Question

A 5.39-kg ball hangs from the top of a vertical pole by a 2.45-m-long string. The ball is struck, causing it to revolve around the pole at a speed of 4.79 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.

What is the tension of the string?

Answer 1

radius of horizontal circle r = L*sintheta

In equilibrium net force = 0

along horzontal

Fnet = 0

T*sintheta - Fc = 0

T*sintheta = Fc

T*sintheta = m*v^2/r ....(1)

along vertical

Fnet = 0

T*costheta - m*g = 0

T*costheta = m*g,..............(2)

from 1 and 2

tantheta = v^2/(r*g)

tantheta = 4.79^2/(2.45*sintheta*9.81)

theta = 50.9 degrees = 51 degrees ( 2 significant figures)

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tension T = mg/costheta = (5.39*9.81)/cos51 = 84 N