The figure shows a machine for throwing spheres through a gutter, which consists of a cam with a radial flat-sided follower, which is held in position by a cantilever leaf spring. When the follower is further to the left, the deflection in the sheet is 3 mm from its straight position, and when it is further to the right, the deflection is 8 mm. As the cam is rotating, the sheet feels a cyclic load with minimum and maximum values. The length "L" of the sheet is 65 mm and the cross section is 6 mm base and 0.8 mm thick. If the sheet is made of AISI 1045 CW steel, determine the Factor of safety based on Soderberg's criteria.

+0 Cam E Follower Bearing (a) Cross section of spring (enlarged) Flat spring Ymax 8.0 mm Ymin 3.0 mm L (b) Ball feed device = =