MEASURING FORCES AXD WEAK IX SWITCIIIXG APPARATUS 



491 



.?, 0.06 



70 2 

 < 



5 

 20 3 



X 



,0< 



40 50 60 70 80 

 STATIC FORCE IN GRAMS 



90 100 110 120 



Fig. 15 — Maximum total motion for no gross slide plotted against normal force. 

 Low curve shows maximum tangential force. 



From the Hertz theory of contaets, " the radius of contact a between 



I\V() spheres is e(itial to 



y\^-^~-'-^) 



(13) 



where r is the radius of the spheres, iV the normal force, mi and cri the 

 shear elastic constant and Poisson's ratio for one sphere and )U2 and a-i 

 the same quantities for the second sphere. If now a tangential force T 

 is applied to one of the spheres directed in the form of a couple, elastic 

 theory shows that the tangential traction is everywhere parallel to the 

 du-ection of the applied force and contours of constant tangential trac- 

 tion are concentric circles. The magnitude of the traction as shown by 

 Fig. 16 rises from one half the average at the center to infinity at the 

 edge of the circle of contact. The displacement of the circle of contact 

 of one sphere with respect to its center is 



8/za 



(14) 



whei'e a is the radius of the contact area which is given in terms of the 

 normal force by Equation (13). 



A feature of this solution that requires further study is the infinite 

 traction at the edge of the circle of contact. Presumably the tangential 

 component of traction cannot exceed the product of the coefficient of 

 friction / and the normal component of traction p, which from tlic Hertz 



