A curious child finds a rope hanging vertically from the ceiling of a large storage hangar. The child grabs the rope and starts running in a circle. The length of the rope is 13.0m. When the child runs in a circle of radius 7.0m, the child is about to lose contact with the floor. How fast is the child running at that time?

Question

v= ?

I know I have to apply the centripetal acceleration, but I don't know where to go about with the distance

Answer 1

the horizontal component of the tension in the rope supplies the centripetal force that keeps the child moving in the circle
... m v^2 / r = T * (7 / 13)

the vertical component of the tension is equal to the child's weight
... m g = T [√(13^2 - 7^2) / 13]

Answer 2

Is the final answer 0.82 m/s

Answer 3

Nevermind, I got 6.6m/s