(a) Explanation Given information: The weight of sphere ( W ) is 2 lb. The radius of sphere ( r ) is 3 ft. The friction is negligible. Calculation: Sketch the free body diagram and kinetic diagram of dish as shown in Figure (1). Refer Figure (1). Find the angle ( θ ) making normal force, N to vertical axis using given equation of parabola: y = r 2 6 (1) Here, y is the variation of depth of parabola. Differentiate Equation (1) with respect to x . d y d x = 2 r 6 = r 3 Here, d y d x is the slope of parabola. Substitute tan θ for d y d x and 3 ft for r . tan θ = 3 3 θ = 45 ° Write the general equation of acceleration ( a n ) of dish in rotation a n = v 2 r Apply Newton’s law of equation along y -axis. Σ F y = 0 N cos θ − W = 0 N = W cos θ (2) Apply Newton’s law of equation along n -axis (b) To determine Find the magnitude of the normal force exerted by the sphere on the inclined surface of the dish.

Vector Mechanics for Engineers: Statics and Dynamics

12th Edition

ISBN: 9781259638091

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

Publisher: McGraw-Hill Education

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Chapter 12.1, Problem 12.41P

(a)

To determine

Find the velocity (v) of the sphere.

(b)

To determine

Find the magnitude of the normal force exerted by the sphere on the inclined surface of the dish.

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Chapter 12.1, Problem 12.39P

Chapter 12.1, Problem 12.42P

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Vector Mechanics for Engineers: Statics and Dynamics

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Find the velocity ( v ) of the sphere.

Solution Summary: The author illustrates how Newton's law of equations is applied along y -axis.