The figure shows a load of mass 40 N suspended in air whereas the others show the same load immersed in water at four different depth.
We can conclude the spring balance readings for each figure as :
(1) When an object is immersed partially or completely in a fluid, the weight of the object reduce and it is called as apparent weight.
(2) The apparent weight depends on the weight of water dispersed/displaced.
(3) The apparent weight is caused by an upward force exerted by the fluid on the object and the force is known as Buoyancy Force
(4) Sketch the following graph:
(b) Archimedes’ Principle
Archimedes’ Principle state that “ When an object is immersed in a fluid (a liquid or a gas) ,the buoyant force ( up thrust force) on the object is equal in size to the weight of fluid displaced by the object.
Density and Buoyancy
From Archimedes’s Principle :
Buoyant Force = Weight of fluid displace
= mg (note : F = ma)
= ρVg (note : ρ = m )
Thus FB = ρ V g
Where FB = Bouyant Force or Upthrust
ρ = Density of fluid
V = Volume of fluid displaced or the volume of the object that immersed in the fluid.
A metal sphere has a volume 5 x 10-4 m3 is immersed in water of density 1 x 103 kgm-3. Determine the upthrust experienced by the sphere?
A wooden block with a density 4 x 103 kgm-3 and a mass of 5 kg is immersed in a liquid of density 1 x 103 kgm-3 . Calculate the buoyant force acting on the wooden block?
An object has a weight of 40 N in air and 36 N in a liquid of density 800 kgm-3 . Determine the volume of the object
Buoyant Force and Flotation
Buoyant force = weight —> the object floats and stationary
Buoyant force > weight—-> the object moves up
Buoyant force < weight —–> the object moves down
The Law of Flotation
A floating object displaces its own weight of fluid in which it floats.
An object of mass 5 kg floats on the surface water. What is the up thrust experienced by the object.
Based on Figure (a), (b) ,(c) and (d) write the equations in words to relate the forces acting on the objects when the objects float and stationary.
The figure shows a glass tube of mass 0.012 kg with uniform diameter and cross-sectional area 4 x 10-4 m2 , and it is filled with sand so that it is made vertical in a beaker containing water.
[ Density of water is 1000 kg m-3 ]
(a) The upthrust
(b) The mass of sand in the glass tube.
Application of Archimedes’ Principle
A ship , though very heavy , floats on the surface of the sea.
This is because the buoyant force = the weight of the ship.
The buoyant force acting on the ship is large enough because the ship is hollow and the volume of water displaced by the ship is sufficiently large. ( FB = ρV g)
The density of sea water varies with location and season. To ensure that a ship is loaded within safe limits , the Plimsoll line marked on the body of the ship acts as a guide.
A submarine can sail on the surface or underneath it. Its outer hull is entirely watertight. Inside the hull are a number of tanks called ballast tanks which is used to control its position and depth from the surface of the sea.
If ballast tanks empty —> Upthrust = weight —-> submarine floats
If ballast tanks full —-> Upthrust < weight —–> submarine sinks
(3) Hydrogen –filled balloon.
A hydrogen-filled balloon will float up into the air if it is released. Air is a fluid and produces an upthrust.
Density of air >>> density of hydrogen gas
The balloon floats and rises upwards because
Upthrust > Weight of hydrogen + weight of balloon + weight of string
The balloon remains stationary in air when
Upthrust = Weight of hydrogen + weight of balloon + weight of string
4) Hot air balloon
Density of hot air <<< density of cold air
The balloon’s height can be controlled by turning the gas burner which heats the air on and off as needed.
The hot air balloon floats and rises upwards when
Upthrust > Weight of hot air (helium gas) + weight of airship fabric + weight of gondola + weight of passengers.
The balloon descends when
Upthrust < Weight of hot air (helium gas) + weight of airship fabric + weight of gondola + weight of passengers
The balloon remains stationary when
Upthrust = Weight of hot air (helium gas) + weight of airship fabric + weight of gondola + weight of passengers
An hydrometer is an instrument used to measure the density of a liquid.
It has a glass bulb which contains some lead to make it float upright , and long narrow neck with a scale marked on it caused the hydrometer more sensitive.
The large air-filled glass bulb is used to displace more liquid and it caused the upthrust increases hence the hydrometer floats.
In a liquid of lesser density , the hydrometer is more submerged.
The hydrometer floats higher in a liquid of higher density.
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