Explanation Given: Weight of sphere is 2 lb . Radius of dish is r = 3 ft . Concept used: Write the equation of parabola. y = r 2 6 ...... (1) Here, y is the vertical distance from origin and r is the radius of parabolic dish. Differentiate equation (1). d y d r = r 3 ...... (2) Here, d y d r is the slope of equation of parabola. Write the expression for the slope of parabola. tan θ = d y d r Substitute r 3 for d y d r in above expression. tan θ = r 3 ...... (3) Here, θ is the angle of sphere from horizontal. Draw the free body diagram of sphere. Write the expression for summation of forces in horizontal direction. ∑ F H = m v 2 r − N cos θ Substitute W g for m in above expression. ∑ F H = W v 2 r g − N cos θ ...... (4) Here, ∑ F H is the net force in horizontal direction, m is the mass of sphere, W is the weight of sphere, g is the acceleration due to gravity and N is the normal reaction of a sphere from a dish. Write the expression for summation of forces in vertical direction. ∑ F V = N sin θ − m g To determine (b) Magnitude of normal force.

12th Edition

ISBN: 9781260265521

Author: BEER

Publisher: MCG

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Chapter 12.1, Problem 12.41P

To determine

(a)

Velocity of sphere.

To determine

(b)

Magnitude of normal force.

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Chapter 12.1, Problem 12.40P

Chapter 12.1, Problem 12.42P

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(a) Velocity of sphere.

Solution Summary: The author explains the velocity of sphere, the radius of the parabolic dish, and the equation of parabola.