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Welcome to class!
In today’s class, we will be talking about upthrust and Archimedes principle. Enjoy the class!
Upthrust and Archimede’s Principle II
The law of floatation
Archimedes’ principle (law of buoyancy)
States that, when a body is partially or totally immersed in a fluid, it experiences an upthrust force which is equal to the weight of fluid displaced
Experiment to show upthrust is equal to the weight of the fluid displaced
(A) is a real weight (weight of an object in the air) 4.5 N
(B) is the apparent weight (weight of an object in fluid) 3.0 N
(C) is the apparent loss of weight (weight of the fluid displaced) 1.5 N
Measuring the weight of the displaced fluid is equal to an apparent loss of weight; this apparent loss is the buoyancy force on an object which is upthrust.
Conclusion
The apparent loss of weight is equal to the weight of the displaced fluid.
Real weight = apparent weight + apparent loss
Since apparent loss is equal to upthrust
Real weight = apparent weight + upthrust
Upthrust =real weight – apparent weight.
Worked examples
(1) A body weighs 5.5 N when measured in air and 3 N when completely immersed in kerosene, what is upthrust experienced by a body.
Solution
Weight of body in the air (Real weight) =5.5 N
The apparent weight of a body when immersed in kerosene = 3 N.
But upthrust = real weight – apparent weight loss
Upthrust = 5.5 N – 3 N
= 2.5 N.
(2) A body weighs 3 N when totally immersed in water contained in an overflow can, if the weight of displaced water was 2.6 N, what is the real weight of an object.
Solution
Apparent weight = 3 N
Upthrust = 2.6 N (according to Archimedes’ principle)
But
Upthrust = real weight – apparent weight
2.6 N = Real weight – 3 N.
Real weight = 2.6 N + 3 N
= 5.6 N.
Floatation
Floatation can be defined as the tendency of an object to rise up to the upper levels of the fluid or to stay on the surface of the fluid.
The opposite of floatation is sinking and can be defined as the tendency of an object to go to the lower levels of the fluid.
The law of floatation
The law of floatation states that a floating body displaces its own weight of the fluid in which it floats.
This means if a log of 200kg (2000N) floats in water displaces 200kg (2000N) of water if the same log is placed in other liquid and be able to float it will displace the same 200kg of fluid in which it floats.
Conditions for objects to float
(1) The average density of the object should be less than the density of the fluid in which the object has to float.
Example, a ship is very heavy, but it floats because it is hollow inside it contains air, this causes its average density to be lower than that of water.
(2) The upthrust force of the fluid on the object must be the equal total weight of the object (law of floatation)
Example, a coin will sink to the bottom when placed on the surface of the water, this is because the upthrust of water on a coin is less than its weight
(3) The volume of an object submerged must be large so as to displace a large amount of fluid.
Relationship between upthrust and the real weight of the floating body
We know that,
Real weight = apparent weight + apparent loss in weight
Apparent loss in weight = weight of fluid displaced = upthrust
Therefore,
Real weight =apparent weight + upthrust
But when an object floats its apparent weight is zero
Apparent weight = 0
Then,
Real weight = 0 + upthrust
Real weight = upthrust.
Therefore the relationship between upthrust and real weight of a floating object is such that upthrust is equal to the real weight, and since upthrust is equal to the weight of the fluid displaced then floating body displaces its own weight of the fluid in which it floats (law of floatation)
In order for an object to float its real weight must be equal to upthrust.
If an object floats the volume of fluid displaced is equal to the volume of an object submerged and the percentage of the volume of an object submerged is equal to the relative density of an object with respect to the density of the fluid in which it floats.
Application of the law of floatation in everyday life
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In transportation by waterways:
The law of floatation is applied in all vessels which travel by waterways that include ships, submarines and ferry boats.
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In transportation by airways:
It is also applied in some vessels which travel by airways such as hot air balloon and airship.
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In decoration:
Balloons of different colours and shapes are filled with lighter gas so that will float in the air.
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In the measurement of specific gravity of liquids:
The hydrometer is an instrument which is used to measure the specific gravity of liquids; in its operation, it employs the law of floatation.
Other uses include making of bulges and transportation of logs down the river.
Pressure formula
Pressure is the force applied by one object on another. It is symbolized by P.
The pressure is articulated as force per unit area articulated as
P =F/A
Where;
F = Force applied by the body(N)
A = Total area of the object (m2)
Derivation
P = Pressure in Pascal
F = Force on the object
A = Area on which the force act
Besides, we often calculate pressure for gases and fluids. In those conditions, the pressure of liquid or gas is equal to the density of that fluid multiplied by the acceleration due to the gravity and the height (depth) of the fluid above a certain point.
Hydrostatic Pressure Formula = density of fluid × acceleration due to gravity × height of the fluid column
P = ρ x g x h
Derivation of the pressure equation
P = Pressure of the object (Pa)
ρ = is the density of the gas or fluid (kg/m3)
g = is the acceleration of the object due to gravity (9.80 m/s2)
h = is the height of the column of gas or fluid (m)
Pressure Formula is made use of to compute pressure, force, area, density, height and gravity if some of these numeric’s are provided. The unit of pressure is Pascal (Pa).
In our next class, we will be talking about Work Done by Force Field. We hope you enjoyed the class.
Should you have any further question, feel free to ask in the comment section below and trust us to respond as soon as possible.
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