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PROCESS PRINCESS
buoyancy force
Bouyancy Force
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When an object floats or submerged caused by the resultant force exerted on it.
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Caused by the increase of pressure in fluids with depth
Bouyant force=difference between two forces
pf:density of fluid
g:gravitational force
Hydrostatic force:
F1=P1A
Fb=P2A-P1A
=pfxgx(Yb)xA-pfxgxYtxA
=pfxg(Yb-Yt)A
=pfxgxVb
Fb=pfxgxVb
Archimedes' principle
Bouyant force equals the weight of water displaced
mb:mass of b
Bouyancy Force:
Fb=pfxgxVb
Vb=(mb/pb)
Fb=pfxgx(mb/pb)
=mbxgx(pf/pb)
In floating body the weigh equals the bouyant force
Fb=W
pfxgxVsub=pbxgxVtotal
SINK OR FLOAT?
To determine if an object floats or sinks, the weight and bouyant force must be compared
W<Fb Float
W>Fb Sink
Example
Mercury
Steel
Determine the submerged depth (D) of a cube of steel 0.30 m on each side floating in mercury.
Given:
SGsteel = 7.8
SGHg = 13.6
}
D
Volume:LxWxH
(0.3x0.3x0.3)
0.027m^3
density of steel:7800kg/m^3
density of mercury:13600kg/m^3
pfxgxVfloat=pbxgxVtotal
(13600kg/m^3)(9,81m/s^2)(0.3mx0.3mxDm)=(7600kg/m^3)(9.81m/s^2)(0.027m^3)
(133416kg/m^2s^2)(0.3mx0.3mxDm)=(2013.012kgm/s^2)
(0.3x0.3xD)=(2013.012kgm/s^2)/(133416kg/m^2s^2)
(0.3x0.3xD)=0.0151m^3
0.09m^2xDm=0.0151m^3
Dm=0.0151m^3/0.09m^2
Dm=0.168m
Try out the question below to test your understanding,
A piece of irregularly shaped metal weighs 300 N in air. When the metal is completely submerged in water, it weighs 232.5 N. Find the volume of the metal.
please leave your answer in the comments!! :)
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