A ball of mass M attached to a string of length L moves in a circle in a vertica

Question

A ball of mass M attached to a string of length L moves in a circle in a vertical plane as shown above. At the top of the circular path, the tension in the string is twice the weight of the ball. At the bottom, the ball just clears the ground. Air resistance is negligible. Express all answers in terms of M, L and g. Determine the magnitude and direction of the net force on the ball when it is at the top. Determine the speed v_o of the ball at the top. The string is then cut when the ball is at the top. Determine the time it takes the ball to reach the ground. Determine the horizontal distance the ball travels before hitting the ground.

Explanation / Answer

a) T_top = 2*M*g

b) Fnet = T_top + m*g

m*a_rad = 2*m*g + m*g

m*vo^2/L = 3*m*g

==> vo = sqrt(3*g/L)

C) HERE, h = 2*L

let t is the time taken.

apply, h = 0.5*g*t^2

==> t = sqrt(2*h/g)

= sqrt(2*2*L/g)

= 2*sqrt(L/g)

d) horizontal distance traveled, x = vo*t

= sqrt(3*g/L)*2*sqrt(L/g)

= 3.46 m/s

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