A Hartnell governor has two rotating balls, of mass 2.7 kg each. The ball radius is 125 mm in the mean position when the ball arms are vertical and the speed is 150 r. p.m. with the sleeve rising. The length of the ball arms is 140 mm and the

length of the sleeve arms 90 mm. The stiffness of the spring is 7 kN/m and the total sleeve movement is 12 mm from the

mean position. Allowing for a constant friction force of 14 N acting at the sleeve, determine the speed range of the

governor in the lowest and highest sleeve positions. Neglect the obliquity of the ball arms​