A 2.0 kg ball is attached to a vertical post with two strings, one 2.0 m long an

Question

A 2.0 kg ball is attached to a vertical post with two strings, one 2.0 m long and the other 1.0 m long as shown in the figure. If the ball is set whirling in a horizontal circle, what is the minimum speed necessary for the lower string to be taught? If the ball has a constant speed of 6 ms-1, find the tension on each string.

A 2.0 kg ball is attached to a vertical post with two strings, one 2.0 m long and the other 1.0 m long as shown in the figure. If the ball is set whirling in a horizontal circle, what is the minimum speed necessary for the lower string to be taught? If the ball has a constant speed of 6 ms-1, find the tension on each string.

Explanation / Answer

a)The tension in the vertical string be T1 and that in the lower string be T2.

Let be angle with vertical.

T1Cos=mg

T1=mg/Cos=2*9.8/Cos30=22.63N

Balancing horizontal forces,

mv2/r-T2=T1Sin

Putting T2=0 for minimum v,

v=sqrt(T1rSin/m)=2.38m/s

b)If v=6m/s

T2=mv2/r-T1Sin=60.68N

T1=22.63N

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