Answered: A 4-kg sphere rests on the smooth…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Question

A 4-kg sphere rests on the smooth parabolic surface.

Determine the normal force the ball A exerts on the surface.

Determine the mass mB of block B needed to hold the ball A in the equilibrium position shown.

Expert Solution

Step 1

Introduction

Using the static equilibrium equation, we will calculate the normal force exerted by ball A on the surface and the mass of block B required to keep ball A in the equilibrium position. Initially, we will analyze the net horizontal and net vertical forces, and then we will compute the mass, ball, and normal force by inserting the known values.

Given data:

$\begin{array}{rcl} the mass of the sphere (m) & = & 4 kg \\ the parabolic curvature (y) & = & 2.5 x^{2} \\ height of the ball A from datum (h) & = & 0.4 m \\ the angle of inclination of the ball A (θ) & = & 60 ° \end{array}$

Determine:

The normal force the ball A exerts on the surface ${(F)}_{A}$

The mass of block B needed to hold ball A in the equilibrium position ${(m)}_{B}$

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