A 0.2 kg ball that is attached to a light string swings in a vertical circle of

Question

A 0.2 kg ball that is attached to a light string swings in a vertical circle of radius 50cm. The speed of the ball is 3 m/s at the instant when the angle of the ball is 60 from the horizontal radial line when the ball moves upward, as shown. The maximum (limiting) tension before the string breaks is 12N. At this given angular position of the ball:
a) Find the tension in string at this position;
b) Find the magnitude of the total acceleration of the ball?
c) what is the maximum speed of this ball before the string breaks ?

Explanation / Answer

1)t=Fc+ mgsin60 =0.2*3^2/0.5 +0.2*9.8sin60= 5.3 N b)a=v^2/r=18m/s^2 c) t=Fc+ mgsin60 thus for t=12=0.2*v^2/0.5 +1.7 thus v= 5.074 m/s is the maximum speed before it breaks

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