7. (a) The pressure difference results in forces applied as shown in the figure. We
consider a team of horses pulling to the right. To pull the sphere apart, the team must
exert a force at least as great as the horizontal component of the total force determined by
“summing” (actually, integrating) these force vectors.
We consider a force vector at angle
θ
. Its leftward component is
Δ
p
cos
dA
, where
dA
is
the area element for where the force is applied. We make use of the symmetry of the
problem and let
dA
be that of a ring of constant
on the surface. The radius of the ring is
r
=
R
sin
, where
R
is the radius of the sphere. If the angular width of the ring is
This is the end of the preview. Sign up
to
access the rest of the document.
 Spring '08
 Any
 Physics, Force

Click to edit the document details