COSMIC PERSPECTIVE
9th Edition
ISBN: 9780135729458
Author: Bennett
Publisher: PEARSON
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Chapter 1, Problem 2EAP
Define astronomical unit and light-year.
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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 1 Solutions
COSMIC PERSPECTIVE
Ch. 1 - Prob. 1VSCCh. 1 - Prob. 2VSCCh. 1 - Prob. 3VSCCh. 1 - Prob. 4VSCCh. 1 - Prob. 1EAPCh. 1 - Define astronomical unit and light-year.Ch. 1 - Explain the statement “The farther away we look in...Ch. 1 - Prob. 4EAPCh. 1 - Prob. 5EAPCh. 1 - What do we mean when we say that the universe is...
Ch. 1 - In what sense are we “star stuff”?Ch. 1 - Use the cosmic calendar to describe how the human...Ch. 1 - Briefly explain Earth’s daily rotation and annual...Ch. 1 - Briefly describe our solar system’s location and...Ch. 1 - Prob. 11EAPCh. 1 - Prob. 12EAPCh. 1 - Prob. 13EAPCh. 1 - Does it Make Sense? Decide whether the statement...Ch. 1 - Prob. 15EAPCh. 1 - Prob. 16EAPCh. 1 - Prob. 17EAPCh. 1 - Prob. 18EAPCh. 1 - Prob. 19EAPCh. 1 - Prob. 20EAPCh. 1 - Prob. 21EAPCh. 1 - Prob. 22EAPCh. 1 - Which of the following correctly lists our ‘cosmic...Ch. 1 - An astronomical unit is (a) any planet’s average...Ch. 1 - The star Betelgeuse is about 600 light-years away....Ch. 1 - Prob. 26EAPCh. 1 - The total number of stars in the observable...Ch. 1 - Prob. 28EAPCh. 1 - Prob. 29EAPCh. 1 - Prob. 30EAPCh. 1 - Prob. 31EAPCh. 1 - Prob. 32EAPCh. 1 - Prob. 34EAPCh. 1 - Thinking About Scale. One key to success in...Ch. 1 - Prob. 36EAPCh. 1 - A Human Adventure. Astronomical discoveries...Ch. 1 - Prob. 38EAPCh. 1 - Prob. 39EAPCh. 1 - Prob. 40EAPCh. 1 - Prob. 41EAPCh. 1 - Prob. 42EAPCh. 1 - Prob. 43EAPCh. 1 - Prob. 44EAPCh. 1 - Prob. 45EAPCh. 1 - Spacecraft Communication. We use radio waves,...Ch. 1 - Prob. 47EAPCh. 1 - Prob. 48EAPCh. 1 - Prob. 49EAPCh. 1 - Driving Trips. Imagine that you could drive your...Ch. 1 - Faster Trip. Suppose you wanted to reach Alpha...Ch. 1 - Prob. 52EAPCh. 1 - Earth Rotation Speed. Mathematical Insight 1.3...Ch. 1 - Order of Magnitude Estimate. Mathematical Insight...
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