The ball has a mass m and is attached to of length 1. The cord is tied at the top to a swivel an is given a velocity vo. Show that the angle which makes with the vertical as the ball travels ar
The ball has a mass m and is attached to of length 1. The cord is tied at the top to a swivel an is given a velocity vo. Show that the angle which makes with the vertical as the ball travels ar
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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![The problem involves a ball with a mass \( m \) attached to a cord of length \( l \). The cord is secured at the top to a swivel, allowing the ball to move with an initial velocity \( v_0 \). The objective is to demonstrate that the angle \( \theta \), which the cord forms with the vertical as the ball follows a circular path, satisfies the equation:
\[
\tan \theta \sin \theta = \frac{{v_0}^2}{gl}
\]
The scenario disregards air resistance and the size of the ball.
**Diagram Explanation:**
The accompanying diagram illustrates the ball at the end of the cord. The cord is shown as a line extending from the swivel point \( O \) (at the top) to the ball, which is moving in a horizontal circular path. The angle \( \theta \) between the vertical line and the cord is depicted. The circle at the bottom represents the path of the ball's travel, with a velocity vector \( v_0 \) indicating the direction of the ball's motion.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9fbf329d-7944-4f84-8902-b0b326aaed6b%2Faa19c9ab-187f-4405-8826-b0e5fd8807a3%2F42ofmxq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The problem involves a ball with a mass \( m \) attached to a cord of length \( l \). The cord is secured at the top to a swivel, allowing the ball to move with an initial velocity \( v_0 \). The objective is to demonstrate that the angle \( \theta \), which the cord forms with the vertical as the ball follows a circular path, satisfies the equation:
\[
\tan \theta \sin \theta = \frac{{v_0}^2}{gl}
\]
The scenario disregards air resistance and the size of the ball.
**Diagram Explanation:**
The accompanying diagram illustrates the ball at the end of the cord. The cord is shown as a line extending from the swivel point \( O \) (at the top) to the ball, which is moving in a horizontal circular path. The angle \( \theta \) between the vertical line and the cord is depicted. The circle at the bottom represents the path of the ball's travel, with a velocity vector \( v_0 \) indicating the direction of the ball's motion.
Expert Solution
Step 1
Given data as per question
m=Mass of ball
l=length of cord
vo =velocity of ball
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