A hollow hemispherical object is filled with air as in part (a) of the figure.
(a) Show that the magnitude of the force due to fluid pressure on the curved surface of the hemisphere has magnitude F = (r2 P, where r is the radius of the hemisphere and P is the pressure of the air. Ignore the weight of the air. [First find the force on the flat surface. What is the net force on the hemisphere due to the air?]
(b) Consider an underwater air bubble to be divided into two hemispheres along the circumference as in part (b) of the figure. The upper hemisphere of the water surface exerts a force of magnitude 2(r( (circumference times force per unit length) on the lower hemisphere due to surface tension. Show that the air pressure inside the bubble must exceed the water pressure outside by ΔP = 2(/r.
(a)

(b)

Transcribed Image Text:

Inside pressure Outside pressure Inside pressure l" Surface tension