Tutorials in Introductory Physics
1st Edition
ISBN: 9780130970695
Author: Peter S. Shaffer, Lillian C. McDermott
Publisher: Addison Wesley
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Chapter 1.2, Problem 1hT
Description of Motion:
Move toward the detector with decreasing speed, then just as you have come to rest, move away, from the detector with increasing speed.
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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 1 Solutions
Tutorials in Introductory Physics
Ch. 1.1 - Each person in your group should obtain a ruler...Ch. 1.1 - Each person in your group should obtain a ruler...Ch. 1.1 - Each person in your group should obtain a ruler...Ch. 1.1 - Each person in your group should obtain a ruler...Ch. 1.1 - Each person in your group should obtain a ruler...Ch. 1.1 - Each person in your group should obtain a ruler...Ch. 1.1 - Each person in your group should obtain a ruler...Ch. 1.1 - A. In the space below, sketch a possible ticker...Ch. 1.1 - B. Together with your classmates, take your ticker...Ch. 1.1 - C. Based on your observations of your tape segment...
Ch. 1.1 - D. Review your earlier interpretation of the speed...Ch. 1.1 - E. Suppose you selected two widely separated dots...Ch. 1.2 - The computer program assumes a particular...Ch. 1.2 - Description of Motion:Ch. 1.2 - Description of Motion:Ch. 1.2 - Description of Motion:Ch. 1.2 - How are the motions in parts C and D similar? How...Ch. 1.2 - Description of Motion:Ch. 1.2 - Description of Motion:Ch. 1.2 - Description of Motion: Move toward the detector...Ch. 1.2 - How do the acceleration graphs for F, G, and H...Ch. 1.2 - Description of Motion: Initially move away from...Ch. 1.2 - Description of Motion:Ch. 1.2 - Description of Motion:Ch. 1.2 - The term decelerate is often used to indicate that...Ch. 1.3 - Draw vectors on your diagram that represent the...Ch. 1.3 - B. In the space at right, compare the velocities...Ch. 1.3 - Consider the change in velocity vector between two...Ch. 1.3 - Use the definition of acceleration to draw a...Ch. 1.3 - Does the acceleration change as the ball rolls up...Ch. 1.3 - Generalize your results thus far to answer the...Ch. 1.3 - Choose two successive points. In the space at...Ch. 1.3 - In the space at right, draw a vector to represent...Ch. 1.3 - Choose a point before the turnaround and another...Ch. 1.3 - Suppose that you had chosen the turnaround as one...Ch. 1.3 - In the space at right, draw a vector that...Ch. 1.4 - Prob. 1aTCh. 1.4 - If you were to choose a different origin for the...Ch. 1.4 - On a separate part of your paper, copy the...Ch. 1.4 - Suppose you were to choose a new point on the...Ch. 1.4 - On a separate part of your paper, copy the...Ch. 1.4 - Suppose the object started from rest at point E...Ch. 1.4 - At several points on each of the diagrams below,...Ch. 1.5 - The second diagram at right shows the positions of...Ch. 1.5 - The picture of the spaceships and shuttle from the...Ch. 1.5 - Prob. 1cTCh. 1.5 - Spaceship C moves so as to remain a fixed distance...Ch. 1.5 - Consider the following statement: "The...Ch. 1.5 - Prob. 1fTCh. 1.5 - Describe the motion of the car and the truck...Ch. 1.5 - Complete the diagram at right by drawing the car...Ch. 1.5 - Use your completed diagram to sketch average...Ch. 1.5 - During a small time interval t from just before to...
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