Have you ever wondered why some objects float while others sink? Did you know that every object in a liquid experiences an upward force from the liquid? Let’s dig in and find out more.
LEARNING OBJECTIVES
By the end of this topic, you are expected to;
INTRODUCTION
All objects in a liquid experience an upward force from the liquid whether they are submerged or floating. This upward force is referred to as the upthrust force. Upthrust force is also called the buoyant force and it is denoted by the letter “u”.
ARCHIMEDES’ PRINCIPLE
A Greek scientist, named Archimedes conducted the first experiments to measure the upthrust on an object in liquid. The Archimedes principle states that “when a body is fully immersed in a fluid, it experiences an upward force that is equal to the weight of the displaced fluid”.
When a solid is immersed in a liquid, the upthrust on this solid will be equal to the weight of the displaced water.
For example, a metal block whose volume is 60 cm3 and weighs 4.80N in the air is submerged in a liquid. Determine the weight of the block when it is fully submerged in a liquid that has a density of 1,200 kgm-3.
Solution
Volume of the displaced liquid = 60cm3 = 6.0 × 10-5 m3.
Weight of the liquid displaced = volume x density 6.0 × 10-5 × 1200 × 10 = 0.72 N
Upthrust = weight of the displaced liquid. Weight of the block in liquid = 4.80 – 0.72 = 4.08 N
FLOATING OBJECTS
Objects that float in liquids are less dense than the liquids in which they float. The relationship between the weight of the displaced liquid and that of the body can be determined.
The weight of the liquid displaced is equal to the weight of a block in the air. This is consistent with the floatation law which states that “a body displaces its own weight”. This relationship can be represented mathematically as shown below;
Weight = volume x density x gravity = v × ρ × g
W = vd × ρ × g where vd is the volume of the liquid displaced.
Note that floatation is a special kind of the Archimedes principle. This is because a floating body sinks until the upthrust is equal to the weight of the body.
RELATIVE DENSITY
Relative density has been established as the ratio of the density of a substance to the density of water. By the law of floatation, an object displaces a fluid that is equal to its own weight therefore, the following mathematical expressions can be established.
Relative density =\(\frac{\textrm{ density of substance}}{\textrm{density of water}}\) = \(\frac{\textrm{weight of substance}}{\textrm{weight of equal }volume of water}\) = \(\frac{\textrm{mass of substance}}{\textrm{mass of equal volume of water}}\)
APPLICATIONS OF RELATIVE DENSITY AND ARCHIMEDES PRINCIPLE
1. Ships. Do you ever wonder why an iron needle sinks immediately in water but not a big ship? The answer is Archimedes' principle. The nail sinks because the weight of the water displaced is lesser than that of the needle- the density of iron is greater than that of water. Archimedes' principle is applied in the building of ships. Large portions of the ship are left hollow to make the ship weigh less than displaced water. A buoyant force with a magnitude equal to the displaced water keeps the ship afloat.
2. Submarines. A submarine can float on water and it can also be submerged. This is achieved by the ballast and compressed tanks. When the ballast tank is filled with water, the submarine is submerged. This is because it has a higher density than the displaced water. When the water in the ballast tank is expelled, with assistance from the compressed tank, the density of the submarine lowers less than the density of displaced water. Therefore, the submarine is able to float.
3. Hot Air Balloons. The balloon rises in the air when the air surrounding the balloon has greater weight than the balloon. When the weight is equal, the balloon stays stationary.
4. Hydrometers. This is an instrument used for measuring the specific gravity or gravity of liquids. It is made up of a hollow tube of glass with a wider base- bulb-shaped and is sealed from both ends. The level of the hydrometer that is submerged in a liquid and water displaced by the hydrometer is measured in order to get the specific gravity of a liquid. If the hydrometer sinks deeper, it shows that the sample soil has less specific gravity.
