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10.29. Consider the rotating swings in Fig. 10.17. Length L= 10 m, and the distance a = be the linear velocity of the seat if the rope is to make an angle of 30° with the vertical? 3 m. What must Ans. 6.73 m/s R Figure 10.17

10.29. Consider the rotating swings in Fig. 10.17. Length L= 10 m, and the distance a = be the linear velocity of the seat if the rope is to make an angle of 30° with the vertical? 3 m. What must Ans. 6.73 m/s R Figure 10.17

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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**Problem Statement:** **10.29.** Consider the rotating swings in Fig. 10.17. Length \( L = 10 \, \text{m} \), and the distance \( a = 3 \, \text{m} \). What must be the linear velocity of the seat if the rope is to make an angle of \( 30^\circ \) with the vertical? **Answer:** \( 6.73 \, \text{m/s} \) **Figure 10.17 Explanation:** The figure illustrates a rotating swing where a seat is attached to a rope of length \( L = 10 \, \text{m} \). The point of attachment is a horizontal distance \( a = 3 \, \text{m} \) from the vertical axis of rotation. The swing rope makes an angle \( \theta = 30^\circ \) with the vertical direction. The goal is to find the linear velocity of the seat that would maintain this angle during rotation. - The diagram shows the seat at a distance \( R \) from the axis, at an angle, in a circular path. - The rope forms the hypotenuse of a right triangle, defining \( R \) as the base of the triangle across from the vertical (distance where the swing rotates horizontally). - The angle \( \theta = 30^\circ \) is also depicted as the angle between the rope and the vertical line. The solution involves calculating the centripetal force required for maintaining the motion and using trigonometric identities to relate the components of the forces and geometry involved.
Transcribed Image Text:**Problem Statement:** **10.29.** Consider the rotating swings in Fig. 10.17. Length \( L = 10 \, \text{m} \), and the distance \( a = 3 \, \text{m} \). What must be the linear velocity of the seat if the rope is to make an angle of \( 30^\circ \) with the vertical? **Answer:** \( 6.73 \, \text{m/s} \) **Figure 10.17 Explanation:** The figure illustrates a rotating swing where a seat is attached to a rope of length \( L = 10 \, \text{m} \). The point of attachment is a horizontal distance \( a = 3 \, \text{m} \) from the vertical axis of rotation. The swing rope makes an angle \( \theta = 30^\circ \) with the vertical direction. The goal is to find the linear velocity of the seat that would maintain this angle during rotation. - The diagram shows the seat at a distance \( R \) from the axis, at an angle, in a circular path. - The rope forms the hypotenuse of a right triangle, defining \( R \) as the base of the triangle across from the vertical (distance where the swing rotates horizontally). - The angle \( \theta = 30^\circ \) is also depicted as the angle between the rope and the vertical line. The solution involves calculating the centripetal force required for maintaining the motion and using trigonometric identities to relate the components of the forces and geometry involved.
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