Engineering Dynamics need help with 4,5,6,7A ball of mass m is moving along a vertical semi-cylinder of radius R as it is guided by the arm OA. The arm moves in a clockwise direction with a constant angular velocity ω. Assume 0° ≤ Φ ≤ 90°.Neglect any friction. Neglect also the size of the ball and the thickness of the arm.Find the relationship between r, R and θ where r is the distance between O and the ball.Draw a free body diagram of the ball assuming that it is in contact with the cylinder and the arm OA.Write the equations of motion in the (r, θ) coordinate system.Find the normal force acting on the ball by the cylinder for Φ = Φ0.Find the normal force acting on the ball by the bar for Φ = Φ0.Determine the angle Φ at which the ball loses contact with the cylinder.Take m = 1 kg, R = 1.4 m, ω = 0.5 rad/s, and Φ = 60° R

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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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Engineering Dynamics need help with 4,5,6,7

A ball of mass m is moving along a vertical semi-cylinder of radius R as it is guided by the arm OA. The arm moves in a clockwise direction with a constant angular velocity ω. Assume 0° ≤ Φ ≤ 90°.

Neglect any friction. Neglect also the size of the ball and the thickness of the arm.

Find the relationship between r, R and θ where r is the distance between O and the ball.
Draw a free body diagram of the ball assuming that it is in contact with the cylinder and the arm OA.
Write the equations of motion in the (r, θ) coordinate system.
Find the normal force acting on the ball by the cylinder for Φ = Φ₀.
Find the normal force acting on the ball by the bar for Φ = Φ₀.
Determine the angle Φ at which the ball loses contact with the cylinder.
Take m = 1 kg, R = 1.4 m, ω = 0.5 rad/s, and Φ = 60°

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