PHYSICS S.S. 0NE (DENSITY) 1ST TERM
FIRST TERM: WEEK 8
TOPIC: - DENSITY AND
UPTHRUST
INSTRUCTIONAL MATERIALS: - Pendulum bob, measuring cylinder and
water.
REFERENCES BOOK: -
1.O. E. FARINDE e tal, Essential
physics FOR SENIOR SECONDARY SCHOOLS,
Tonads publishers.
2. M. W. ANYAKOHA (2011), NEW SCHOOL PHYSICS FOR SENIOR SECONDARY
SCHOOLS, Africana first publishers
3.Olatunbosun
K. (2004), CALCULATION IN PHYSICS FOR SSS,
PREVIOUS KNOWLEDGE: - Students have been familiar with floating
body.
OBJECTIVES: - At the
end of the lesson students should be able to: -
1. Define
density
2.
Explain the determination of density of a substance.
3.
State Archimede’s principle.
4. Solve
mathematical problems on density and upthrust.
CONTENT: -
DENSITY
AND UPTHRUST
Density is defined as the mass per unit
volume of a substance.
Density is denoted by a Greek letter rho (ρ)
Density
= mass /volume; ρ = m / v ; m = ρ×v
Since
mass is measured in kg and volume in m3 then the SI unit of density
is the kilogram per cubic meter (kg/m3 or kgm-3)
1g/cm3=
1000kg/m3
DETERMINATION OF DENSITY OF A
SUBSTANCE
Measuring a regular shape:
Obtain the mass by direct weight using instrument (e.g. spring balance).
Also obtain volume using formula.
Volume of cylinder= πr2h; volume of cone = 1/3 πr2h; volume of sphere = 4/3 πr3
Density is
the ratio of mass to volume
Measuring an irregular shape:
Obtain the mass by direct weighing using instrument, in order to obtain
the volume, get a measurable container filled with water, immerse the object
into the water, the volume of water displaced is equal to the volume of that
solid object.
Density =
Densities of important substances
|
SUBSTANCES |
DENSITIES
(kgm-3) |
|
Water Iron Aluminium Air Lead Wood Ice Paraffin Sand Mercury |
1000 7900 2700 1.3 1130 4000 920 9000 2600 13600 |
RELATIVE DENSITY
Relative density is the density of water compared with the density
of other substances.
Relative density (R.d) =
Relative density (R.d) =
Relative density (R.d) =
Relative density has no unit.
|
Density |
Relative
density |
|
1. is
a ratio of mass to volume of a body |
Is the ratio of mass of the body to mass of
an equal quantity of water |
|
2.
measured in Kgm-3 |
Has no unit |
Example
1. Find the density of petrol if 50.3g occupy 75cm3.
Solution
M= 50.3g; V=75cm3; d=?
d = m/v = 50.3g/ 75cm3 = 0.67gcm-3
2. The figure alongside shows a measuring cylinder which contains
water initially at level A. When a solid of mass 11g is immersed in water the
level raises to B. Determine the density of the solid.
Solution
Volume of solid = VB - VA
48 cm3 - 33 cm3 = 15 cm3
ρ = m/v =11g/15cm3
= 0.73gcm-3
UPTHRUST
Upthrust is defined as the
reaction force exerted on a body when wholly or partially immersed in a fliud.
It depends on : i. Nature of the liquid
i.e. density. Ii.
volume of the solid immersed
iii.
volume of the fluid displaced.
ARCHIMEDE’S PRINCIPLE
Achimede’s principle states that when a body is totally or
partially immersed in a fluid, the upthrust (apparent loss of weight) on it is
equal to the weight of the fluid displaced.
Relative density =
PRINCIPLE OF FLOATATION
The principle of floatation states that when a body is totally or
partially immersed in a fluid, its weight is equal to the weight of the fluid
displaced.
Weight of
body floating = weight of fluid displaced.
Factors that affecting floatation are its density and shape.
WHY SHIP FLOAT
A ship floats in water because its large volume displaces a large
volume of water whose weight counterbalances the weight of the ship. Similarly
a balloon filled with gas lighter than air will float if the weight of the
balloon and content equal the upthrust
of the air on the balloon.
The vertical position of a submarine can be controlled by flooding
or emptying the buoyancy tank when it is afloat, the buoyancy tanks to submerge
the submarine.
