Principles of Physics: A Calculus-Based Text
5th Edition
ISBN: 9781133104261
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Chapter 17, Problem 9OQ
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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 17 Solutions
Principles of Physics: A Calculus-Based Text
Ch. 17.2 - Prob. 17.1QQCh. 17.3 - Prob. 17.2QQCh. 17.3 - Prob. 17.3QQCh. 17.5 - Prob. 17.4QQCh. 17.6 - Characterize the paths in Figure 17.10 as...Ch. 17.7 - (i) How does the internal energy of an ideal gas...Ch. 17.10 - Prob. 17.7QQCh. 17 - Prob. 1OQCh. 17 - A 100-g piece of copper, initially at 95.0C, is...Ch. 17 - Prob. 3OQ
Ch. 17 - Prob. 4OQCh. 17 - Prob. 5OQCh. 17 - Prob. 6OQCh. 17 - Prob. 7OQCh. 17 - Prob. 8OQCh. 17 - Prob. 9OQCh. 17 - Prob. 10OQCh. 17 - Star A has twice the radius and twice the absolute...Ch. 17 - If a gas is compressed isothermally, which of the...Ch. 17 - When a gas undergoes an adiabatic expansion, which...Ch. 17 - Ethyl alcohol has about one-half the specific heat...Ch. 17 - Prob. 15OQCh. 17 - Prob. 1CQCh. 17 - Prob. 2CQCh. 17 - Pioneers stored fruits and vegetables in...Ch. 17 - Why is a person able to remove a piece of dry...Ch. 17 - Prob. 5CQCh. 17 - Prob. 6CQCh. 17 - It is the morning of a day that will become hot....Ch. 17 - You need to pick up a very hot cooking pot in your...Ch. 17 - Rub the palm of your hand on a metal surface for...Ch. 17 - Prob. 10CQCh. 17 - Prob. 11CQCh. 17 - Prob. 12CQCh. 17 - On his honeymoon, James Joule traveled from...Ch. 17 - Consider Joules apparatus described in Figure...Ch. 17 - Prob. 3PCh. 17 - Prob. 4PCh. 17 - Prob. 5PCh. 17 - Prob. 6PCh. 17 - Prob. 7PCh. 17 - Prob. 8PCh. 17 - Prob. 9PCh. 17 - Prob. 10PCh. 17 - Prob. 11PCh. 17 - Prob. 12PCh. 17 - Prob. 13PCh. 17 - Prob. 14PCh. 17 - In an insulated vessel, 250 g of ice at 0C is...Ch. 17 - Prob. 16PCh. 17 - Prob. 17PCh. 17 - Prob. 18PCh. 17 - A 1.00-kg block of copper at 20.0C is dropped into...Ch. 17 - A resting adult of average size converts chemical...Ch. 17 - Prob. 21PCh. 17 - Prob. 22PCh. 17 - An ideal gas is enclosed in a cylinder with a...Ch. 17 - Prob. 24PCh. 17 - Prob. 25PCh. 17 - A sample of an ideal gas goes through the process...Ch. 17 - A thermodynamic system undergoes a process in...Ch. 17 - A gas is taken through the cyclic process...Ch. 17 - Consider the cyclic process depicted in Figure...Ch. 17 - Why is the following situation impossible? An...Ch. 17 - An ideal gas initially at 300 K undergoes an...Ch. 17 - In Figure P17.32, the change in internal energy of...Ch. 17 - Prob. 33PCh. 17 - Prob. 34PCh. 17 - Prob. 35PCh. 17 - Prob. 36PCh. 17 - Prob. 37PCh. 17 - One mole of an ideal gas does 3 000 J of work on...Ch. 17 - A 1.00-mol sample of hydrogen gas is heated at...Ch. 17 - A sample of a diatomic ideal gas has pressure P...Ch. 17 - Prob. 41PCh. 17 - Prob. 42PCh. 17 - Prob. 43PCh. 17 - Review. This problem is a continuation of Problem...Ch. 17 - Prob. 45PCh. 17 - A 2.00-mol sample of a diatomic ideal gas expands...Ch. 17 - Prob. 47PCh. 17 - An ideal gas with specific heat ratio confined to...Ch. 17 - Prob. 49PCh. 17 - Prob. 50PCh. 17 - Prob. 51PCh. 17 - Prob. 52PCh. 17 - Air (a diatomic ideal gas) at 27.0C and...Ch. 17 - Prob. 54PCh. 17 - Prob. 55PCh. 17 - Prob. 56PCh. 17 - Prob. 57PCh. 17 - Prob. 58PCh. 17 - Prob. 59PCh. 17 - Prob. 60PCh. 17 - Prob. 61PCh. 17 - Prob. 62PCh. 17 - The surface of the Sun has a temperature of about...Ch. 17 - Prob. 64PCh. 17 - At high noon, the Sun delivers 1 000 W to each...Ch. 17 - A theoretical atmospheric lapse rate. Section 16.7...Ch. 17 - Prob. 67PCh. 17 - A sample of a monatomic ideal gas occupies 5.00 L...Ch. 17 - An aluminum rod 0.500 m in length and with a...Ch. 17 - Prob. 70PCh. 17 - Prob. 71PCh. 17 - Prob. 72PCh. 17 - Prob. 73PCh. 17 - Prob. 74PCh. 17 - Prob. 75PCh. 17 - Prob. 76PCh. 17 - Prob. 77PCh. 17 - Prob. 78PCh. 17 - Prob. 79PCh. 17 - Prob. 81PCh. 17 - Prob. 82PCh. 17 - Prob. 84PCh. 17 - Prob. 85PCh. 17 - Prob. 86PCh. 17 - Prob. 87PCh. 17 - Prob. 88PCh. 17 - Water in an electric teakettle is boiling. The...
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