1st Edition

ISBN: 9781938168048

Author: Paul Peter Urone, OpenStax, Roger Hinrichs

Publisher: OpenStax

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Chapter 18, Problem 59PE

Integrated Concepts

The practical limit to an electric field in air is about 3.00×10⁶¹ N/C. Above this strength, sparking takes place because air begins to ionize and charges flow, reducing the field, (a) Calculate the distance a free proton must travel in this field to reach 3,00% of the speed of light, starting from rest, (b) Is this practical in air, or must it occur in a vacuum?

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Chapter 18, Problem 58PE

Chapter 18, Problem 60PE

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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 18 Solutions

College Physics

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