A ball of mass m is attached to a string of length L. It is swungin a vertical circle with enough speed to keep the string tautthroughout the motion. Assume the ball travels freely in the circlewith negligible loss of mechanical energy. Determine if thefollowing six statements are true or false.
1. The acceleration of the ball at the top of the circle isdirected `up'.
2. The tension in the string at the top of the circle can begreater, equal, or less than the weight of the ball, depending onthe speed of the ball.
3. The magnitude of the difference between the kinetic energy ofthe ball at the top and the bottom of the circle is 2mgL.
4. mvb2/L = Tb+mg, where vb and Tb are the speed of the ball andthe tension of the string at the bottom of the circle.
5. The tension in the string is less at the top of the circle thanat the bottom of the circle.
6. The difference between the tensions at the top and at the bottomof the circle is independent of the speed of the ball.
A ball of mass m is attached to a string of length L. It is swungin a vertical circle with enough speed to keep the string tautthroughout the motion. Assume the ball travels freely in the circlewith negligible loss of mechanical energy. Determine if thefollowing six statements are true or false.
1. The acceleration of the ball at the top of the circle isdirected `up'.
2. The tension in the string at the top of the circle can begreater, equal, or less than the weight of the ball, depending onthe speed of the ball.
3. The magnitude of the difference between the kinetic energy ofthe ball at the top and the bottom of the circle is 2mgL.
4. mvb2/L = Tb+mg, where vb and Tb are the speed of the ball andthe tension of the string at the bottom of the circle.
5. The tension in the string is less at the top of the circle thanat the bottom of the circle.
6. The difference between the tensions at the top and at the bottomof the circle is independent of the speed of the ball.
