A point mass whirls around in a vertical circle at the end of a string. Assuming

Question

A point mass whirls around in a vertical circle at the end of a string. Assuming that there is no air resistance, show that the tension in the string at the bottom of the swing is greater than the tension in the string at the top of the swing by 6 times the gravitational force acting on the mass.
Please show work clearly
A point mass whirls around in a vertical circle at the end of a string. Assuming that there is no air resistance, show that the tension in the string at the bottom of the swing is greater than the tension in the string at the top of the swing by 6 times the gravitational force acting on the mass.
Please show work clearly

Explanation / Answer

at bottom point

T1-mg =mv1^(2)/r (1)

at top mg+T2=mv2^(2)/r (2)

energy conservation v1^(2)=v2^(2)+4gr (3)

(2)-(1) using (3)

T2-T1+2mg=-4mg

T2-T1=6mg

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