Physics
Physics
5th Edition
ISBN: 9781260487008
Author: GIAMBATTISTA, Alan
Publisher: MCGRAW-HILL HIGHER EDUCATION
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Chapter 5, Problem 21P

(a)

To determine

The tension in the string.

(b)

To determine

The time period.

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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 5 Solutions

Physics

Ch. 5.4 - Prob. 5.8PPCh. 5.4 - Prob. 5.4CPCh. 5.4 - Prob. 5.9PPCh. 5.4 - Prob. 5.10PPCh. 5.5 - Prob. 5.5CPCh. 5.5 - Prob. 5.11PPCh. 5.5 - Conceptual Practice Problem 5.12 Analysis of the...Ch. 5.6 - Prob. 5.6CPCh. 5.6 - Prob. 5.13PPCh. 5.7 - Prob. 5.14PPCh. 5 - Prob. 1CQCh. 5 - Prob. 2CQCh. 5 - Prob. 3CQCh. 5 - Prob. 4CQCh. 5 - Prob. 5CQCh. 5 - Prob. 6CQCh. 5 - Prob. 7CQCh. 5 - Prob. 8CQCh. 5 - Prob. 9CQCh. 5 - Prob. 10CQCh. 5 - Prob. 11CQCh. 5 - Prob. 12CQCh. 5 - Multiple-Choice Questions 1-4 and Problem...Ch. 5 - Questions 1–4: A satellite in orbit travels around...Ch. 5 - 3. What is the direction of the satellite’s...Ch. 5 - 4. What is the direction of the satellite’s...Ch. 5 - 5. An object moving in a circle at a constant...Ch. 5 - 6. A spider sits on a DVD that is rotating at a...Ch. 5 - 7. Two satellites are in orbit around Mars with...Ch. 5 - Questions 8-9: A boy swings in a tire swing....Ch. 5 - 9. When is the tension in the rope the...Ch. 5 - Questions 10–11 concern these three...Ch. 5 - 11. An object is in nonuniform circular motion...Ch. 5 - 12. An astronaut is out in space far from any...Ch. 5 - Prob. 1PCh. 5 - 2. Convert these to radian measure: (a) 30.0°, (b)...Ch. 5 - 3. Find the average angular speed of the second...Ch. 5 - 4. An elevator cable winds on a drum of radius...Ch. 5 - 5. A wheel of radius 30 cm is rotating at a rate...Ch. 5 - 6. A soccer ball of diameter 31 cm rolls without...Ch. 5 - 7. A bicycle is moving at 9.0 m/s. What is the...Ch. 5 - 8. Dung beetles are renowned for building large...Ch. 5 - Prob. 9PCh. 5 - 9. In the construction of railroads, it is...Ch. 5 - Problems 10–12. Five flywheels are spinning as...Ch. 5 - Prob. 12PCh. 5 - Prob. 13PCh. 5 - 13. Objects that are at rest relative to Earth’s...Ch. 5 - Prob. 14PCh. 5 - Prob. 17PCh. 5 - Prob. 16PCh. 5 - Prob. 18PCh. 5 - Prob. 19PCh. 5 - Prob. 20PCh. 5 - 21. A conical pendulum consists of a bob (mass...Ch. 5 - Prob. 22PCh. 5 - Prob. 25PCh. 5 - Prob. 26PCh. 5 - A roller coaster car of mass 320 kg (including...Ch. 5 - Prob. 24PCh. 5 - Prob. 27PCh. 5 - Prob. 31PCh. 5 - Prob. 29PCh. 5 - Prob. 30PCh. 5 - Prob. 28PCh. 5 - Prob. 32PCh. 5 - Prob. 33PCh. 5 - Prob. 34PCh. 5 - Prob. 37PCh. 5 - Prob. 38PCh. 5 - Prob. 35PCh. 5 - Prob. 36PCh. 5 - Prob. 39PCh. 5 - Prob. 40PCh. 5 - Prob. 41PCh. 5 - Prob. 42PCh. 5 - Prob. 43PCh. 5 - Prob. 44PCh. 5 - Prob. 45PCh. 5 - Prob. 46PCh. 5 - Prob. 47PCh. 5 - Prob. 48PCh. 5 - Prob. 49PCh. 5 - Prob. 50PCh. 5 - Prob. 51PCh. 5 - Prob. 52PCh. 5 - Prob. 53PCh. 5 - Prob. 54PCh. 5 - Prob. 55PCh. 5 - 56. Find the tangential acceleration of a freely...Ch. 5 - Prob. 57PCh. 5 - Prob. 58PCh. 5 - Prob. 59PCh. 5 - Prob. 62PCh. 5 - Prob. 61PCh. 5 - Prob. 60PCh. 5 - Prob. 63PCh. 5 - Prob. 64PCh. 5 - Prob. 65PCh. 5 - Prob. 66PCh. 5 - Prob. 67PCh. 5 - Prob. 68PCh. 5 - Prob. 69PCh. 5 - Prob. 70PCh. 5 - Prob. 71PCh. 5 - Prob. 72PCh. 5 - Prob. 73PCh. 5 - Prob. 74PCh. 5 - Prob. 75PCh. 5 - Prob. 76PCh. 5 - Prob. 77PCh. 5 - Prob. 78PCh. 5 - Prob. 79PCh. 5 - Prob. 80PCh. 5 - Prob. 81PCh. 5 - Prob. 82PCh. 5 - Prob. 83PCh. 5 - Prob. 84PCh. 5 - Prob. 85PCh. 5 - Prob. 86PCh. 5 - Prob. 87PCh. 5 - Prob. 88PCh. 5 - Prob. 89PCh. 5 - Prob. 90PCh. 5 - Prob. 91PCh. 5 - Prob. 92PCh. 5 - Prob. 93PCh. 5 - 94. Two blocks are connected by a light string...Ch. 5 - Prob. 95PCh. 5 - Prob. 96P
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