Final answer:
This high school physics question asks about the conditions required for a ball swinging in a vertical circle to complete its path around a peg, and about calculating the tension in the string at various points during its motion.
Step-by-step explanation:
The question involves a ball being swung in a vertical circle at the end of a string that remains taut. From the description, this is a physics problem dealing with concepts such as gravitational potential energy, centripetal force, and tension in the string.
To ensure the ball swings around the peg, the initial height must be greater than 3a/5. This height requirement is derived from considering the conversion of gravitational potential energy to kinetic energy necessary to overcome the weight of the ball at the top of the swing. At the bottom of the circle, the tension is greatest because it must support the weight of the ball and provide the centripetal force for circular motion. The tension at different points in the circle can be found using formulas involving the mass of the ball, gravitational acceleration, and the ball's velocity.
For a freely swinging pendulum, the energy conservation principle applies – the potential energy at the height A converts into kinetic energy at the lowest point B. If friction and string mass are negligible, the mechanical energy of the pendulum system remains constant throughout the swing. Understanding these principles helps us solve problems related to circular motion and oscillations.