[Ans. 174.3 r.p.m. ; 8.5 r.p.m.] In a Porter governor, the upper and lower arms are each \( 250 \mathrm{~mm} \) long and are pivoted on the axis of rotation. The mass of each rotating ball is \( 3 \mathrm{~kg} \) and the mass of the sleeve is \( 20 \mathrm{~kg} \). The sleeve is in its lowest position when the arms are inclined at \( 30^{\circ} \) to the governor axis. The lift of the sleeve is \( 36 \mathrm{~mm} \). Find the force of friction at the sleeve, if the speed at the moment it rises from the lowest position is equal to the speed at the moment it falls from the highest position. Also, find the range of speed of the governor.
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