Physics
Physics
7th Edition
ISBN: 9780321733627
Author: Douglas C. Giancoli
Publisher: PEARSON
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Chapter 5, Problem 73GP
To determine

The minimum speed of a roller coaster so that the passenger’s upside down at the top of the circle do not fail out.

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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 5 Solutions

Physics

Ch. 5 - Prob. 9QCh. 5 - 10. A car maintains a constant speed v as it...Ch. 5 - Prob. 11QCh. 5 - Prob. 12QCh. 5 - Does an apple exert a gravitational force on the...Ch. 5 - Why is more fuel required for a spacecraft to...Ch. 5 - Would it require less speed to launch a satellite...Ch. 5 - Prob. 16QCh. 5 - The Sun is below us at midnight, nearly in line...Ch. 5 - 18. When will your apparent weight be the...Ch. 5 - Prob. 19QCh. 5 - Prob. 20QCh. 5 - Is the centripetal acceleration of Mars in its...Ch. 5 - The mass of the '‘planet" Pluto was not known...Ch. 5 - Prob. 23QCh. 5 - Prob. 1MCQCh. 5 - Prob. 2MCQCh. 5 - Prob. 3MCQCh. 5 - Prob. 4MCQCh. 5 - Prob. 5MCQCh. 5 - Prob. 6MCQCh. 5 - Prob. 7MCQCh. 5 - Prob. 8MCQCh. 5 - Prob. 9MCQCh. 5 - Prob. 10MCQCh. 5 - Prob. 11MCQCh. 5 - 'A penny is placed on a turntable which is...Ch. 5 - A child sitting 1.20 m from the center of a...Ch. 5 - A jet plane traveling 1890 km/h (525 m/s) pulls...Ch. 5 - Prob. 3PCh. 5 - What is the magnitude of the acceleration of a...Ch. 5 - 5. (II) A 0.55-kg ball, attached to the end of a...Ch. 5 - How fast (in rpm) must a centrifuge rotate if a...Ch. 5 - Prob. 7PCh. 5 - How large must the coefficient of static friction...Ch. 5 - Prob. 9PCh. 5 - Prob. 10PCh. 5 - How many revolutions per minute would a...Ch. 5 - Prob. 12PCh. 5 - Prob. 13PCh. 5 - Prob. 14PCh. 5 - Prob. 15PCh. 5 - Prob. 16PCh. 5 - Prob. 17PCh. 5 - Prob. 18PCh. 5 - Prob. 19PCh. 5 - Prob. 20PCh. 5 - Prob. 21PCh. 5 - Prob. 22PCh. 5 - Prob. 23PCh. 5 - Determine the tangential and centripetal...Ch. 5 - Prob. 25PCh. 5 - For each of the cases described below, sketch and...Ch. 5 - Prob. 27PCh. 5 - Calculate the force of Earth's gravity on a...Ch. 5 - At the surface of a certain planet, the...Ch. 5 - At what distance from the Earth will a spacecraft...Ch. 5 - Prob. 31PCh. 5 - Prob. 32PCh. 5 - Prob. 33PCh. 5 - Prob. 34PCh. 5 - Prob. 35PCh. 5 - Prob. 36PCh. 5 - Prob. 37PCh. 5 - Prob. 38PCh. 5 - Prob. 39PCh. 5 - Prob. 40PCh. 5 - 41. (II) Every few hundred years most of the...Ch. 5 - 42 (II) Four 7.5-kg spheres are located at the...Ch. 5 - 43. (II) Determine the distance from the Earth's...Ch. 5 - 44.(II) A certain neutron star has five times the...Ch. 5 - 45. (I) A space shuttle releases a satellite into...Ch. 5 - 46. (I) Calculate the speed of a satellite moving...Ch. 5 - Prob. 47PCh. 5 - Prob. 48PCh. 5 - Calculate the period of a satellite orbiting the...Ch. 5 - Prob. 50PCh. 5 - What will a spring scale read for the weight of a...Ch. 5 - Prob. 52PCh. 5 - Prob. 53PCh. 5 - A Ferris wheel 22.0 m in diameter rotates once...Ch. 5 - At what rate must a cylindrical spaceship rotate...Ch. 5 - (a) Show that if a satellite orbits very near the...Ch. 5 - Neptune is an average distance of 4.5 x 109 km...Ch. 5 - The asteroid Icarus, though only a few hundred...Ch. 5 - Prob. 59PCh. 5 - Determine the mass of the Earth from the known...Ch. 5 - Prob. 61PCh. 5 - Prob. 62PCh. 5 - Prob. 63PCh. 5 - Prob. 64PCh. 5 - Prob. 65PCh. 5 - Prob. 66PCh. 5 - Prob. 67GPCh. 5 - Prob. 68GPCh. 5 - Prob. 69GPCh. 5 - Prob. 70GPCh. 5 - Prob. 71GPCh. 5 - Prob. 72GPCh. 5 - Prob. 73GPCh. 5 - Prob. 74GPCh. 5 - Two equal-mass stars maintain a constant distance...Ch. 5 - How far above the Earth's surface will the...Ch. 5 - Prob. 77GPCh. 5 - Prob. 78GPCh. 5 - The rings of Saturn are composed of chunks of ice...Ch. 5 - Prob. 80GPCh. 5 - Prob. 81GPCh. 5 - Prob. 82GPCh. 5 - Prob. 83GPCh. 5 - Prob. 84GPCh. 5 - A satellite of mass 5500 kg orbits the Earth and...Ch. 5 - Prob. 86GPCh. 5 - Prob. 87GPCh. 5 - Prob. 88GPCh. 5 - Prob. 89GPCh. 5 - Prob. 90GP
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