Thanks a lot. A ball whirls around in a vertical circle at the end of a string.

Question

Thanks a lot.

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. 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, for velocity at the bottom, and R for radius of the circle.) Tb = 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 = 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*vt^2/R - m*g

c) Tb-Tt = 2*m*g + m*vb^2/R - m*vt^2/R

Tb -Tt = 2*m*g + m*vb^2/R - m*vt^2/R

= 2*m*g + (2/R)*(1/2)*m*(vb^2-vt^2)
= 2*m*g + (2/R)*2*m*g*R

Tb = Tt + 3*m*g*


here Tb and tt are opposite direction

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