A spring-controlled governor has two balls, each of mass 2.3 kg. The mean speed is to be 500 rev/min and the variation 2 per cent. The extreme radii of the path of the balls are 110 mm and 85 mm. Find the controlling force at the balls in each case. If the effect of friction be 45n N at each ball, find the highest and lowest speeds rising. The length of the ball arms is 140 mm and the length of the sleeve arms is 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 position. Neglect the obliquity of the ball arms.