A tennis ball connected to a string is spun around in a vertical, circular path

Question

A tennis ball connected to a string is spun around in a vertical, circular path at a uniform speed. The ball has a mass m = 0.153 kg and moves at v = 5.08 m/s. The circular path has a radius of R = 0.99 m

1)

What is the magnitude of the tension in the string when the ball is at the bottom of the circle?

N

2)

What is the magnitude of the tension in the string when the ball is at the side of the circle?

N

3)

What is the magnitude of the tension in the string when the ball is at the top of the circle?

N

4)

What is the minimum velocity so the string will not go slack as the ball moves around the circle?

m/s

(Survey Question)

5)

Below is some space to write notes on this problem

Explanation / Answer

1) T - mg = mv^2/r
T = m(v^2/r + g)
T = 0.153(5.08^2/0.99+9.8) = 5.49 N

2) T = mv^2/r = 3.99 N

3) T + mg = mv^2/r
T = m(v^2/r - g) = 0.153(5.08^2/0.99-9.8) = 2.49 N

d) if T = 0

mv^2/r = mg

v = sqrt(rg) = 3.1 m/s

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