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SCHEME OF WORK (NEW)
1 Introduction to Physics

2 Fundamental quantities and Units: Measurement of Mass, Weight, Length and Time.

3. Motion in Nature, Force, Circular Motion, Centripetal and Centrifugal Forces

4. Frictions

5. Vector and Scalar Quantity, Distance/Displacement, Speed/Velocity, Acceleration, Distance/Displacement-Time Graph, Speed/Velocity-Time Graph

6. Density and Relative Density

7. Upthrust, Archimedes Principle, Law of floatation, Pressure

8. Work, Energy and power.

9 Work Done in a Force Field, Types of Energy and Energy Conversion

10. Viscosity

11. Revision


REFERENCE TEXTS:
1. Senior Secondary School Physics by P.N. Okeke et al. 2011.
2. New School Physics for Senior Secondary Schools by Anyakoha, M.W. 2010
3. Comprehensive Certificate Physics by Olumuyiwa Awe and Okunola, O.O. 2009.
4. Science Teachers Association of Nigeria Physics for Senior Secondary School, Book 1. New
Edition; 2012.
5. Melrose Physics for Senior Secondary School, Book 1 by Akano, O and Onanuga, O.O. 2012.

TOPIC: INTRODUCTION TO PHYSICS
CONTENT:
1. Definition & Importance of Physics, Meaning of Physics
2. Aspects/Career in Physics, Branches of physics.
3. Major Concepts in Physics
4. The Scientific Methods, Theory and Experiment
5. Relation to Mathematics and Other Sciences


1: DEFINITION OF PHYSICS
The word ‘’PHYSICS’’ originates from the Greek word, ‘’PHYSIS’’, which means nature and natural characteristics.
Physics as a body of scientific knowledge, deals with the study of events in the universe, both remote and immediate universe.
In actual sense, physics deals with the behaviour of matter as well as the interaction of matter and natural forces.
Physics is the study of matter in relation to energy.


(1) In simple tense, physics means the science that deals with the ideas of matter and energy.
(2) It can also be defined as the scientific study of matter, force and the way they relate to each other.
(3) It can also be defined as the study of properties, behavior and interaction between matter and energy.

WHY DO WE NEED TO STUDY PHYSICS AS A SUBJECT
(1) Because physics played an important role in our life, we cannot live without physics.
(2) To understand the laws of nature and how nature affects human action.
(3) Without physics there will be no electricity, no computer, no air conditioner etc.


Meaning of Physics
Physics is the scientific study of matter and energy and how they interact with each other. This energy can take the form of motion, light, electricity, radiation, gravity etc. Physics deals with matter on scales ranging from sub-atomic particles (i.e. the particles that make up the atom and the particles that make up those particles) to stars and even the entire galaxies. It can also be defined as a natural science that involves the study of matter and its motion through space-time, as well as all applicable concepts, such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves. Physics is one of the oldest academic disciplines, perhaps the oldest through its inclusion of astronomy. Over the last two millennia, physics had been considered synonymous with philosophy, chemistry, and certain branches of mathematics and biology, but during the scientific revolution in the 16th century, it emerged to become a unique modern science in its own right. However, in some subject areas such as in mathematical physics and quantum chemistry, the boundaries of physics remain difficult to distinguish. Physics is both significant and influential, in part because advances in its understanding have often translated into new technologies, but also because new ideas in physics often resonate with other sciences, mathematics, and philosophy. For example, advances in the understanding of electromagnetism or nuclear physics led directly to the development of new products which have dramatically transformed modern-day society, such as television, computers, domestic appliances, and nuclear weapons; advances in thermodynamics led to the development of motorized transport; and advances in mechanics inspired the development of calculus.

https://youtu.be/b1t41Q3xRM8

IMPORTANCE OF PHYSICS
Physics is very useful in our society in most of our daily activities.
(1) Physics is used in cooking food.
(2) It is used in cleaning clothes.
(3) It is also used in watching television.
(4) It is also used in playing sports.

Why is physics important to farmer?
So they can do more things with less effort. Do things faster and easier. Tractor is the product of the laws of physics.
Why is physics important in the health sector?
The detecting machines used in clinic and hospitals now for effective and with less effort is also the product of the laws of physics.

