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Chapter 10

PHYS 22000 Chapter Notes - Chapter 10: Buoyancy

Course Code
PHYS 22000
Moffett Thomas

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Physics Chapte r 10 Notes
10.1 De ns ity
p = m/V
Solid Water Floats in Liquid Water
The solid form of a particular subs ta nce is a lmost alwa ys dens e r tha n the liquid form of the
substa nce, with one very significa nt exce ption: liquid water a nd s olid ice
10.2 P ressure Exerte d by a Fluid
Pascals First Law
An incre a s e in the pressure of a s ta tic, e nclos e d fluid a t one pla ce in the fluid ca us e s a
uniform incre a s e in pressure throughout the fluid
Pa rticle s inside a conta ine r move ra ndomly in a ll dire ctions , whe n we pus h harder on one of
the s urfa ces of the containe r, the fluid compre ss es ne a r the s urface
The mole cule s ne ar the s urfa ce collide more freque ntly with the ir neighbors farthe r from
the s urfa ce
The y in turn collide more fre que ntly with the ir neighbors
The extra pre ss ure e xerted a t the one s urfa ce quickly spre a ds a nd soon the re is incre a s e d
pres s ure throughout the fluid
10.3 P res s ure Va ria tion with De pth
Pa s ca ls firs t la w s ta te s tha t an incre a s e in the pre s s ure in one part of an e nclos e d fluids
re s ults in a n incre a se a t all othe r pa rts of the fluid
Press ure become s gre ater a t dee per le vels
Why Does Pressure Vary at Different Levels?
The pres s ure is lowes t a t the top of the fluid a nd gre a te s t a t the bottom
At e ach la yer, the pre ss ure is the sa me in all dire ctions
How Can We Quantify Pressure Change with Depth?
Pa s ca ls s econd la w - varia tion of pre s s ure with de pth: The pre s s ure P 1 in a s tatic fluid a t
pos ition y1 ca n be dete rmine d in the rms of the press ure P 2 a t pos ition y2 a s follows:
P1 = P2 + pfluid(y2-y1)g, whe re pfluid is the fluid de ns ity, a ss umed cons ta nt throughout the
fluid, and g = 9.8 N/kg a nd the pos itive y-dire ction is up
When using P a sca ls s e cond la w, picture the situa tion a nd be sure to include a vertica l y-
axis tha t points upwa rd and ha s a define d origin, or ze ro point. The n choos e the two points
of intere s t a nd ide ntify the ir vertica l y-pos itions rela tive to the a xis , which le ts you re late the
pres s ure s a t thos e two points
10.4 Me asuring Atmosphe ric P re s sure :
Measuring Atmospheric Pressure
Torrice llis hypothe s is is tha t atmos phe ric pre s sure limits the height of the liquid be ing lifte d
in a s uction pump
The atmos pheric pre ss ure (101,000 N/m²) ca n pus h mercury of de ns ity (13,600 kg/m^3) 760
mm up a column
10.5 Buoya nt Force :
The le vel of wate r in a conta ine r ris es a s more of the block is submerge d in the wate r
The Magnitude of the Force of Fluid on a Submerged Object
Archime des principle - the buoya nt force: a s tationa ry fluid e xerts a n upwa rd buoyant force
on an obje ct tha t is tota lly or pa rtia lly subme rged in the fluid
The magnitude of the force is the product of the fluid dens ity pfluid, the volume Vfluid of the
fluid tha t is dis pla ce d by the obje ct, and the gra vita tional cons ta nt g: FF on O = pfluidVfluidg
If a n obje t is comple te ly submerge d in the fluid, the volume is jus t the volume of the obje ct
If the object floa ts , the volume in the e qua tion then e qua ls the volume of space ta ke n up
by the obje ct be low the fluids s urfa ce
10.7 Buoya ncy: Putting It All Togethe r:
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