Part 1
If water does not spill at the top point of the circular motion then for the minimum speed condition we can say normal force will be zero at the top position



given that
R = 1 m
g = 9.8 m/s^2
now from above equation we have

Part b)
for minimum value of angular speed we will have



The work done to pull the sister back on the swing is equal to the increase in potential energy of the sister:

(1)
where m is the sister's mass, g is the gravitational acceleration and

is the increase in altitude of the sister with respect to its initial position.
By calling

the angle of the chain with respect to the vertical, the increase in altitude is given by

(2)
where L is the length of the chain.
Putting (2) inside (1), we find

from which we can find the mass of the sister:
I'm sorry but I don't really understand the question. What is the quest actually asking???
Wouldn't everything fall?
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