A small ball is attached to a string of length L which hangs from the ceiling. A

Question

A small ball is attached to a string of length L which hangs from the ceiling. A very thin peg sticks out, at a distance of 2/3 L straight below where the string hangs from. After the ball is pulled to one side and released, the string hits the peg and wraps around it as the ball keeps swinging, in a new circle with smaller radius. Find the smallest angle ? so that when the ball swings around the peg the string never goes slack (it barely stays tight at the top of the swing).

Can you please make any relevant drawings or diagrams as well? Thank you!! Will give a thumbs up :-)

Explanation / Answer

here,

length of the string is l

let the mass of ball be m

for the stick not to slack

at the top point ,

m*v^2/(l/3) = m * g

v^2 = gl/3

and

using conservation of energy

0.5 * m * v^2 = m * g * ( L - L * cos(theta))

0.5 * g * l/3 = g * l * ( 1- cos(theta))

1- cos(theta) = 0.165

theta = 33.38 degree

the angle theta is 33.38 degree

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