PHY4: ARCHIMEDES’ PRINCIPLE

ARCHIMEDES’ PRINCIPLE

When a body is wholly or partially immersed in a fluid, it experiences an up trust equal to the weight of the fluid displaced.

EXPERIMENT TO VERIFY ARCHIMEDE’S PRINCIPLE

Place a displacement can on a table fill it with water to the brim. Place a beaker under the spout when no water drops from the can. Tie a solid body such as a stone to a string and suspend it on a spring balance.

Determine the weight of the body in air, W_a.

Carefully lower it in the can and determine the weight when completely immersed, W_w. the displaced water will pour in the beaker. Pour the water in a measuring cylinder and determine its volume.

Calculate weight of displaced water from weight = density x volume x g.  up thrust = weight in air – weight in water.

If up trust = weight of displaced water then Archimedes’s principle is verified.

Relative density of a liquid by using Archimedes’ principle

Weight a solid in air first, then in water and finally in a liquid e.g. white spirit. Since the same solid is used the two apparent losses in weight will be apparent losses in weight will be weight of equal volume of spirit and water respectively.

Where

w_a – weight of solid e.g glass stopper in air.

Wa, – weight of solid in spirit or other liquid used

W_w – weight of solid in water

BALOONS

A hydrogen filled balloon rises in air because air is much denser than hydrogen

The total weight of the fabric and hydrogen is much less than the weight of air it displaces.

Ship and submarines

Bodies which are much less dense than water, those denser. A piece of solid steel sinks but a ship made of steel floats because a ship is hollow and contains air ,its average density is less than that of water.

The buoyancy of a submarine depends on the quantity of water in its tanks. When it’s required to dive water is admitted to special tanks. When the water is ejected from the tanks the submarine rises to the surface and floats.

Floating bodies

A piece of wood or other material sinks until its weight is equal to the weight of water displaced.

In this state the body then floats.

A balloon containing hydrogen gas may raise in air at a steady rate but it can be made to float if the gas it contains is adjusted so that the average density of the balloon is equal to the density of the surrounding air.

The weight of the displaced air is then equal to the weight of the balloon.

Law of flotation

A floating body displaces its own weight of the fluid in which it floats. This is Archimedes’s principle applied to a special case.

EXPERIMENT TO VERIFY LAW OF FLOTATION

A measuring cylinder is half filled with water and the water level reading v₁ noted. The test tube is placed in the water and lead shot added to the tube a little at a time until it floats. The new water level reading is noted and recorded as v_2.

The volume of displaced water is calculated from v₂ — v₁. Since density of water is lgcm’, mass of displaced water = density x volume

The test tube together with lead shot in it is then suspended on the spring balance and its weight, W_a determined.

It’s noted that weight of test tube and contents in air = weight of displaced water.

Hence the law of flotation is verified.

Examples

1. A spring balance reads I OON when a metal ball is suspended in air .The density of the metal is 7800kgnf³ .The ball is lowered into water
2. What is the volume of the displaced water?
3. What is the reading of the spring balance when the ball is in water?

THIS VIDEO EXPLAINS MORE ABOUT THE ARCHIMEDES’ PRINCIPLE