HYDROMETER
A practical hydrometer is an instrument in which gives a direct
density reading of the liquid in which it floats. It consist of :
i. a hollow harrow glass
tube or steam ii. a paper scale
inside, graduated in densities
iii. a wide bulb B iv. a loaded end, S containing lead shot
Hydrometer are used to test the concentration of acid in
batteries. They are also used in testing the purity of a liquids whose
densities are known. They are used in testing
the quality of milk.
EXAMPLE
1. A solid object is measured in air having a mass of 5Kg,
immersed in liquid and water with masses 2Kg and 3Kg respectively. Find the
density and the upthrust if the object placed ½ of its size in the liquid. Let
the density of that solid object = 19300 Kgm-3
Solution
M1= 5Kg , M2= 2Kg; M3 = 3Kg
From Achimede’s principle
Relative density =
Since density = R.d X 1000 = 1.5 X 1000 = 1500Kgm-3
Volume of solid = mass/density
= 5/19300 = 2.59X 10-4
Also, from Achimede’s principle
Upthrust = ½ volume of object X density of liquid X g
= ½ X2.59X 10-4 X1500 X10 = 1.94N
2. The mass of a density bottle is 20.0g when empty, 70.0g when
full of water and 55.0g when full of a second liquid x. Calculate the density
of the liquid (take density of water to be 1g/cm3)
Solution
Mass of empty density bottle = 20.0g; Mass of density bottle + water = 70.0g
Mass of water in density bottle = 50.0g; Volume of density bottle = m = 50.0 g = 50cm3
ρ 1g/cm3
Mass of density bottle + liquid =
55.0g; Mass
of liquid filling the bottle = 55.0 - 20.0 = 35.0g
Volume of
liquid = volume of density bottle = 50 cm3
ρ of liquid x
= m/v = 35.0g/ 50 cm3 = 0.7g/cm3 = 700kg/m3
2. In an experiment to determine the density of a certain solid D,
the following readings were obtained using a density bottle
a) Mass of empty density bottle = 8g; b) Mass of a
density bottle and solid D =96g
c) Mass of density bottle +30g water +solid D=132g; d) Mass of density bottle +water =88 g
Calculate
Mass of water in density bottle in part d). = 88 g - 8 g = 80 g = 0.080 kg
Volume of water in d) , V = m/ρ
m= 0.080 kg; (take
density of water be 1000kg/m3)= 1000kg/m3
v = 0.08/1000= 0.00008 m3
i)Volume of the density bottle = Volume of water filling it.
Volume of the
density bottle = 0.000008 m3
ii) Mass of solid D in part b)
96 - 8g = 88g = 0.088 kg
iv) Density of solid D: ρ
= m/v
= 0.088 kg/0.00008
m3 = 1100 kg/m3
v) Volume of water in c): V
= m/ρ
= 0.030 kg/1000 kg/m3 =
0.000030m3
vi) Mass of solid D in d):
m = ρ×v
m =
1100×(0.000080-0.000030); m = 0.055 kg
PRESENTATION
STEP I: The teacher revises the previous topic with the students.
STEPII: The teacher introduces the topic to the student.
STEP III: The teacher explains the determination of density of a
substances.
STEP IV: The teacher explains relative density
STEP V: The students chorus the definition of Achimede’s principle
and principle of floatation
STEPVI: The teacher leads the students in solving mathematical
problems on density and upthrust.
EVALUATION
The teacher
evaluates the lessons by asking the following questions:
1.
Define density
2.
Explain the determination of density of a substance.
3.
State Archimede’s principle.
4.
Determine the density in kg/m3
of a solid whose mass is 40g and whose dimensions in cm are 30×40×3.
Solution
V = L×W×h = 30×3×4 = 360cm3;
;ρ = m/v =40g/360cm3 = 0.11111 gcm-3 =111.1 kg/m3
[1gcm-3 = 1000kgm-3]
ASSIGNMENT
1. The diagram below shows the change in volume of water in a
measuring cylinder when an irregular solid is immersed in it.
Given that the mass of the solid is 56.7g determine the density of
the solid in g/cm3 (give answer correct to 2decimal places)
Solution
Volume of solid = VB - VA
50 cm3 - 33 cm3 = 17 cm3
ρ = m/v =56.7g/17cm3
= 3.34gcm-3
2. A solid weighs 4.8g in air, 2.8g in water and
3.2g in kerosene. Calculate the ratio of the density of the solid to that of
the kerosene. [ans = 3: 1]
Solution
Mass of solid
in air= 4.8g; Mass of solid in water=
2.8g; Mass of solid in kerosene =3.2g
Relative density (R.d) =
Relative
density (R.d) =
The ratio of
density of the solid to that of kerosene = 3:1
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