Physics: Circular Motion?

Question

A 0.75-kg ball is attached to a 1.0-m rope and whirled in a vertical circle. The rope will break when the tension exceeds 450 N. What is the maximum speed the ball can have at the bottom of the circle without breaking the rope?

Answer 1

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Maximum force at the bottom is weight+centrifugal force

F = mg + mv^2/R = m (g + v^2/R)

radius of path R is equal to length of rope

extract v

F/m = g + v^2/R

v^2/R = F/m - g

v^2 = R (F/m - g)

v = sqrt(R (F/m - g))

v = sqrt(1* (450/0.75 - 9.8)) = 24.29 m/s