
[Ended]Physics Tutoring Session #8 Density and Relative Density on Tue. 1st March, 2016 @ 4:00  5:00pm
Physics
Chima Sunday (Tutor)
01032016 13:40:00 +0000The concept Density and Relative Density is one of the fundamentals in Fluid Dynamics, often tested in JAMB and other exams. so lets take a quick look on this topics. Come along with your questions. and were you need more explanations, and i promised to do best within my power to make the time worth.
Welcome and enjoy your time.
This section has ended=========Density and Relative Density============
Density
The density of a substance is define as the mass of the substance per unit volume. In a literal sense Density means how many quantity of matter in a substance can occupy a volume of one unit. Mthematically, Density = mass/volume,
i.e Density = m/v, The unit of density is in kg/m^{3}To determine the density of a substance of regular shape, one can measure the mass using beam balance and the get the dimensions of the shape and then use an appropriate formular to get the volume. Hence use the above formular for its calculation. i.e Density = m/v.
To determine the density of an irregular shaped object we still use the beam balance. But for its volume, we use euraka can or a caliberated cylinder to measure its volume using the principle of Archimedes which state that when an object is imerse in water it displaces equal volume of water equivalent to its volume. Thereafter, we employ the formular for density.
To determine the density of a liquid we use a convenient volume like pipette, or a measuring cylinder or even a galon of known volume like one litre, 2litre as on. Then to get its mass we first weigh an empty can on a balance and obtain its mass (m_{1}), and then put the liquid you want to determine its density inside the can and weigh again to get a new mass m_{2}. Hence, the mass of the liquid can be gotten by subtracting m_{1} from m_{2}
i.e m_{2}  m_{1} = mass of the liquid(m)
Relative Density(R.D) Relative density of a substance is defined as the mass of a volume of a substance to the mass of an equal volume water. In a literal sense, relative density means, if we measure a mass of substance m_{s} at a particular volume, then we measure also the mass of water m_{w} with that same volume. Then if take their ratio
i.e m_{s}/m_{w} we called the result the relative density of the substance.
Also note that density is proprtional to weight and density, hence in place of mass we can still use density of the substance all over the density of water OR the weight of substance all over the weight of equal volume of water.
Note that relative density has no unit.
To determine the relative density of liquid we use density bottle(specific gravity bottle). this is to ensure that equal volume of liquids and water are used.
To use the density bottle we first measure the bottle empty and record its mass as m, then fill the bottle with the liquid you want to measure its relative density and measure the bottle again to obtain mass m_{1}. Now empty the bottle and fill it back with water and measure its mass as m_{2}
Hence mass of liquid = m_{1}  m
mass of water = m_{2}  m
then relative density = (m_{1}  m)/m_{2}UPTHRUST Upthrust is define as the reaction force exerted on a body when whooly or partially immersed in a fluid(fluid is is any thing that can flow e.g is liquid or gas).
So upthrust is = weight in air  weight in a fluid(apparent weight)ARCHIMEDES PRINCIPLE This principle state thus that when a body is partially or wholly immersed in a fluid, the upthrust on it is equal to the weight of the fluid displaced.
simply put this way that upthrust = weight of fluid displaced.
One important thing about this principle is that we can calculate the relative density of liquid with it.
Note that the volume of liquid or that of water diplaced when a body is totally imersed in them is same as the volume of the bodyPRINCIPLE OF FLOATATION
Hydrometers is an instrument used for determing the density or relative density of a liquid, its principle is base on floatation.
this principle states that for a body to float when totally or partially immersed in a fluid, its weight must equal the fluid it displaces.
i.e weight of tghe floating body = weight of fluid displaced
Types of hydrometer are (1)simple hydrometer (2) Practical hydrometer.
Example JAMB 2015 Question 23 An empty relative density bottle has a mass of 30g. When filled with paraffin, its mass is 70g. Calculate the mass of the bottle when it is filled with water [Relative density of paraffin = 0.8]
Option A 40g
Option B 20g
Option C 60g
Option D 80g
solution
recall that R.D of paraffin = mass of paraffin/mass of equal volume of water
from the question mass of paraffin = 70  30 = 40
R.D of paraffin = 0.8
by subject formular, mass of equal volume of water = mass of paraffin/R.D = 40/0.8 = 50g
But the question asked us to Calculate the mass of the bottle when it is filled with water, so it is 50 + 30 = 80g
Answer is Option D
Solve
JAMB 2013 Question 8 A piece of cork floats in a liquid. What fraction of its volume will be immersed in the liquid? [density of the cork = 0.25 x 103kgm3, density of the liquid = 1.25 x 103kgm3]
Option A 0.8
Option B 0.5
Option C 0.2
Option D 0.1
JAMB 2013 Question 15 What volume of alcohol will have same mass as 4.2m3 of petrol? [density of alcohol = 8.4 x 102kgm3, density of petrol = 7.2 x 102kgm3]
Option A 1.4m3
Option B 3.6m3
Option C 4.9m3
Option D 0.8m3

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