I can not seem to get this question right. How is it not coming out to 4.16 revo

Question

I can not seem to get this question right. How is it not coming out to 4.16 revolutions until the object breaks?
My calculated values are 8.33 rads, 2.464 m/s^2, and 4.0568 seconds

Problem 8.62 Part A A 600 g steel block rotates on a steel table while attached to a 1.20 m -long hollow tube. Compressed air fed through the tube and ejected from a nozzle on the back of the block exerts a thrust force of 5.01 N perpendicular to the tube. The maximum tension the tube can withstand without breaking is 50.0 N. Assume the coefficient of kinetic friction between steel block and steel table is 0.60. (Figure 1) f the block starts from rest, how many revolutions does it make before the tube breaks? 4 Submit My Answers Give Up Incorrect, Try Again; 3 attempts remaining Provide Feedback Continue Figure 1 of 1 Air 1.2 m Tube Pivot

Explanation / Answer

m = 600 g = 0.6 kg

r = 1.2 m

F1 = 5.01 N

Fb = 50 N

k = 0.6

Now

Net F = F1 - µmg = 5.01 - 0.6*0.6*9.8 = 1.482 N

a = Fn/m = 1.482/0.6 = 2.47 m/s^2

= a/r = 2.47/1.2 = 2.06 rad/sec²

Breaking force = Fb = 50 = mr² where ² = 2

50/(2mr) = = 16.86 radians = 2.68 rev

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