Question

The controlling force Fc and radius of rotation of a spring controlled governer is given by the expression, Fc = 2000 r – 76. The mass of the ball is g kg and extreme radii of rotation of the ball are 0.1 m and 0.175 m respectively for maximum and minimum speeds. If the friction on the governor is 5N at each ball find the co-efficient of insensitiveness of the governor at extreme radii.

Answer 1

Given Fc = 2000r – 76, m = 5 kg, r1 = 0.1 m, r2 = 0.175 m, F = 5 N.

(i) Maximum and Minimum speeds of equilibrium without considering friction:

Let N2 and N1 be maximum and minimum speeds of the equilibrium respectively.

The controlling force is given by the expression, Fc = 2000r – 76

Controlling force at the minimum radius of rotation (i.e. at r1= 0.1 m)

Fc1 = 2000 x 0.1 – 76 = 124 N

Controlling force at the maximum radius of rotation (i.e. at r2= 0.175 m)

Fc2 = 2000 x 0.175 – 76 = 274 N

(ii) Maximum and Minimum speeds of equilibrium with considering friction: Let N1’ and N1’’ be minimum and maximum speeds of the governor considering friction at minimum radius of rotation. Frictional force at each ball FB = 5 N

Let N1’ and N1’’ be minimum and maximum speeds of the governor considering friction at minimum radius of rotation.

(iii) Co-efficient of Insensitiveness:

w.k.t Co-efficient of sensitiveness at minimum radius of rotation

Co-efficient of sensitiveness at maximum radius of rotation