Upthrust force, also known as buoyant force, is the upward force exerted by a fluid (liquid or gas) on an object that is submerged or floating within it. This force acts in the opposite direction to the force of gravity and is what makes objects float or appear lighter when submerged in a fluid. Therefore, objects will weigh less in water than in air.
Take a spring balance and hang some mass on it. Determine the weight of the mass and then push the mass up slightly with your hand. What have u observed?
When you place some upward force on a mass hanging on the spring, it’s weight is seemed to reduce as observed by lesser leading of the spring balance.
When you apply a force upward on the object hanging on a spring balance, you are providing some force that is acting opposite to the weight of the object. Weight is always acting downward on a straight line that is directed towards the center of the earth.
When you push the object upward, you are reduce the overall resultant downward force by providing some force acting opposite to the weight.
From the law of addition of forces, when two forces are acting in opposite direction on the same object, then one force is considered positive force and the other one taken as negative force . The total resultant force acting on the object is the algebraic sum of the forces acting on that object Consider the setup below that shows some weight acting on an object hanging freely on air.
We consider the force acting on the object which is it’s weight as W and any force applied upward as U as shown.
The resultant force will be given as :
Where W’ represents the reduced weight.
If U is greater than W’, then the object will accelerates upward, otherwise it will accelerates downward with reduced force.
The downward acceleration force is balancing with tensional forces on the spring causing some extension, hence the object remains on the spring balance but causing it to extend in length.
Upthrust Force
When an object is immersed in a fluid, the upward forces on the object are provided by pressure in the fluid. That is why objects weighs less in water because some weight of the object is being cancelled out by the upward forces in water. This upward forces produced by fluid on an object is known as the upthrust force. It is the same force that causes object to float in water.
However, it is important to note that, for heavier objects falling in air, the upthrust by air is so small such that it cannot be notices. We say that upthrust of air on an object is negligible.
Example question
An object weighs 6kg on air but when immersed into water, it’s weight is observed as 4.7 Kilogram. What is the upthrust water upon the object.
solution
Upthrust force by water =( weight in air) – (weight in water)
weight in air = 6.0 kg x 10 Nkg-1 = 60.0 N
weight in water = 4.7 kg X 10 Nkg-1 = 47.0 N
hence Upthrust force by water = 60.0 N -47.0 N = 13.0 N
Paper and Stone
If you release a piece of paper and a stone from a distance above the ground, you will notice something. The stone reaches the ground faster than the paper. This happens because the weight of a piece of paper is very small. The upthrust force on paper is comparable to its weight. However, the stone weight is much more than the upthrust provided by paper. Therefore, the resultant downward forces on the stone are larger than those on the paper. This causes more acceleration downward.
Later on, we will see that upthrust fall is characteristic of the object’s volume. It is also a characteristic of the fluid’s density.
causes of upthrust
Consider a cylindrical solid of cross-section area A which is totally immersed in a fluid of density ρ as shown.
The pressure due to liquid column is usually given by P=ρgh.
Pressure at the top of the solid will be given by, PT = h1ρg.
Where h1 is the height of the liquid column above the top of the object.
Pressure at the lower end of the object will be given by
Pb=h2ρg where h2 is the height of the liquid above the lover surface of the cylinder .
The pressure at the top of the cylinder will provide downward force exerted by the liquid up on the object.
From the pressure laws, F=pressure P x Area A.
i.e F=PA.
Taking the area of the cylinder at the top, the force from the liquid acting on that surface is Given by :
F=PT x A=h1ρgA.
Similarly, pressure at the bottom is given as F=PB x A=h2ρgA.
The total resultant upwardward force F is this given as
F=F2-F1
Hence F=h2ρgA-h1ρgA
Factoring out the common factors: F=ρgA (h2-h1)
Let h be the difference between liquid column on top and the one at bottom h2 such that h=h2-h1
Hence F=ρgAh
But Volume is always given by V=Ah
The resultant force F is the upthrust force U and will thus be expressed as.
F=U=Aρpg=pgV
where V is the volume of the liquid displaced.
Mass of the liquid is usually given by density x volume. Hence mass m of liquid displaced will be given by m=Ahρ
Weight is usually given as Weight W=mg
Hence weight of liquid displaced will be W=U=Ahρg which represents the upthrust force we calculated earlier. This confirms the archimedes principle that upthrust force is equal to the weight of the fluid it displaces.
Our mathematical arguments show that the magnitude of the upthrust force is a function of the object’s volume. It is also a function of the density of the liquid. This holds true considering that the gravitational pull g is a constant.
Related topics
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- Density
- Mass
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- central tendency in statistics
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