Homework Problem The cord can withstand a maximum tension of 50.0 N. What is the maximum speed of the ball before the A ball of mass 0.500 kg is attached to the end of a cord 1.50 m long. The ball is whirled in a horizontal circle. cord breaks?
Homework Problem The cord can withstand a maximum tension of 50.0 N. What is the maximum speed of the ball before the A ball of mass 0.500 kg is attached to the end of a cord 1.50 m long. The ball is whirled in a horizontal circle. cord breaks?
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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![# Homework Problem
A ball of mass 0.500 kg is attached to the end of a cord 1.50 m long. The ball is whirled in a horizontal circle. The cord can withstand a maximum tension of 50.0 N. What is the maximum speed of the ball before the cord breaks?
## Explanation
In this problem, we are asked to find the maximum speed at which a ball can be whirled in a horizontal circle before the tension in the cord exceeds its maximum limit and breaks. The given parameters are:
- Mass of the ball (m) = 0.500 kg
- Length of the cord (r) = 1.50 m
- Maximum tension the cord can withstand (T) = 50.0 N
### Relevant Formulas
To solve this problem, we can use the formula for the tension in the cord when an object is moving in a circular path, which is given by:
\[ T = \frac{m \cdot v^2}{r} \]
Where:
- \( T \) is the tension in the cord,
- \( m \) is the mass of the ball,
- \( v \) is the velocity of the ball,
- \( r \) is the radius of the circle.
The goal is to find \( v \), the maximum speed of the ball:
\[ v = \sqrt{\frac{T \cdot r}{m}} \]
### Solution
Substituting the given values into the formula:
\[ v = \sqrt{\frac{50.0 \, \text{N} \cdot 1.50 \, \text{m}}{0.500 \, \text{kg}}} \]
Calculate \( v \) to find the maximum speed of the ball.
(Note: The image contains handwritten calculations that seem to follow these steps, but they are not entirely clear due to the quality of the image.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F097e4ba6-b3f3-4468-a4b3-d5ca2a9f0e8d%2Fcd8025c4-4240-4728-8542-aa49fb16743b%2Fbpd99aa.jpeg&w=3840&q=75)
Transcribed Image Text:# Homework Problem
A ball of mass 0.500 kg is attached to the end of a cord 1.50 m long. The ball is whirled in a horizontal circle. The cord can withstand a maximum tension of 50.0 N. What is the maximum speed of the ball before the cord breaks?
## Explanation
In this problem, we are asked to find the maximum speed at which a ball can be whirled in a horizontal circle before the tension in the cord exceeds its maximum limit and breaks. The given parameters are:
- Mass of the ball (m) = 0.500 kg
- Length of the cord (r) = 1.50 m
- Maximum tension the cord can withstand (T) = 50.0 N
### Relevant Formulas
To solve this problem, we can use the formula for the tension in the cord when an object is moving in a circular path, which is given by:
\[ T = \frac{m \cdot v^2}{r} \]
Where:
- \( T \) is the tension in the cord,
- \( m \) is the mass of the ball,
- \( v \) is the velocity of the ball,
- \( r \) is the radius of the circle.
The goal is to find \( v \), the maximum speed of the ball:
\[ v = \sqrt{\frac{T \cdot r}{m}} \]
### Solution
Substituting the given values into the formula:
\[ v = \sqrt{\frac{50.0 \, \text{N} \cdot 1.50 \, \text{m}}{0.500 \, \text{kg}}} \]
Calculate \( v \) to find the maximum speed of the ball.
(Note: The image contains handwritten calculations that seem to follow these steps, but they are not entirely clear due to the quality of the image.)
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