Answer to Question #81868 in Mechanics | Relativity for taru

Question

In a spring controlled governor the curve of a controlling force is a straight line. When the balls are 400 mm apart the controlling force is 1200 N and when 200 mm apart the controlling force is 450 N. At what speed will the governor run when the balls are 250 mm apart. What initial tension on the spring would be required for isochronism and what would then be the speed. The mass of each ball is 9 kg.

Answer 1

k=ΔF/Δx=(1200-450)/(400-200)=3.75 N/mm.

The tension on the spring:

F=450+3.75(250-200)=637.5 N

F=(mv^2)/r

The speed is

v=√(Fr/m)=√((637.5)(0.25/2)/(2(9)))=2.1 m/s.