WE I GHT W I S T HE FO RC E AC T I N G VE RT I C AL LY DO W NWARDS, T HRO UG H T HE C E N T RE O F

G RAVI T Y G. W HAS A T E N DE NC Y T O S I NK T HE B O DY.

WHI L E UPT HRUST F B O F L I Q UI D AC T I N G VE RT I C ALLY UPWAR DS, T HRO UG H T HE

C E N T RE O F B O U YANC Y B I .E . T HE C E N T RE O F G RAVI T Y O F T HE DI S PL AC E D L I Q U I D.

NO T E : B C O I NC I DE S W I T H G FO R A B O DY WI T H UN I FO R M C O M PO SI T I O N, I F T HE B O DY

I S C O M PLE T E LY SUB ME RG E D.B L I E S VE RT I C AL LY B E L O W T HE C E NT RE O F

G RAVI T Y, I F T HE B O DY I S FL O AT I NG WI T H I T S PART SU B M E RG E D.

FLOATATION AND RELATIVE DENSITY –

GRADE 9

W = volume of the body X density of the body X g

FB = volume of submerged part of the body X density of liquid X g

•THE BODY WILL SINK•W-F B WILL BE THE APPARENT WEIGHT

ACTING VERTICALLY DOWNWARDS

Case 1 W > FB (this is the case when the density of

solid > density of the liquid.

•THE BODY WILL JUST FLOAT BELOW THE SURFACE OF THE LIQUID

• APPARENT WEIGHT OF THE BODY WILL BE ZERO.

Case 2 W = FB (this is the case when the density of

body = density of the liquid.

•THE BODY WILL FLOAT PARTIALLY ABOVE AND PARTIALLY BELOW THE

SURFACE OF THE LIQUID•ONLY THAT MUCH PORTION GETS

SUBMERGED BY WHICH THE WEIGHT OF DISPLACED LIQUID

BECOMES EQUAL TO THE WEIGHT OF THE BODY.

•W ACTS AT THE CENTRE OF GRAVITY OF THE BODY, WHILE FB

ACTS AT THE CENTRE OF BUOYANCY B WHICH IS VERTICALLY BELOW G

•W= FB ONLY DUE TO THE SUBMERGED PART OF THE BODY.

Case 3 W < FB (this is the case when the density of

body < density of the liquid.

PRINCIPLE OF FLOATATION

The weight of a floating body is equal to the weight of the liquid displaced by its submerged part.

Thus the weight of the body is balanced by upthrust (weight of the liquid displaced by its submerged part) on it .

APPARENT WEIGHT = TRUE WEIGHT – UPTHRUST = 0

Thus a floating body appears to have no weight (or its apparent weight is zero)

W = V ρs gFB = v ρL gFor floatation W = FB

V ρs g = v ρL g

 

APPLICATIONS OF THE PRINCIPLE OF FLOATATION

Floatation of iron ship An iron nail sinks in water while a ship floatsA loaded ship is more submerged while an

unloaded ship is less submergedA ship begins to submerge more as it sails

from sea water to river waterPlimsoll line indicates the safe limit for

loading the ship in waterAn unloaded ship is filled with sand at its

bottom

Floatation of human body – It is easier for a man to swim in sea water

than in fresh water e.g. a man can easily swim in dead sea with very small portion of his body inside water and shoulders all the time above water.

Floatation of Submarines –Submarine is a fish shaped water-tight boat

provided with several ballast tanks. It can be made to dive into water or rise up to

the surface of water as and when desired.

Floatation of ice-bergThe density of ice (0.917 g/< density of water

1 g/)

Floatation of fishWhen the fish has to rise up in water, it

diffuses gas from its fluid into the bladder so its volume increases and its average density decreases.

When it has to come down, it empties its bladder to the required extent so its volume decreases and density increases

Rising of balloonsLighter gases like hydrogen or helium is filled

in a balloon.The weight of he air displaced by he inflated

balloon (upthrust) becomes more than the weight of the gas filled balloon and it rises up.

The balloon does not rise indefinitely.