Life in the Universe (4th Edition)
4th Edition
ISBN: 9780134089089
Author: Jeffrey O. Bennett, Seth Shostak
Publisher: PEARSON
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Chapter 3, Problem 30TYU
Using new, powerful telescopes, biologists today announced that they had discovered evidence of complex organic molecules in the atmosphere of an extrasolar planet.
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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 \((-180^{\circ},180^{\circ}]\).
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Chapter 3 Solutions
Life in the Universe (4th Edition)
Ch. 3 - List three major ideas of astronomy that help...Ch. 3 - Briefly define and describe each of the various...Ch. 3 - Describe the solar system as it looks on the...Ch. 3 - Prob. 4RQCh. 3 - Prob. 5RQCh. 3 - Prob. 6RQCh. 3 - Prob. 7RQCh. 3 - What do we mean when we say that Earth and life...Ch. 3 - Imagine describing the cosmic calendar to a...Ch. 3 - Prob. 10RQ
Ch. 3 - Prob. 11RQCh. 3 - Prob. 12RQCh. 3 - What is the difference between matter in the...Ch. 3 - Define and give examples of kinetic energy,...Ch. 3 - Prob. 15RQCh. 3 - Prob. 16RQCh. 3 - Briefly describe the four major features of our...Ch. 3 - Briefly describe the nebular theory and how it...Ch. 3 - What was the close encounter hypothesis for our...Ch. 3 - How have recent discoveries led scientists to...Ch. 3 - Prob. 21TYUCh. 3 - At a middle school talent show, 14-year-old Sam...Ch. 3 - SETI researchers announced today that if they...Ch. 3 - A noted physicist today announced that he has...Ch. 3 - Prob. 25TYUCh. 3 - Astronomers have discovered a galaxy in the far...Ch. 3 - Inventor John Johnson has patented a device that...Ch. 3 - Prob. 28TYUCh. 3 - Prob. 29TYUCh. 3 - Using new, powerful telescopes, biologists today...Ch. 3 - Prob. 31TYUCh. 3 - Prob. 32TYUCh. 3 - A television advertisement claiming that a product...Ch. 3 - When we say the universe is expanding, we mean...Ch. 3 - Prob. 35TYUCh. 3 - The age of our solar system is about (a) one-third...Ch. 3 - Prob. 37TYUCh. 3 - How many of the planets orbit the Sun in the same...Ch. 3 - Prob. 39TYUCh. 3 - Prob. 40TYUCh. 3 - Explaining the Past. Is it really possible for...Ch. 3 - A Strange Star System. Suppose that we discovered...Ch. 3 - Prob. 44IFCh. 3 - Alien Technology. Some people believe that Earth...Ch. 3 - Atomic Terminology Practice. a. The most common...Ch. 3 - Prob. 49IFCh. 3 - Prob. 50IFCh. 3 - Patterns of Motion. In one or two paragraphs,...Ch. 3 - Two Kinds of Planets. The jovian planets differ...Ch. 3 - Pluto and Eris. How does the nebular theory...Ch. 3 - Rocks from Other Solar Systems. Many leftovers...Ch. 3 - Prob. 55IFCh. 3 - Prob. 56IFCh. 3 - Scale of the Solar System. The real diameters of...Ch. 3 - Prob. 58IFCh. 3 - Prob. 59IFCh. 3 - Prob. 60IFCh. 3 - Prob. 61IFCh. 3 - Prob. 62IFCh. 3 - Prob. 63IFCh. 3 - Prob. 67WPCh. 3 - Tour of the Solar System. Visit one of the many...
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