3. A ball of mass m is attached to a string of length l. The string is tied to a support and the ball is free to swing. The ball is released from rest when the string is horizontal. a) How fast is the ball moving at the lowest point in its path? b) How fast is the ball moving when the string makes an angle of 30 degrees with the vertical? c) Calculate the tension on the string in each of the cases described above
   

 

 

 

 

the law of cnoservation is at work here.
E total at 9 o'clock = E total 6 o'clock
     Again, the law of cnoservation is at work here. The energy inventory shows in line 3. Theta is the angle made by the string with the vertical.
   

 When the ball is in the vertical position, two colinear forces act on it---T- the tension caused by the rope and mg.

For applications such as Tarzan swinging from a vine, if he starts his swing when he is level with the point of attachment, his arms will be expected to supply 3 mg at his lowest point
     The tension on the string is zero at 9 o'clock and T = 3mg at six o'clock. Between those two points, T is something in between and regulated by theta.