwise).At \(t=0\) the system is released from rest with \[\theta_1(0)=120^{\circ}, \qquad\theta_2(0)=-10^{\circ}, \qquad\dot{\theta}_1(0)=\dot{\theta}_2(0)=0 .\]Using the exact nonlinear equations of motion (no small-angle or planar-pendulumapproximations) and assuming the rods never stretch or slip, determine the angle\(\theta_2\) at the instant\[t = 10.0~\mathrm{s}.\]Give the result in degrees, in the interval \((-180^{\circ},180^{\circ}]\).

Chapter 2 Solutions

COSMIC PERSPECTIVE

Ch. 2 - On a clear, dark night, the sky may appear to be...Ch. 2 - Why does the local sky look like a dome? Define...Ch. 2 - Prob. 5EAPCh. 2 - What are circumpolar stars? Are more stars...Ch. 2 - What are latitude and longitude? Does the sky vary...Ch. 2 - What is the zodiac, and why do we see different...Ch. 2 - Suppose Earth’s axis had no tilt. Would we still...Ch. 2 - Briefly describe key facts about the solstices and...Ch. 2 - What is precession? How does it affect what we see...Ch. 2 - Briefly describe the Moon’s cycle of phases. Can...Ch. 2 - Why do we always see the same face of the Moon?Ch. 2 - Why don’t we see an eclipse at every new and full...Ch. 2 - What do we mean by the apparent retrograde motion...Ch. 2 - Prob. 16EAPCh. 2 - Prob. 17EAPCh. 2 - Prob. 18EAPCh. 2 - Prob. 19EAPCh. 2 - Prob. 20EAPCh. 2 - Does It Make Sense? Decide whether the statement...Ch. 2 - Does It Make Sense? Decide whether the statement...Ch. 2 - Prob. 23EAPCh. 2 - Does It Make Sense? Decide whether the statement...Ch. 2 - Does It Make Sense? Decide whether the statement...Ch. 2 - Does It Make Sense? Decide whether the statement...Ch. 2 - Quick Quiz Choose the best answer to each of the...Ch. 2 - Quick Quiz Choose the best answer to each of the...Ch. 2 - Quick Quiz Choose the best answer to each of the...Ch. 2 - Prob. 30EAPCh. 2 - Quick Quiz Choose the best answer to each of the...Ch. 2 - Quick Quiz Choose the best answer to each of the...Ch. 2 - Quick Quiz Choose the best answer to each of the...Ch. 2 - Quick Quiz Choose the best answer to each of the...Ch. 2 - Quick Quiz Choose the best answer to each of the...Ch. 2 - Quick Quiz Choose the best answer to each of the...Ch. 2 - Earth-Centered or Sun-Centered? Decide whether...Ch. 2 - Shadow Phases. Many people incorrectly guess that...Ch. 2 - Earth-Centered Language. Many common phrases...Ch. 2 - Group Activity: Lunar Phases and Time of Day. Make...Ch. 2 - New Planet. A planet in another solar system has a...Ch. 2 - Your View of the Sky. a. What are your latitude...Ch. 2 - View from the Moon. Assume you live on the Moon,...Ch. 2 - View from the Sun. Suppose you lived on the Sun...Ch. 2 - A Farther Moon. Suppose the distance to the Moon...Ch. 2 - A Smaller Earth. Suppose Earth were smaller. Would...Ch. 2 - Observing Planetary Motion. Find out which planets...Ch. 2 - 47. A Connecticut Yankee. Find the book A...Ch. 2 - Be sure to show all calculations clearly and state...Ch. 2 - Be sure to show all calculations clearly and state...Ch. 2 - Be sure to show all calculations clearly and state...Ch. 2 - Be sure to show all calculations clearly and state...Ch. 2 - Prob. 57EAPCh. 2 - Prob. 58EAPCh. 2 - Be sure to show all calculations clearly and state...
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