**Problem 4:**A 3-kg ball is attached to a rope connected to the center of a table and initially traveling in a circle of constant radius 4 m with a speed of 3 m/s. The rope is then pulled inward through a hole in the center of the table with a constant speed of 1 m/s. Determine the ball's velocity and speed at the instant that its distance from the center of the table is 2 m. Also calculate the amount of work done by the rope. Neglect friction.**Diagram Explanation:**The diagram shows a top view of a table with a ball attached to a rope. The ball is moving in a circular path around the center of the table. The rope is shown passing through a hole in the center of the table as it is being pulled inward, reducing the radius of the circle.

Given: The mass of the ball: →m=3 Kg Initial radius→R1=4 m final radius→R2=2 m Initial speed→V1=3m/s…

Answered: 4. A 3-kg ball is attached to a rope…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

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**Problem 4:**

A 3-kg ball is attached to a rope connected to the center of a table and initially traveling in a circle of constant radius 4 m with a speed of 3 m/s. The rope is then pulled inward through a hole in the center of the table with a constant speed of 1 m/s. Determine the ball's velocity and speed at the instant that its distance from the center of the table is 2 m. Also calculate the amount of work done by the rope. Neglect friction.

**Diagram Explanation:**

The diagram shows a top view of a table with a ball attached to a rope. The ball is moving in a circular path around the center of the table. The rope is shown passing through a hole in the center of the table as it is being pulled inward, reducing the radius of the circle.

Expert Solution

Step 1

Given:

The mass of the ball:

$\to m = 3 K g$

Initial radius $\to R_{1} = 4 m$

final radius $\to R_{2} = 2 m$

Initial speed $\to V_{1} = 3 m / s$

Rope velocity $\to V_{R} = 1 m / s$

Because rope velocity is constant so the tension in the rope will be constant and hence the centrifugal force acting on the ball will be constant.

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