Question

A 1.10-kg ball is tied to a 1.30-m long string is being spun in a vertical circle at a constant speed and with a period of 2.05 s. What is the minimum tension in the string?

Answer 1

Minimum tension in vertical circular motion is at the top most point of motion which is given by:

Using Force balance in vertical direction:

F_net = W + F_T

W = Weight of ball = m*g

F_T = tension in string = ?

F_net = m*ac (from newton's 2nd law)

ac = Centripetal acceleration = V^2/R = w^2*R

w = angular speed = 2*pi/T = 2*pi/2.05 = 3.065 rad/sec

T = time period = 2.05 sec

R = radius of circular motion = 1.30 m

So,

m*w^2*R = m*g + F_T

F_T = m*w^2*R - m*g

F_T = 1.10*3.065^2*1.30 - 1.10*9.81

F_T = 2.64 N = minimum tension in string

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