Tennis Ball A tennis ball connected to a string is spun around in a vertical, ci

Question

Tennis Ball 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 " 5.11 m/s. The circular path has a radius of R 1 m 1) What is the magnitude of the tension in the string when the ball is at the bottom of the circle? N Submit 2) What is the magnitude of the tension in the string when the ball is at the side of the circle? N Submit 3) What is the magnitude of the tension in the string when the ball is at the top of the circle? N t Submit 4) What is the minimum velocity so the string will not go slack as the ball moves around the circle? s Submit

Explanation / Answer

1) T - mg = mv^2/r

T = m(v^2/r + g)

= 0.153*(5.11^2/1 + 9.8)

= 5.5 N

2) T = mv^2/r = 0.153*5.11^2/1 = 4 N

3) T + mg = mv^2/r

T = m(v^2/r - g)

= 0.153*(5.11^2/1 - 9.8)

= 2.5 N

4) This occurs when Tension is 0 N at the top
mg = mv^2/r
v = sqrt(gr) = sqrt(9.8*1) = 3.13 m/s

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