(a) The maximum speed of the ball is approximately .
(b) The minimum period of the ball is approximately .
To solve this problem, we’ll first use the relationship between centripetal force, mass, velocity, and radius. The centripetal force required to keep an object of mass moving in a circle of radius with a speed is given by:
Given:
We need to determine the maximum speed at which the cord can hold the ball without breaking. Using the centripetal force formula:
Solving for :
The period is the time it takes for the ball to make one complete revolution around the circle. The relationship between the speed , the period , and the radius of the circle is given by:
Solving for the period :
Using the maximum speed :
This chatbot (Alphonsio) provides automated responses generated by machine-learning algorithms and relies on the accuracy of the underlying language models. While this Chatbot is programmed to provide accurate and relevant information, its information may not always be exhaustive, accurate, up-to-date or tailored to individual circumstances. It is not a substitute for professional advice or consultation with qualified experts. This chatbots and its responses are intended for informational purposes only and should not be used for commercial or business purposes. The creators of this chatbot are not liable for any damages or losses incurred as a result of using the information provided. By using our website, you acknowledge and agree to these terms. The data you submit to this chatbot is used to improve our algorithms. Under no circumstances should you submit sensitive data such as, but not limited to, personal data or passwords. The data you submit could then be made public.