A ball whirls around in a vertical circle at the end of a string. The other end

Question

A ball whirls around in a vertical circle at the end of a string. The other end of the string is fixed at the center of the circle. Assume that the total energy of the ball-Earth system remains constant.     (a) What is the tension in the string at the bottom? (Use the following as necessary: m for mass of the ball, g for gravitational acceleration, vb for velocity at the bottom, and R for radius of the circle.)
    Tb =                         
    
    (b) What is the tension in the string at the top? (Use the following as necessary: m, g, vt for velocity at the top, and R.)
    Tt =                         
    
    (c) How much greater is the tension at the bottom? (Use the following as necessary: m, g.)
    Tb = Tt +               

Explanation / Answer

a)

Tb = m*g+m*Vb^2/R

b)

Tt = m*(Vb^2-4*g*R)/R - mg = m*Vb^2/R -5mg

c)

Tb = Tt + 6mg

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