Bukhovtsev-et-al-Problems-in-Elementary-Physics

(1
A6000-"""'------------..li.....-
1
According to the cosine rule,
F=V F~+F:-2FIF2 cos p=
Fig. 976
4 .. /~R~8---r6---2""!!!'R..... 8r-S-c-o-s-=p
=3"nymp V zr+(12-d 2) 2 11(lI-d 2) ~5.8XIO-t gf
233. The sought force of attraction is the geometrical sum of the forces
created by separate elements of the sphere. The small elements 01 and 0'2
(Fig. 377) are cut out of the sphere as cones with vertices at point A obtained
when the generatrix Be revolves around axis 8 182 • The areas of the elements
( AS )2ro (AS )1ro (AS )2 rop
are 1 and 2 respectively and their masses are _ .....1_~
cos (Xl cos (X2 " cos (Xl
and (AS 2 )2 rop , where (J) is the solid angle at which both elements can be
cos (Xl
seen from point A; p is the surface density of the sphere (the mass
per unit
of surface); L. (Xl= L. (X2' since StOSI is an isosceles triangle. The forces of
attraction created by the elements are equal, respectively, to:
and
m (AS 1 )2