Calculate pressure on each side of spherical ball :
Heavy spherical ball of weight W rests in V shaped trough whose sides are inclined at the angles and to the horizontal. Find pressure on each side of trough. If second ball of equal weight be placed on side of inclination, so as to rest above the first, find pressure of the lower ball on side of inclination.
Sol.: Let
R_{1} = Reaction of inclined plane AB on
the sphere or required pressure on AB
R_{2} = Reaction of inclined plane AC on
the sphere or required pressure on AC
The O is in equilibrium under the action of
following three forces: W, R1, R2
Case - 1:
Apply lami's theorem at point O
R_{1}/sinß = R_{2}/sin(180 -α ) = W/sin(α +β )
or R1 = Wsinβ /sin(α +β ) .......ANS
and R2 = Wsinα /sin(α + β ) .......ANS Fig 6.74
Case - 2: Let
R_{3} = Reaction of inclined plane AC on the bottom sphere or required pressure on AC
As the two spheres are equal, the center line O1O2 is parallel to plane AB.
When the two spheres are considered as single unit, the action and reaction between them at the point of contact cancel each other. Considering equilibrium of the two spheres taken together and resolving the forces along Line O1O2, we get
R3cos{90° - (α +β )} = Wsinα + Wsinα
R_{3}sin(α + β ) = 2Wsinα
Or, R_{3} = 2Wsin α /sin(α + β ) .......ANS