Solved Examples on Buoyancy
Example 1: Find the volume of the immersed object if M is 10000 kg.
Solution:
ρ = 997 kg/m3
10000 kg × g = g × 997 kg/m3 V
1000 kg = 997 kg/ m3 V
Example 2: A block of wood with length = 3.2 m, width = 0.8 m, and height = 0.6 m. The density of water is 1000 kg/m3. If the block is placed in the water, what is the buoyant force? Acceleration due to gravity is 10 N/kg.
Solution:
Volume of the block (V) = length × width × height = 3.2 × 0.8 × 0.6 = 1.53 m3
Density = 1000 kg/m3
Gravity = 10 N/Kg
F = density × gravity × volume
F = 1000 × 10 × 1.53 = 15300N
F = 15300N
Example 3: The weight of an object in the air is 108 N. The object is placed in a liquid. The increase in the volume of liquid is 1.8 m3. If the specific weight of the liquid is 10 N/m3, what is the weight of the object in the liquid?
Solution:
Object’s weight in liquid = object’s weight in air – buoyant force
Object’s weight in liquid = 108 N – buoyant force
F = ρ g V
The density of liquid is 1 kg/m3
F = ρgV = 1 × 10 × 1.8 = 18 kg m/s2 = 18N.
Object’s weight in fluid = 108N – 18 N = 90N
Example 4: An object weighs 12N in air. When immersed fully in water, it weighs only 9N. What would be the weight of the liquid displaced by the object?
Solution:
According to Archimedes’s law:
Apparent weight = Weight of object (in the air) – Thrust force (buoyant force)
Apparent weight = 9N
Weight of object (in the air) = 12N
Thrust force (buoyant force) = ?
Apparent weight = 12N – Fb
Fb = 12N – 9N = 3N
Example 5: The weight of an object in the air is 108 N. The object is placed in a liquid. The increase in the volume of liquid is 1.8 m3. If the specific weight of the liquid is 10 N/m3, what is the weight of the object in liquid?
Solution:
Object’s weight in liquid = object’s weight in air – buoyant force
Object’s weight in liquid = 108 N – buoyant force
FA = ρ g V
The density of liquid is 1 kg/m3
FA = ρgV = (1kg/m3)(10m/s2)(1.8m3) = 18kgm/s3 = 18N
Object’s weight in fluid = 100 N – 18 N = 82N
Example 6: A piece of marble tile weighs 285 g in air. If its density is 3.5 g/cc, what will be its weight in water?
Solution:
Weight in air = 285 g
Volume = 285g /(3.5 g/cc) = 81.4 cc
Weight in water = 285 g – 81.4g = 203.6 g
Buoyant Force
Buoyancy is a phenomenon due to the buoyant force that causes an object to float. When you put an object in a liquid, an upward force is exerted on the object by the liquid. This force is equal to the weight of the liquid that has been displaced. The amount of liquid that has been displaced depends upon the density and the volume of the object immersed in the liquid. Have you ever wondered why an iron nail sinks in water, but a ship made up of iron floats? And why does an iron ball sink but a plastic ball of the same size floats in water? These wonders happen due to the phenomenon known as Buoyancy. Let’s learn the buoyancy definition, buoyancy equation, and its examples in detail.
Table of Content
- What is Buoyant Force?
- What causes Buoyant Force?
- Archimedes’ Principle
- Formula for Archimedes’ Principle
- Derivation of the Formula
- Demonstration of Buoyant Force
- Why does an Object float or sink in the water?
- Types of Buoyancy
- Applications of Buoyancy
- Solved Examples on Buoyancy
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