Find the Speed of the governor:

In a Hartung governor the mass of each of the ball is equal to 5 kg and the stiffness of the spring that is with each of ball is 20 N/cm. The sleeve arm is equal to 15 cm and ball arm is 13.5 cm. The compression in each of spring while ball arm is vertical is  equal to 6.25 cm. The load at the sleeve is 210 N. Find the following:

 (1) Speed of the governor for ball arm in vertical position, and

 (2) The speed for sleeve tending to move up if friction at the sleeve is 20 N.

Solution

Mass of each ball 'm' = 5 kg

Stiffness of spring = 120 N/cm

Load at sleeve = 210 N

By Compression in the Spring

P = 120 × 6.25 = 750 N

 (1)       Taking moment about pivot 0

 (F _C - 750) × 13.5 = (210/2) × 15

∴          F_C   = 750 + 105 × (15/13.5) = 866.7 N

Or        N = 324.6 rpm

 (b)       The friction at the sleeve = 20 N

Or        N′ = 326.7