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A small ball of mass 61 g is suspended from a string of length 62 cm...

A small ball of mass 61 g is suspended from a string of length 62 cm and whirled in a circle lying in the horizontal plane. If the string makes an angle of 25◦ with the vertical, find the centripetal force experienced by the ball. The acceleration of gravity is 9.8 m/s 2 . Answer in units of N

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Answer #1

Gravitational acceleration = g = 9.8 m/s2

Mass of the ball = m = 61 g = 0.061 kg

Length of the string = L = 62 cm = 0.62 m

Angle the string makes with the vertical = = 25o

Tension in the string = F

From the free body diagram the vertical component of the tension supports the weight of the ball and the horizontal component of tension provides the necessary centripetal force for the ball's circular motion.

FCos = mg

FCos(25) = (0.061)(9.8)

F = 0.66 N

Centripetal force experienced by the ball = Fc

Fc = FSin

Fc = (0.66)Sin(25)

Fc = 0.279 N

Centripetal force experienced by the ball = 0.279 N

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