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]
Both of those answers were marked as incorrect by Webassign, but I've worked this problem over dozens of times and it's always the same. Am I doing something wrong?
v = 2 rps * 2π(0.6) = 1.68π m/s
BUT it says 1.4 rps, not 2
Oops, that's a typo. With 1.4, it works out to the 1.68π m/s velocity I use in the next step. Did you see anything else?
Your calculations look correct, so it's possible that there might be a small error or misunderstanding in the problem setup or the calculations. Let's go through the steps to see if we can identify any potential mistakes:
1. Calculate the weight force (Fg) of the ball: Fg = mg = (0.2 kg)(9.8 m/s^2) = 1.96 N. This step is correct.
2. Calculate the linear velocity (v) of the ball: v = 1.40 rev/s * 2π * 0.6 m = 5.28π m/s. This step is correct.
3. Calculate the force in the horizontal direction (FTx) using the centripetal force formula: FTx = Fc = (mv^2)/r = [(0.2 kg)(5.28π m/s)^2]/0.6 m = 87.324 N. This step is correct.
4. Calculate the resultant force (FT) using the Pythagorean theorem: FT^2 = FTx^2 + FTy^2. FT = √(FTx^2 + FTy^2) = √(87.324^2 + 1.96^2) = 87.352 N (rounded to three decimal places). This step is correct.
5. Calculate the angle (phi) using the vertical component of FT: FTy = FT sin(phi). sin^(-1)(FTy / FT) = sin^(-1)(1.96 N / 87.352 N) = 1.275 degrees (rounded to three decimal places). This angle is very small, which suggests that the string is nearly horizontal. Please note that 11.9 degrees, as you mentioned, seems to be a different angle from the overall problem.
Based on these calculations, it seems like your answers were correct. If Webassign marked them as incorrect, double-check if there were any specific rounding or format requirements for the answers that you missed.
If the issue persists, I would recommend reaching out to your instructor or checking the problem statement once again to ensure there are no additional instructions or details that you might have missed.