ARCHIMEDES' PRINCIPLE AND LAW OF FLOTATION

Archimedes' Principle

Archimedes'  principle  indicates  that  the  upward  buoyant  force  that  is  exerted  on  a  body

immersed in a fluid, whether fully or partially submerged, is equal to the weight of the fluid that

the body displaces.

The Concept of Upthrust

Explain the concept of upthrust

If  a  heavy  object  is  lifted  while  immersed  in  water,  it  may  be  raised  more  easily  than  when

outside the water. This is due to the reason that when anything is placed in liquid, it receives an

upward force called upthrust. A body appears to have lost some weight when immersed in water

due to the upthrust exerted on the body by the water.

By  definition  upthrust  is  referred  as  an  upward  force  exerted  by  the  body  when  it s

partially or totally immersed in water.

Consider the experiment below to verity the concept of upthrust.

From this experiment, it will be observed that W

>W

. This is because:

1

2

39

When a body is partially or totally immersed in any liquid, the liquid exerts an upward force.

A weight  recorded on the spring balance of a  body that is totally or partially immersed in any

liquid is called apparent weight. E.g. W

and the force, which temporally reduces the weight of

2

the body, are called upthrust (u).

Verification of the Archimedes' Principle

Verify the archimedes principle

This is the principle which shows the relationship between the upthrust acting on a body and the

weight  of  fluid  it  displaces  when  partially  or  completely  immersed  in  the  fluid.  It  was  first

discovered by a Greek scientist called Archimedes (287 to 121 BC).

The  principle  states  that,  ”when  a  body  is  partially  or  totally  immer sed  in  a  fluid  it

experiences an upthrust which is equal to the weight of the fluid displaced.”

This principle can be verified by the following experiment.

Results:Weight of a body in air = W

1

40

Verification of the Archimedes' Principle

Weight of a body in water = W

(apparent weight)

2

Uptrust = Loss of weight in water

U = W

–W

1

2

Example 1

Weight of a body in air = 10.0N

Weight of a body when immersed in water = 9.2N find the upthrust.

Solution:

Data given

Weight of a body in air (W

)= 10.0N

1

Weight of a body when in water (W

) = 9.2N

2

Formula

41

Upthrust = Loss of weight in water = W

-W

1

2

= 10.0N – 9.2N

= 0.8N

The upthrust is 0.8

Example 2

The  weight  of  a  body  when  totally  immersed  in  liquid  is  4.2N.  if  the  weight  of  the  liquid

displaced is 2.5N, find the weight of the body in the air.

Solution;

Data;

Apparent weight (W

) = 4.2N

2

Weight of liquid displaced (u) = 2.5N

Weight of body in air=?

Formular;

U = W

–W

1

2

W

= 4.2 +2.5 = 6.7N

1

Weight of body in air is 6.7N

The Archimedes' Principle in Determining Relative Density

Apply the archimedes principle to determine relative density

Relative density (R.D) of a substance can be defined as a ratio of the mass of a certain volume of

the substance to the mass of an equal volume of water.

Relative  density  =  Mass  or weight  of given  volume of  a  substance  overMass or  weight  of an

equal volume of water.

R.D = weight of a substance in air over Weight of  displaced water.

42

R.D = weight of a substance in air

From  Archimedes  principle the weight of an equal volume  of water  is equal  to the weight of

water displaced by  the  object,  which  is  equal to  the  upthrust  loss  in  weight.  By  weighing an

object in air and then in water, the relative density can be determined.

Weight of a body in air = W

1

Weight of a body in water = W

2

Apparent loss in weight = W

-W

1

2

Relative density = W1/W1 - W2

Example 3

A piece of glass weigh 1.2N in air and 0.7N when completely immersed water. Calculate its:

1.

Relative density

2.

Density of a glass

Given that density of water = 1000kg/cm

3

And acceleration due to gravity = 10N/kg

Solution

Weight of the glass in air (W

) = 1.2N

1

Weight of the glass in water (W

) = 0.7N

2

R.D = W

/W1 – W2

1

1.2N/(1.2 – 0.7)

1.2/0.5

R.D = 2.4

R.D = Density of glass/Density of water

43

Density of a glass = R.D x Density of water

= 2.4 x 1000kg/cm

= 2400kg/m

3

NB: Relative density has no SI unit

Law of Flotation

Difference between Floating and Sinking of Objects

Distinguish floating and sinking of objects

As we have discussed in upthrust, different objects with different density can sink or float. The

object with higher density than water density will sink while that object with a density lower than

water s density will float. For example, a coin sinks in water and a large ship floats on water.

