A 5.11-kg ball hangs from the top of a vertical pole by a 2.33-m-long string. The...

A 5.11-kg ball hangs from the top of a vertical pole by a 2.33-m-long string. The ball is struck, causing it to revolve around the pole at a speed of 4.47 m/s in a horizontal circle with the string remaining taut. Calculate the angle, between 0° and 90°, that the string makes with the pole. Take g = 9.81 m/s2.

Expert Solution

consider the force diagram along the vertical direction, force equation is given as

T Cos = mg eq-1

r = radius of circle = L Sin

consider the force diagram along the horizontal direction, force equation is given as

T Sin = mv²/r eq-2

dividing eq-2 by eq-1

tan = v²/(rg)

tan = v²/(L Sin g)

Sin²/Cos = 4.47²/(2.33 x 9.8)

(1 - Cos²)/Cos = 0.88

Cos = 0.65

= 49.5

genius_generous answered 2 years ago

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