Gravity and Rotation?

Question

A ball on the end of a string is revolved at a uniform rate in a vertical circle of radius 60.0 cm, as shown in Fig. 5-33. Its speed is 4.10 m/s and its mass is 0.300 kg.

a) Calculate the tension in the string when the ball is at the top of its path.
Answer in Newtons.
(b) Calculate the tension in the string when the ball is at the bottom of its path.
Answer in Newtons.

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Answer 1

a = v^2/r = 4.10^2 / 0.600 = 28.0 m/s^2 towards the centre.
At the top of its path, the net aceleration is 28.0 m/s^2 downwards, so F_string = m(28.0 - 9.8) = 0.300(18.2) = 5.46 N.
At the bottom of the path, the net acceleration is 28.0 m/s^2 upwards, so F_string = 0.300(28.0 + 9.8) = 11.3 N.