Density

Density of an object is the ratio of the mass of the object to its volume. It is a salar quantity. It is measured in kilogram per metre cube (kg/m cube) or gram per centimetre cube (g/cm cube).

The density of a substance can be better explained by the composition, structure and nature of the substance using the kinetic theory of matter

Density In Relation To Kinetic Theory Of Matter

According to the kinetic theory of matter, the molecules of matter in solids are tightly packed together more than that of liquid and in comparison with gases, great.
Density has to do with the ratio of masses to volume and any substance which has a greater mass(quantity of matter) will most likely have a density which is higher in value compared to those with lesser quantity of matter.
This explains that since the molecules of solids are closely packed together,the quantity of matter(mass) is more, harder,in its volume,compared with a liquid of the same volume.

For Example

Two buckets of 5liters each is filled to full capacity where Bucket A is filled with Clay Bucket B is filled with Water. a) Determine if bucket A or B will have a greater density than the other and explain the reason for choosing the answer.

Explanation

Clay is a substance which posses molecules packed together as a solid,enables it to take a shape unlike water which cannot have it's distinct shape unless it takes the shape of the container,So there is more matter in a given unit of clay than in the same unit of water
Thus, Clay is more dense than water,even though they occupy the same volume of bucket,they have different quantity of matter (mass), You will notice this when the weight of both buckets are compared, the bucket filled with clay will definitely be more heavier than that of water.

Formula for Calculating Density

Since density is the ratio of mass of object to its voume, the formula for calculating density is as stated below:
Density = mass of object m / volume of object, v
Density = m/v Also,
Density = mass / l * b * h Or
Density = mass / (area of object * height of object)
Density = mass / (area of object * thickness of object) Where,
L = length; b = breadth; h = height (of object)

Measurement of Density of a Substance

The density of a substance can be measured or determine by dividing the mass of the substance by the volume of the substance. The mass of the substance is obtained by using spring balance to measure its mass while its volume is determined by calculation using any suitable formula. For an irregular object, the method explained below is used to determine its volume by law archimedes’ principle.

Relative Density, Archimedes Principle and Upthrust

The term relative simply means comparison or to describe a term using another reference term, In physics Relative Motion has to do with the motion of a body in reference to another body also in motion,
Relative Density also simply tells us the density of a substance in reference to another substance.
Relative Density is calculated as R.D= Density of substance/Equal volume of water.

Relative Density in solids

The relative density between solid has to do with the changes in weigth of a particular mass of a substance in different mediums.
For Example
If a metal weighs 2kg in air, and in water weighs 1.8kg, to calculate the relative density of the substance you simply have to find the difference in the weights of the iron in air and in water then divide by the refrrence medium weight (weight of water)i.e
R.D= 2 -1.8 / 1.8
= 0.2/1.8
=0.11 as its relative density

Relative Density In Liquids

When we compare the weights of a substance with a particular density in different media e.g
To compare the weight of a stone weighing 4.5kg in air, 2.8 in petrol and 3.2kg in water.(remember air is less dense than water and petrol so the weight is higher in it than the rest.),we can label
weight/mass in air (m1)= 4.5kg
weight/mass in petrol(m2)= 3.2kg
weight/mass in water(m3)= 2.8kg
We simply need to find out the difference in mass of the substance in petrol divided by the difference in mass of the substance in water
mass of substance in air - mass of substance in liquid/ mass of substance in air - mass of substance in water M1 - M2/ M1 - M3 (Remember it should always be a positive difference), 4.5 - 3.2/4.5 - 2.8
1.3/1.7
= 0.7647= 0.76 as it's relative density (remember R.D does not have a unit as the units are divided out during calculations)

Archimedes Principle and Upthrust

Archimedes' principle states that the upward buoyant force that is exerted on a body immersed in a fluid, whether fully or partially, is equal to the weight of the fluid that the body displaces.

The concept of Upthrust is established with the explanation of Archimedes principle
The weight of an object was be taken with a spring balance in air with a reading of 36gt(Note gt is used as the unit of weight here instead of kg or Newtons(N)) and when immersed into water shows a reading of 22gt on the spring balance(which is as a result of an upward force exerted by the liquid) Calculating
loss in weigth of object= w1 - w2
where w1 is weight of object in air (36gt) and w2 is weight of object in liquid (22gt)
loss in weight= 36 - 22

=14gt.
But also notice that the amount of liquid displaced by the object is equivalent to the loss in weight of liquid

remember the density of water= mass or weight/volume of water
since we know the density of water in g/ml is 1g/l we can calculate...
d= m/v ,

1g/ml = m/14ml

m= 14g but since its unit is in weight w= 14gt.

From the above we can see that,
loss in weight(Upthrust)= weight of liquid displaced in liquid.

Upthrust(Buoyance Force)

It is the upward force or opposition force which results when a substance is dropped into a liquid medium ,It affects the weight of that substances as molecules of liquid are opposing the motion of the liquid.
Upthrust (U) can be calculated as
U= weight of substance in less dense meduim(e.g air) - weight of substance in liquid or denser medium(e.g water)

U= w1 - w2