Explanation Given data: θ = 35 ° . Formula used: The expression of angular velocity is given by, ω = v r (1) Here, v is the translational velocity and r is the radius. The expression for moment of inertia of a spherical shell is given by, I = 2 3 m r 2 (2) Here, m is the mass. Total energy is given as, E = 1 2 m v 2 + 1 2 I ω 2 + m g h (3) Here, g is the acceleration due to gravity which have a standard value of 9.8 m s 2 and h is the height. Displacement along x- axis is given as, x = v 0 x t + 1 2 a x t 2 (4) Here, v 0 x is the initial velocity along x -axis, t is the time period, and a x is the acceleration along x -axis. Time taken is given as, t = v y − v 0 y − g (5) Here, v y is the final velocity along y -axis and v 0 y is the initial velocity along y -axis. Calculation: The direction of force is given according to the direction of the axis. As the ball moves down the hill the potential energy is converted to kinetic energy. But the kinetic energy of ball is shared between translational and rotational energy. The total energy of the system is zero, so the total potential energy at the top of the hill is been converted into total kinetic energy at the bottom of the hill then the equation (3) becomes, 1 2 m v 2 + 1 2 I ω 2 = m g h (6) Substitute equation (1) and (2) in equation (6), 1 2 m v 2 + 1 2 ( 2 3 m r 2 ) ( v r ) 2 = m g h 1 2 m v 2 + 1 2 ( 2 3 m r 2 ) ( v 2 r 2 ) = m g h 1 2 v 2 + 1 3 v 2 = g h 5 6 v 2 = g h v 2 = 6 5 g h v = 6 5 g h (7) At the bottom where the ball is placed, The vertical component of the velocity of the ball which has a velocity of v is, v 0 y = v sin θ (8) The horizontal component of the velocity of the ball which has a velocity of v is, v 0 x = v cos θ (9) As the horizontal acceleration of the ball is zero

11th Edition

ISBN: 9781119326342

Author: CUTNELL

Publisher: WILEY

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Question

Chapter 9, Problem 58P

To determine

The range x .

Expert Solution & Answer

Chapter 9 Solutions

Physics

Ch. 9.1 - 1. The drawing shows an overhead view of a...Ch. 9.1 - Prob. 2CYU Ch. 9.1 - 3. Is it possible (a) for a large force to produce...Ch. 9.1 - Prob. 4CYU Ch. 9.2 - Prob. 5CYU Ch. 9.2 - Prob. 6CYU Ch. 9.3 - 7. Starting in the spring, fruit begins to grow on...Ch. 9.3 - Prob. 8CYU Ch. 9.4 - 10. Three massless rods (A, B. and C) are free to...Ch. 9 - Prob. 1FC

Ch. 9 - Prob. 3FC Ch. 9 - Prob. 6FC Ch. 9 - Prob. 8FC Ch. 9 - Prob. 10FC Ch. 9 - Prob. 12FC Ch. 9 - Prob. 13FC Ch. 9 - Prob. 16FC Ch. 9 - Prob. 17FC Ch. 9 - Prob. 18FC Ch. 9 - Prob. 1P Ch. 9 - Prob. 2P Ch. 9 - Prob. 3P Ch. 9 - Prob. 4P Ch. 9 - Prob. 5P Ch. 9 - Prob. 6P Ch. 9 - Prob. 7P Ch. 9 - Prob. 8P Ch. 9 - Prob. 9P Ch. 9 - **10. A rotational axis is directed perpendicular...Ch. 9 - Prob. 11P Ch. 9 - 12. The drawing shows a person (weight, W = 584 N)...Ch. 9 - Prob. 13P Ch. 9 - Prob. 14P Ch. 9 - Prob. 15P Ch. 9 - Prob. 16P Ch. 9 - 17. Review Multiple-Concept Example 8 before...Ch. 9 - 19. Review Conceptual Example 7 as background...Ch. 9 - Prob. 21P Ch. 9 - 22. A man holds a 178-N ball in his hand, with the...Ch. 9 - Prob. 23P Ch. 9 - Prob. 24P Ch. 9 - *25. A 1220-N uniform beam is attached to a...Ch. 9 - *26. A person is sitting with one leg outstretched...Ch. 9 - Prob. 27P Ch. 9 - **28. A man drags a 72-kg crate across the floor...Ch. 9 - Prob. 30P Ch. 9 - Prob. 31P Ch. 9 - 32. A clay vase on a potter’s wheel experiences an...Ch. 9 - Prob. 33P Ch. 9 - Prob. 34P Ch. 9 - Prob. 35P Ch. 9 - Prob. 36P Ch. 9 - Prob. 37P Ch. 9 - Prob. 40P Ch. 9 - *42. A 15.0-m length of hose is wound around a...Ch. 9 - Prob. 43P Ch. 9 - Prob. 44P Ch. 9 - *45. A stationary bicycle is raised off the...Ch. 9 - Prob. 46P Ch. 9 - Prob. 47P Ch. 9 - Prob. 48P Ch. 9 - Prob. 49P Ch. 9 - Prob. 50P Ch. 9 - Prob. 51P Ch. 9 - Prob. 52P Ch. 9 - Prob. 53P Ch. 9 - Prob. 54P Ch. 9 - Prob. 55P Ch. 9 - Prob. 57P Ch. 9 - Prob. 58P Ch. 9 - Prob. 59P Ch. 9 - Prob. 60P Ch. 9 - Prob. 61P Ch. 9 - Prob. 63P Ch. 9 - Prob. 64P Ch. 9 - Prob. 66P Ch. 9 - Prob. 67P Ch. 9 - Prob. 69AP Ch. 9 - Prob. 70AP Ch. 9 - Prob. 71AP Ch. 9 - Prob. 72AP Ch. 9 - 73. A rotating door is made from four rectangular...Ch. 9 - Prob. 74AP Ch. 9 - Prob. 75AP Ch. 9 - Prob. 76AP Ch. 9 - Prob. 84TP Ch. 9 - Prob. 85TP

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