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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
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 Spring '08
 Any
 Physics, Force

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