Question

3. The formation of a bubble indicates that there is excess pressure AP inside the bubble above the atmospheric pressure. For a bubble of radius R having a surface tension Os, the excess pressure AP is given by: 205 AP R a. Draw a free-body diagram of half a bubble indicating the force balance (4 marks) b. Derive the above equation (4 marks) C. Everything else being the same, do you expect the air bubble to be larger when formed at the top or base of a mountain (2 marks)

Answer 1

the bubble = Poutside let us say. pressure inside the bubble Pio. pressure outside Patmosphere - Patm. Pin-Patm excess pressure, Apa bubble of radius, R. Surface tension, os liquid drop: a Pout when we cut it into two parts of equal sizes. osa Pout X A. Pixe 'SxC Area Here, A = of bubble= C = circumference of bubble = 2tR. = TIR By force balance > Net applied force due to excess pressure equal to Net resistive force Pen XA - Pout XA = Os xo (Pin - Pout) x A TSXC Дрх (ТАУ) os X (2016) AP= 20$ R

let us we know that Paton = Patong-egh (R2) pressure at base > pressure at top say mountain of height, h atmospheric pressure at the base of mountain = at the Top of mountain atmospheric pressure Apa 20s Patmb.=P, ند and Pations TRU Patry-egh=P2 R R § same the size bubble R Pin-Path. (Pin-Patm) = 205 Here R is of bubble, if everything size of depends upon Pin - Path AP KL R At Base AP,=Pin-Patma 0 Ri At top APPin-( Patmegh) ad R2 > > 2

Now from the above relations 0 & 9 AP₂ > AP, i. RzLR, Size of bubble at at top R is less than size of bubble at bottom R1 .
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