1. Physics is constantly striving to make sense of the universe. This is seen in the development of theories and new theories used for better understanding of the universe.
2. When we study physics, we acquire the knowledge and skills to understand how and why natural things happen the way they do, and to make reliable predictions about their future occurrences. (e.g mirage, eclipse, earthquake, thunder,…)
3. The knowledge of physics gives us a better understanding of our immediate and natural environment.
4. The study of physics has enhanced the communication and the transportation world, thus, making the world a ‘’global village’’.
5. Human health has been improved from the study of physics through the invention of modern medical equipment.

https://youtu.be/TTHazQeM8v8

EVALUATION:
1) What Greek word is physics derived from?
2) Define physics.
3) State five importance of physics.



ASPECTS/ CAREERS IN PHYSICS
Physics is divided into two main branches.
(1) Mechanics: which is the study of the behavior of forces and objects acting due to those forces.
(2) Electricity and magnetism: which is the study of atoms.

Other aspects of physics are:
1. Mathematical physics
2. Classical electrodynamics
3. Quantum mechanics
4. Thermodynamics and statistical mechanics
5. Condensed matter physics
6. Nuclear physics
7. Quantum field theory
8. Astronomy and astrophysics.

Physics has several applications on health, technology & engineering, agriculture and applied sciences. As a results, below are some of the aspects/careers related to physics.

https://youtu.be/bGeOtXqJElo

A: IN HEALTH
We have:
i. Human medicine and surgery
ii. Nursing & midwives
iii. Radiotherapy
iv. Pharmacology
v. Physiology
vi. Anaesthesia
vii. Veterinary etc.

B: IN ENGINEERING
We have:
i. Electrical engineering
ii. Electronic engineering
iii. Mechanical engineering
iv. Aeronautic engineering
v. Petroleum engineering etc.

C: IN AGRICULTURE
We have:
i. Agricultural engineering
ii. Agricultural production engineering
iii. Horticulture etc.


D: IN BASIC/APPLIED SCIENCES
We have:
i. Geophysics
ii. Applied physics
iii. Biophysics
iv. Medical physics
v. Space physics
vi. Astronomical physics
vii. Engineering physics etc.

https://youtu.be/R9ZUIalX5wE

Evaluation:
Mention any four (4) careers related to physics in:
i. Health
ii. Basic science
iii. Engineering.



BRANCHES OF PHYSICS
The following are the branches of physics.
1. Mechanics
2. Heat
3. Electricity
4. Optics
5. Sound
6. Magnetism
7. Atomic physics
8. Nuclear physics
NOTE: No. 7 & 8 above had been combined and addressed with the current name, ‘’NUCLEAR PHYSICS’’, since the energy comes from the nucleus of the atom. The OLD NAME is ATOMIC PHYSICS.





https://youtu.be/NaV1zHQxW7c

Evaluation:
1. Develop a mnemonic for branches of physics.
2. Mention the branches of physics.
3. What is the recent name for atomic physics?
4. What do you understand by the term “physics’’?
5. State the step involve in scientific method


The Scientific Method
Physicists use the scientific method to test the validity of a physical theory, using a methodical approach to compare the implications of the theory in question with the associated conclusions drawn from experiments and observations conducted to test it. Experiments and observations are to be collected and matched with the predictions and hypotheses made by a theory, thus aiding in the determination or the validity/invalidity of the theory. Theories which are very well supported by data and have never failed any competent empirical test are often called scientific laws, or natural laws. Of course, all theories, including those called scientific laws, can always be replaced by more accurate, generalized statements if a disagreement of theory with observed data is ever found.
https://youtu.be/pGGCekUDQKc

