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I was asked the question:

A band brake is installed on a drum rotating at 250rpm and a diameter of 900mm. The angle of contact is 1.5pi radians and one end of the brake band is fasted to a fixed pin while the other end to the brake artm is 150m from the fixed pin. The coefficient of friction is 0.25 and the straight brake arm is 1000mm long and is placed perpendicular to the diameter bisecting the angle of contact. What should be the width in milimeters of a steel band with maximum tensile stress of 55MPa and 3.0mm thick will be used?

Answer is 37mm.

I honestly see no way to solve this without any indication of power or force of some sort... here's my attempt

$${ S_{max} = \frac{F_1}{w\times t} }$$ $${ 55 Mpa = \frac{F_1}{w\times 3.0 mm} }$$

$${ \frac{F_1}{F_2} = e^{(\theta \times friction)} }$$ $${ \frac{F_1}{F_2} = e^{(1.5rad \times 0.25)} }$$

Trying to find F1 seems to be the flaw. There are just no formulas I know of which doesn't require either power, force, torque?

$${ T = F \times d }$$ $${ P = 2\pi T N }$$

Is the problem set flawed? What am I missing? Is there another way?

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