Estimate the force a person must exert on a string attached to a 0.170 kg ball t

Question

Estimate the force a person must exert on a string attached to a 0.170 kg ball to make the ball revolve in a circle when the length of the string is 0.600 m. The ball makes 1.60 revolutions per second. Do not ignore the weight of the ball. In particular, find the magnitude of FT, and the angle ? it makes with the horizontal. [Hint: Set the horizontal component of FT equal to maR; also, since there is no vertical motion, what can you say about the vertical component of FT?]
FT = ? N
? = ?°

Please include formulas and explanations.

Explanation / Answer

Mass of the ball is attached to the string is m = 0.170 kg Length of the string is r = 0.600m angular velocity of the ball is = 1.60 rev / s                                                   = 1.60 *2 rad /s From Newtons second law F = m a                                                   = m * v ^2 / r                                                  = m r^2                                                  = 0.170 kg * 0.600 m * 1.6 *2                                                = 10.29 N                                             F_g = mg                                                       = 0.170 kg * 9.8                                                       = 1.66N     F _person = (10.29N)^2 + ( 1.66N)^2                       = 10.4 N b )   Angle = tan^-1 ( 1.66 N / 10.29 N)                      = 9.1 degrees

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