Explanation Given information: Mass of the sphere, (m) = 0.6kg. Radius of sphere, (r a ) = 0.5m. Central force, (F) = 80 r 2 N. Velocity of sphere at point A, v a =20m/s. Calculation: Law of conservation of angular momentum between the point A and B. r a m a v a sin 60 o = r m m m v m 0.5 × 0.6 × 20 × sin 60 o = r m × 0.6 × v m v m = 8.66 r m ( 1 ) The kinetic energy at point A, E a = 1 2 m a v a 2 E a = 1 2 × 0.6 × 20 2 E a = 120 J Potential energy at point A, U a = f F d r U a = f 80 r 2 d r U a = − 80 r U a = − 80 0.5 U a = − 160 J The kinetic energy at point B, E b = 1 2 m m v m 2 E b = 1 2 × 0 To determine (b) Maximum and minimum velocity.

Vector Mechanics for Engineers: Dynamics

11th Edition

ISBN: 9780077687342

Author: Ferdinand P. Beer, E. Russell Johnston Jr., Phillip J. Cornwell, Brian Self

Publisher: McGraw-Hill Education

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Chapter 13.2, Problem 13.99P

To determine

(a)

Maximum and minimum distances of point O.

To determine

(b)

Maximum and minimum velocity.

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Chapter 13.2, Problem 13.98P

Chapter 13.2, Problem 13.100P

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(a) Maximum and minimum distances of point O.

Solution Summary: The author calculates the law of conservation of angular momentum between the point A and B.