Important topics for JEE mains : Buoyancy & Archimedes Principle
In this blog you will read the basic concept of Buoyancy & Archimedes. It is an Important topics for JEE mains.
The hydrostatic thrust comes from the fact that the pressure of a fluid increases with depth and the fact that this increased pressure is exerted in all directions (Pascal’s Principle) so that there is a net imbalance upward force, exerted on the bottom of the submerged object.
Since the “water ball” on the left is in equilibrium, and exactly supported by the difference in pressure at all its points, and the solid object on the right experiences the same pressure environment, it follows that the pushing force on the solid object it is equal to the weight of the displaced water (weight of the water ball) (Archimedes Principle).
Objects of equal volume, experience equal hydrostatic thrusts.
Suppose we have balls of equal size, cork, aluminum and lead, with their respective specific weights of 0.2, 2.7, and 11.3. If the volume of each of them is 10 cubic centimeters, their masses will be 2, 27 and 113 grs
Each one will dislodge 10 grams of water, producing apparent masses of -8, (the cork would accelerate upwards), 17 and 103 grams, respectively.
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If from the rest in the water, we released the three balls, their behaviors would undoubtedly be different. The cork would rise to the surface, the aluminum would sink, and the lead would sink more quickly. But the pushing force on each one of them is the same, because the pressure environments are identical and the water eviction is the same. The difference in behavior comes from the comparison of that pushing force with the weight of the object.
In the first place, the thrust is proportional to the volume of the object: the more water displaces our ball, the more water we have to lift when we sink it and the more force we have to perform.
Second, the thrust is proportional to the density of the fluid. If instead of submerging the ball in water we do it in mercury, which is much more dense, we will have to raise a volume of mercury much heavier than if it were water.
Third, the thrust is proportional to the acceleration of gravity. If you tried to sink a ball into a pool of Jupiter, although the mass of water you raise was the same as here, the force required would be much greater by the tremendous Jovian gravity.
Observe, above all, what the push does not depend on: the weight of our ball. It does not matter how much you weigh, the thrust will always be the same as long as it has the same volume. This does not mean, of course, that the mass does not influence what happens at all, but does not influence the push.
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The true principle of Archimedes was enunciated by the Syracusan in a treatise in two volumes probably published in the year 250 a. C. The treatise, On Floating Bodies, is the first scientific book on hydrostatics, and Archimedes is undoubtedly the father of this science.
In the first volume, Archimedes states the law or principle that bears his name, and that in a modern language he says the following:
Any body partially or totally immersed in a fluid suffers an upward vertical force, called thrust, which is equal to the weight of the fluid it dislodges.
What does the principle say if we dismantle it in parts? It says basically three things, in order of detail:
- First, something happens whenever a body (or part of it) is immersed in a fluid: liquid, gas or plasma.
- In the second place it says what this something consists of: it is a force that pushes it upwards.
- In the third place, it quantifies this force: it is identical to the weight of the fluid dislodged by the body.
Let’s see an example:
Hmm! The crown seems lighter under the water!
The force of hydrostatic thrust on a submerged object is equal to the weight of the liquid dislodged by the object. For water, with a density of one gram per cubic centimeter, this provides a convenient way to determine the volume of an irregularly shaped object, and then determine its density.
BUT the density of gold is 19.3cm3, the crown has lower density, it’s not made of gold! Or at least, not entirely.
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The force of hydrostatic thrust on a submerged object is equal to the weight of the dislodged fluid. This principle is useful for determining the volume and therefore the density of an irregularly shaped object, by measuring its mass in air, and its effective mass when immersed in water (density = 1 gram per cubic centimeter). This effective mass under water, will be its real mass minus the mass of the fluid dislodged. Therefore, the difference between the real and effective masses, gives us the mass of the evicted water and allows the calculation of the volume of the irregularly shaped object (like the king’s crown in Archimedes history). The mass divided by the volume thus determined gives us a measure of the average density of the object. Archimedes found that the density of the king’s crown supposedly made of gold, was actually less dense than the known density of gold – inferring that it was hollow or filled with a less dense substance.
The examination of the nature of buoyancy shows that the force of hydrostatic thrust on a volume of water and a submerged object of the same volume, are equal. Since this supports exactly the volume of water, it follows that the force of hydrostatic thrust on a submerged object is equal to the weight of the water dislodged. This is the essence of Archimedes’ principle.
Sinking of Object
For the description of the sinking of an object from a resting position, both the buoyancy force and the viscous resistance should be included.
Using the net gravitational acceleration
takes us to the limit speed
and the characteristic time
The velocity at time t can be expressed as a function of the terminal velocity and the characteristic time.
The distance traveled in time t is
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This movement can be modeled for a spherical object, using the expression for viscous resistance in terms of fluid viscosity.
- The principle of Archimedes says absolutely nothing about that the level of a fluid rises when you introduce an object in it.
- By immersing anything in a fluid – liquid, gas or plasma – that object suffers an upward force, called thrust.
- The cause of the push is the fact that the fluid tends to descend due to its own weight, and therefore to push up the objects to occupy the space they are occupying.
- The thrust depends on the volume of the object, the density of the fluid in which it is submerged and the gravity of the place.
If you want you to read more about the concept you can go through this book.
Best of luck!