Foundations of Astronomy
13th Edition
ISBN: 9781305079151
Author: Michael A. Seeds, Dana Backman
Publisher: Cengage Learning
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Chapter 5, Problem 29RQ
According to Kepler’s first law, planets move in elliptical orbits. Why is that considered accelerated motion? According to Newton, what is the force causing that acceleration?
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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
Foundations of Astronomy
Ch. 5 - According to the Aristotle, if earth and water...Ch. 5 - Today, what do we call the Aristotelean violent...Ch. 5 - Which of Keplers or Newtons laws best describes...Ch. 5 - Why would Aristotles explanation of gravity not...Ch. 5 - According to the principles of Aristotle, what...Ch. 5 - If you drop a feather and a steel hammer at the...Ch. 5 - What is the difference between mass and weight?Ch. 5 - When a person says he gained weight, does he mean...Ch. 5 - An astronaut working in space near the...Ch. 5 - What is the difference between speed and velocity?
Ch. 5 - A car is on a circular off ramp of an interstate...Ch. 5 - How many accelerators does a car have? What are...Ch. 5 - You put your astronomy textbook and your No. 2...Ch. 5 - An astronaut is in space with a baseball and a...Ch. 5 - You are at a red light in your car. The red light...Ch. 5 - You weigh 100 pounds, your friend weighs 200...Ch. 5 - Why did Newton conclude that some force had to...Ch. 5 - Why did Newton conclude that gravity has to be...Ch. 5 - Prob. 19RQCh. 5 - You are sitting next to a person who has twice as...Ch. 5 - You are sitting next to a person who has twice as...Ch. 5 - You are sitting next to a person who has twice as...Ch. 5 - How does the concept of a field explain action at...Ch. 5 - Why cant a spacecraft go beyond Earths gravity?Ch. 5 - Prob. 25RQCh. 5 - Balance a pencil lengthwise on the side of your...Ch. 5 - Prob. 27RQCh. 5 - Why cant you leave Earths gravitational field when...Ch. 5 - According to Keplers first law, planets move in...Ch. 5 - How do planets orbiting the Sun and skaters doing...Ch. 5 - If a planet were to slowly migrate inward toward...Ch. 5 - If you hold this textbook out at shoulder height...Ch. 5 - Today at the beach you see the highest of all high...Ch. 5 - Why is the period of an open orbit undefined?Ch. 5 - In what conditions do Newtons laws of motion and...Ch. 5 - Prob. 36RQCh. 5 - When you ride a fast elevator upward, you feel...Ch. 5 - Prob. 38RQCh. 5 - How is gravity related to acceleration? Are all...Ch. 5 - Near a massive planet, is gravitational...Ch. 5 - Prob. 41RQCh. 5 - How Do We Know? Why is it important that a theory...Ch. 5 - Prob. 1DQCh. 5 - Prob. 2DQCh. 5 - Prob. 3DQCh. 5 - Prob. 4DQCh. 5 - Prob. 5DQCh. 5 - Prob. 6DQCh. 5 - Prob. 7DQCh. 5 - An astronomy textbook is to be dropped from a tall...Ch. 5 - Compared to the strength of Earths gravity at its...Ch. 5 - Compare the force of gravity on a 1 kg mass on the...Ch. 5 - Prob. 4PCh. 5 - The International Space Station is in orbit around...Ch. 5 - If a small lead ball falls from a high tower on...Ch. 5 - What is the circular velocity of an Earth...Ch. 5 - What is the circular velocity of an Earth...Ch. 5 - What is the orbital speed at Earths surface?...Ch. 5 - Prob. 10PCh. 5 - Prob. 11PCh. 5 - Describe the shape of the orbit followed by the...Ch. 5 - Prob. 13PCh. 5 - Prob. 14PCh. 5 - Prob. 15PCh. 5 - Prob. 16PCh. 5 - A moon of Jupiter takes 1.8 days to orbit at a...Ch. 5 - Why can the object shown here be bolted in place...Ch. 5 - What is the flux at position 2 compared to...Ch. 5 - Why is it a little bit misleading to say that this...
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