The Conditions for a Substance to Float in Fluids

Explain the conditions for a substance to float in fluids

When an object is completely or partially immersed in fluids, there are two forces acting on it,

the weight (W) acting downwards and the upstrust (u) acting upwards. Refer to the figure below:

Conditions

44

Conditions for a body to float include:

1.

If W>U, there is downward movement of the body which is termed as sinking.

2.

If W

3.

If W=U, the body is equilibrium under the action of two equal and opposite force. Thus,

the body floats.

Relationship between Upthrust and Weight of Floating Body

Relate upthrust and weight of floating body

The relationship can be determined by considering the following experiment.

Upthrust and Weight of Floating Body

45

Principle of Floatation

State the law of flotation

The above experiment shows that, the upthrust is equal to the weight of the liquid displaced and

therefore the upthrust is equal to the weight of the floating body as the two forces are equal.

The mass of the floating body is equal to the mass of fluid displaced; in the above experiment is

the  same  as  the  weight  of  the  piece  of  wood.  This  result  is  agreement  with  the  principle  of

floatation.

The principle of floatation states “A floating body displaces a weight of the fluid which is equal

to its own weight.”

The Law of Floatation in Everyday Life

Apply the law of flotation in everyday life

Floating of ship

Iron is much denser than water and a block of iron sinks immediately in water. Ships are made

with  hollowness  such  that  their  total  densities  are  less  than  that  of  water.  Therefore,  a  ship

displaces water equal to its weights.

The upthrust of the water is sufficient to support the weight of the ship. When the ship is loaded

with cargo it sinks lower in the water. The volume of water displaced by the ship and its cargo

depends upon whether it is floating in  fresh  water or in  seawater.  It floats lower in fresh water

(R.D= 1.0) than in seawater (R.D=1.025) the mass of fresh water displaced.

46

For example, if a ship weighs 20,000 tons, then it must displace 20,000 tones of water to float. If

2,000 tones of  cargo is added, the ship lowers in water until an extra 1,000 tons of water have

been displaced

Plimsoll line;

This line indicates the safe limit of loading. Many plimsoll lines may be marked on

a ship to show minimum heights above different types of water in different seasons.

Balloons

Figure  below  shows  the  type  of  balloons  used  to  carry  instruments  to  a  high  altitude  for

recording meteorological measurements when filled with gas. E.g. helium, it displaces a volume

of air equal to its volume.

Air has greater density compared to the density of a gas in the balloon. Therefore, the weight of

air displaced is greater than that of balloon. The balloon drifts up by a f orce, which is equal to

the difference between the upthrust and the total weight of the balloon (W).

Submarine

The buoyancy  of a submarine  depends on the quantity  of water in its ballast tanks. When it  is

required to drive, water is admitted to special tanks. When the water is ejected from the tanks by

means of compressed air, the submarine raises to the surface and floats just like any other ship.

47

The mode of Action of a Hydrometer

Describe the mode of action of a Hydrometer

A hydrometer is an instrument used for measuring the densities of liquids such as milk, alcohol

and  acids.  The greater the density of  the  liquid  the  shorter  the  stem  of  hydrometer immersed.

Hydrometer sinks lower in kerosene and floats higher in water.

Construction of a Simple Hydrometer

Construct a simple Hydrometer

Single hydrometer can be made using pieces of straws or test tubes weighed down with wax.

Hydrometer in Determining the Relative Density of Different Liquids

Use Hydrometer to determine the relative density of different liquids

48

The relative density of liquid is measured directly by using a suitable hydr ometer, it contains:

1.

A heavy sinker, containing mercur y or lead shots that keep the hydrometer upright when

it floats.

2.

An air bulb to increase the volume of displaced liquid, and overcomes the weight of the

sinker.

3.

The stem is thin so that small changes in density give large differ ences in r eadings.

4.

The hydrometer is made up of glass so it does not soak up liquids.

READ TOPIC 6: Structure And Properties Of Matter