A ball of mass m is tied to a string and is rotating in a vertical plane. The st

Question

A ball of mass m is tied to a string and is rotating in a vertical plane. The string is elastic (it stretches), which causes the path to be elongated vertically rather than perfectly circular. At the top of the path, the speed has the minimum value that still allows the ball to complete its circular path. Find: the length of the string when it makes an angle with respect to the horizontal. The following quantities are known: Mass of the ball , m Elastic constant of the string, k Length of the string when the ball is at the top , r0 and angle .

Explanation / Answer

the direction of the restoring force is towards center of the circle

then reslving this restoring force F into two components

one is vertical component and other is horizontal component

balancing the vertical components

F*sin(theta) = m*g

K*x = m*g/sin()

elongation x = (m*g)/(K*sin())

length of the string is L = ro+x = ro + (mg)/(K*sin())

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