MEASURING FORCES AND WKAR IX SWITCHIXG APPARATUS 503 



open circuit voltage will be iiidci)eiicleut of whether the force is applied 

 uniformly over the surface or at a point. This follows from the fact that 

 E-i is independent of .c and // and hence 



Ez\ \ dxdii=-2{Qn-Qn)hA / T.dxdy (37) 



Jo •'O ''0 -^0 



Integrating over the surface gives the total force F for the light side and 

 liencc 



■fT 2(Qii — Qn)S2JiF . . .„„. 



Vz = -^ 1 J — "^ '^^^ units (38) 



1.98 X 10~%F . ,, 

 = J— in volts 



For a ceramic 0.1 cm by 0.1 cm in cross-section and 0.05 cm thick a 

 tangential force of 100 grams should generate a voltage of 9.7 volts. 



REFERENCES 



1. L. Vieth and C. F. Wiebusch, "Recent Developments in Hill and Dale Re- 



corders," J. Soc. Motion Pictures Engrs., Jan., 1938. 



2. W. P. Mason and R. F. Wick, "A Barium Titanate Transducer Capable of 



Large Motion at an Ultrasonic Frequency," J . Acous. Soc. of A., 23, pp. 

 209-214, Mar., 1951. 



3. R. D. Mindlin, W. P. Mason, T. F. Osmer, and H. Deresiewicz, "Effects of 



an Oscillating Tangential Force on the Contact Surfaces of Elastic Spheres," 

 presented before First National Congress of Applied Mechanics, June 14, 

 1951. The results of this paper are summarized here. 



4. Measurements have been made by T. F. Osmer. 



5. This circuit was devised by G. A. Head. 



6. W. P. Mason, Piezoelectric Crystals and Their Application to Ultrasonics, 



D. Van Nostrand, Chapter XII, 1950. 



7. The data of Figs. 2 and 4 were obtained by L. Egerton. 



8. Elizabeth A. Wood, "Detwinning Ferroelectric Crystals," Bell System Tech. 



J., 30, No. 4, Part I, pp. 945-955, Oct., 1951. 



9. W. P. Mason, Piezoelectric Crystals and Their Application to Ultrasonics, 



D. Van Nostrand, Chap. XII, 1950. 



10. The photographs of Fig. 6 were obtained by T. E. Davis. 



11. R. D. Mindlin, "Compliance of Elastic Bodies in Contact," J. Appl. Mech., 



pp. 259-268, September, 1949. 



12. A. E. H. Love, Theory of Elasticity, 4th Edition, page 198, Cambridge Univer- 



sity Press. 



13. I. Simon, O. McMahon and R. J. Bowen, "Dry Metallic Friction as a Function 



of Temperature Between 4.2°K and 600°K.,"" J. App. Phys., 22, pp. 170-184, 

 Feb., 1951. 



14. W. P. Mason, Piezoelectric Crystals and Their Application to Ultrasonics, 



D. Van Nostrand, Chap. XII, p. 300. 



15. S. Timoshenko, Theory of Elasticity, McGraw-Hill Co., p. 311. 



16. W. P. Mason, Piezoelectric Crystals and Their Application to Ultrasonics, 



D. Van Nostrand, Appendi.x A9, p. 490. 



