Astronomy
1st Edition
ISBN: 9781938168284
Author: Andrew Fraknoi; David Morrison; Sidney C. Wolff
Publisher: OpenStax
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Chapter 16, Problem 20E
Explain what it means when we say that Earth’s oceans are in hydrostatic equilibrium. Now suppose you are a scuba diver. Would you expect the pressure to increase or decrease as you dive below the surface to a depth of 200 feet? Why?
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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 16 Solutions
Astronomy
Ch. 16 - How do we know the age of the Sun?Ch. 16 - Explain how we know that the Sun’s energy is not...Ch. 16 - What is the ultimate source of energy that makes...Ch. 16 - What are the formulas for the three steps in the...Ch. 16 - How is a neutrino different from a neutron? List...Ch. 16 - Describe in your own words what is meant by the...Ch. 16 - Two astronomy students travel to South Dakota. One...Ch. 16 - What do measurements of the number of neutrinos...Ch. 16 - Do neutrinos have mass? Describe how the answer to...Ch. 16 - Neutrinos produced in the core of the Sun carry...
Ch. 16 - What conditions are required before proton-proton...Ch. 16 - Describe the two main ways that energy travels...Ch. 16 - Someone suggests that astronomers build a special...Ch. 16 - Earth contains radioactive elements whose decay...Ch. 16 - The Sun is much larger and more massive than...Ch. 16 - A friend who has not had the benefit of an...Ch. 16 - Which of the following transformations is (are)...Ch. 16 - Why is a higher temperature required to fuse...Ch. 16 - Earth’s atmosphere is in hydrostatic equilibrium....Ch. 16 - Explain what it means when we say that Earth’s...Ch. 16 - What mechanism transfers heat away from the...Ch. 16 - Suppose you are standing a few feet away from a...Ch. 16 - Give some everyday examples of the transport of...Ch. 16 - Suppose the proton-proton cycle in the Sun were to...Ch. 16 - Do you think that nuclear fusion takes place in...Ch. 16 - Why is fission not an important energy source in...Ch. 16 - Why do you suppose so great a fraction of the...Ch. 16 - Explain how mathematical computer models allow us...Ch. 16 - Estimate the amount of mass that is converted to...Ch. 16 - How much energy is released when a proton combines...Ch. 16 - The Sun converts 4109 kg of mass to energy every...Ch. 16 - Assume that the mass of the Sun is 75% hydrogen...Ch. 16 - In fact, the conversion of mass to energy in the...Ch. 16 - Now suppose that all of the hydrogen atoms in the...Ch. 16 - Models of the Sun indicate that only about 10% of...Ch. 16 - Show that the statement in the text is correct:...Ch. 16 - Every second, the Sun converts 4 million tons of...Ch. 16 - Raymond Davis Jr.’s neutrino detector contained...
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