Estimate the force a person must exert on a string attached to a 0.200 kg ball to make the ball revolve in a circle when the length of the string is 0.600 m. The ball makes 1.40 revolutions per second. Do not ignore the weight of the ball. In particular, find the magnitude of FT, and the angle phi 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
Angle = ? degrees
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MY WORK:
FTy = Fg = (9.8)(.2) = 1.96 N
v = 2 rps * 2π(0.6) = 1.68π m/s
FTx = Fc = (mv^2)/r
FTx = [(.2)(1.68π)^2]/(0.6)
FTx = 9.28532 N
FT^2 = FTx^2 + FTy^2
FT = root(90.0587675)
FT = 9.4899 [FINAL ANSWER]
FTy = FTsin(angle)
sin^-1(1.96)/(9.4899) = angle
Angle = 11.9 degrees [FINAL ANSWER]
...so, what exactly am I doing wrong? The Webassign grader told me both were incorrect, but I've worked this over a million times and it's always come out the same.
1 answer
Where is the 90.06 coming from?