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3.5 Archimedes Principle

(a) Introduction.

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.

clip_image002

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

Or

(4) Sketch the following graph:

clip_image004

(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.

clip_image006

Density and Buoyancy

From  Archimedes’s Principle :

Buoyant Force     = Weight of fluid displace

=  mg                 (note : F = ma)

= ρVg                       (note : ρ = m )

V

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.

Example  1

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?

Solution

 

Example  2

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?

Solution

 

Example 3

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

Solution

 

Buoyant Force and Flotation

clip_image008

If

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.

Example 4

An object of mass 5 kg floats on the surface water. What is the up thrust experienced by the object.

Solution

 

Example 5

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.

clip_image010

Solution

Example 5

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 ]

clip_image012

Determine

(a) The upthrust

(b)  The mass of sand in the glass tube.

Solution

Application of  Archimedes’ Principle

(1) Ship

clip_image014

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.

(2) Submarine

clip_image016

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.

clip_image018

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

clip_image020

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

(4) Hydrometer

clip_image022

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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  2. […] 3.5 Archimedes Principle February 2010 4 […]

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