Question

In a Hartnell governor, the mass of each ball is 2.5 kg. The maximum and minimum centrifugal forces on the balls arc 2000 N and 100 N correspondings to radii 20 cm and 15 cm respectively. The lengths of vertical and horizontal arms of the bell-crank levers are the same, then what is the spring stiffness in N/cm?
1. 100
2. 200
3. 400
4. 800

Answer 1

Correct Answer - Option 4 : 800

Concept:

Spring stiffness (K) for a Hartnell governor is,

\(K = 2{\left( {\frac{a}{b}} \right)^2}\left( {\frac{{{F_2} - {F_1}}}{{{r_2} - {r_1}}}} \right)\)

Calculation:

Given, For a Hartnell governor,

Mass of each ball (m) = 2.5 kg

Maximum centrifugal force (F2) = 2000 N

Minimum centrifugal force (f1) = 100 N

Max. Radius of ball (r2) = 20 cm

Min. radius of ball (r1) = 15 cm and

Lengths of vertical and horizontal arms of the bell-crank levers are the same i.e., a = b

Spring stiffness (k) for a Hartnell governor is,

\(k = 2{\left( {\frac{a}{b}} \right)^2}\left( {\frac{{{F_2} - {F_1}}}{{{r_2} - {r_1}}}} \right)\)

\(k = 2{\left( 1 \right)^2}\left( {\frac{{2000 - 100}}{{20 - 15}}} \right)\)

∴ K = 760 N/cm

Nearest option is 800 N/cm