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 -0.15 kg and moves at v - 4.89 m/s. The circular path has a radius of R - 0.94 m What is the magnitude of the tension in the string when the ball is at the bottom of the circle? What is the magnitude of the tension in the string when the ball is at the side of the circle? What is the magnitude of the tension in the string when the ball is at the top of the circle? What is the minimum velocity so the string will not go slack as the ball moves around the circle?

Explanation / Answer

Here,

v = 4.89 m/s

R = 0.94 m

mass , m = 0.15 kg

1) at the bottom of the circle

magnitude of tension = m * g + m* v^2/r

magnitude of tension = 0.15 * (9.8 + 4.89^2/0.94)

magnitude of tension = 5.29 N

2)

in the side of the circle

T = m * v^2/r

T = 0.15 * 4.89^2/0.94

T = 3.82 N

the tension is 3.82 N

3)

at the top of the circle

T = m * v^2/r - mg

T = 0.15 * *(4.89^2/.94 - 9.8)

T = 2.345 N

the tension in the cable at the top is 2.345 N

4)

let the velocity is v

for goinf around the circle

0 = m * g - m * v^2/r

9.8 - v^2/0.94 = 0

v = 3.04 m/s

the minimum speed of ball is 3.04 m/s

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