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What makes a boat float ?What makes a boat float ?

BouyancyBouyancy

StabilityStability

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Demotivation .com

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Stability of Floating ObjectStability of Floating Object stable ifstable if equilibrium after smallequilibrium after small

disturbancedisturbance

vertical & rotational stabilityvertical & rotational stability

(why no horizontal stability ?)(why no horizontal stability ?)

upward buoyant forceupward buoyant force centre of buoyancycentre of buoyancy

centroid of the displaced fluidcentroid of the displaced fluid

weight forceweight force centre of gravitycentre of gravity

rigid bodyrigid body centre of mass is fixedcentre of mass is fixed

(but not necessarily within object)(but not necessarily within object)

does not always coincide with geometric centredoes not always coincide with geometric centre

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Archimedes

Principle

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Archimedes PrincipleArchimedes Principle

The bouyancy force exerted on an objectThe bouyancy force exerted on an object

in a fluid is equal to the weight of fluid itin a fluid is equal to the weight of fluid it

displacesdisplaces

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For a FLOATING object:

FB = Wobj

= mobjg

= Vobj Vobj g

= WH2Odisp

= mH2Odispg

= VH2Odispl VH2Odispl g

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Mass(ship + cargo) = mass(displaced H2O)

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Stability of Floating ObjectStability of Floating Object

stable ifstable if

equilibrium restored after small disturbanceequilibrium restored after small disturbance

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Which is more stable ? Why ?

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upward buoyant forceupward buoyant force centre ofcentre of

buoyancybuoyancy centroid of thecentroid of the

displaced flu

iddisplaced flu

id

weight forceweight force centre of gravitycentre of gravity

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Which is more stable ? Why ?

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Calculating the metacentreCalculating the metacentre

centre of masscentre of mass

averageaverage of positions of particles making up aof positions of particles making up a

bodybody

(relative to datum)(relative to datum)

weightedweighted by theirby theirmassesmasses mmii

MM== 77mmii

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cylindrical

buoy - pine

(SG=0.5)

lead

(SG=11.3)

weight

depth ofimmersion in

seawater?(SG

=1.03)

centre mass? Centre

bouyancy?

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