Theory and Experiment
The culture of physics has a higher degree of separation between theory and experiment than many other sciences. Since the twentieth century, most individual physicists have specialized in either theoretical physics or experimental physics. In contrast, almost all the successful theorists in biology and chemistry have also been experimentalists, although this is changing as of late. Theorists seek to develop mathematical models that both agree with existing experiments and successfully predict future results, while experimentalists devise and perform experiments to test theoretical predictions and explore new phenomena. Although theory and experiment are developed separately, they are strongly dependent upon each other. Progress in physics frequently comes about when experimentalists make a discovery that existing theories cannot explain, or when new theories generate experimentally testable predictions, which inspire new experiments. It is also worth noting there are some physicists who work at the interplay of theory and experiment who are called phenomenologists. Phenomenologists look at the complex phenomena observed in experiment and work to relate them to fundamental theory.
https://youtu.be/IET9VX_Ufrc

Relation to Mathematics and The Other Sciences
In the Assayer (1622), Galileo noted that mathematics is the language in which Nature expresses its laws. Most experimental results in physics are numerical measurements, and theories in physics use mathematics to give numerical results to match these measurements. Physics relies upon mathematics to provide the logical framework in which physical laws may be precisely formulated and predictions quantified. Whenever analytic solutions of equations are not feasible, numerical analysis and simulations may be utilized. Thus, scientific computation is an integral part of physics, and the field of computational physics is an active area of research. A key difference between physics and mathematics is that since physics is ultimately concerned with descriptions of the material world, it tests its theories by comparing the predictions of its theories with data procured from observations and experimentation, whereas mathematics is concerned with abstract patterns, not limited by those observed in the real world. The distinction, however, is not always clear-cut. There is a large area of research intermediate between physics and mathematics, known as mathematical physics.
Physics is also intimately related to many other sciences, as well as applied fields like engineering and medicine. The principles of physics find applications throughout the other natural sciences as some phenomena studied in physics, such as the conservation of energy, are common to all material systems. Other phenomena, such as superconductivity, stem from these laws, but are not laws themselves because they only appear in some systems.
Physics is often said to be the "fundamental science" (chemistry is sometimes included), because each of the other disciplines (biology, chemistry, geology, material science, engineering, medicine etc.) deals with particular types of material systems that obey the laws of physics. For example, chemistry is the science of collections of matter (such as gases and liquids formed of atoms and molecules) and the processes known as chemical reactions that result in the change of chemical substances. The structure, reactivity, and properties of a chemical compound are determined by the properties of the underlying molecules, which may be well-described by areas of physics such as quantum mechanics, or quantum chemistry, thermodynamics, and electromagnetism.

https://youtu.be/zOKDtMHzqL8

GENERAL EVALUATION:
a) What do you understand by the term, ‘Physics’?
b) How has physics made the world, ‘a global village’?
c) State five importance of physics.
d) Mention five careers each related to physics in the following areas.
i. Engineering ii. Health iii. Applied sciences
e) Mention the branches of physics.

ASSIGNMENT
Objective
1. Which of the following is not a discipline related to physics.
A. Biophysics
B. Medical physics
C. Engineering physics
D. Accountancy

2. Physics originate from the Greek word ---
A. Physis
B. Phycik
C. Physic
D. Physes

3. One of the following is not a career in basic and applied science.
A. Geophysics
B. Applied physics
C. Space physics
D. Leap physics

4. The following are health related disciplines. Except ---
A. Radiotherapy
B. Pharmacology
C. Physiology
D. Electronic physics

5. Which of the following is not a branch of physics?
A. Sound
B. Engineering
C. Optics
D. Mechanics


1. Physics is a branch of science (a) true (b) false (c) cannot say
2. Physics is related to mathematics (a) true (b) false (c) cannot say
3. Physic is not useful for non-related science subjects (a) true (b) false (c) cannot say
4. Physics relies upon mathematics to provide the logical framework in which physical laws may be precisely formulated and predictions quantified. (a) true (b) false (c) cannot say
5. Galileo noted that English is the language in which nature expresses its laws. (a) true (b) false (c) cannot say

THEORY
1. What do you understand by the term “physics”?
2. How is physics related to mathematics and other sciences
3. Discuss the applications of physics in the following areas of life:
i. Health/Medicine
ii. Transportation
iii. Agriculture
iv. Communication.


READING ASSIGNMENT
Read up the topic: ‘’Fundamental and Derived Quantities’’ in the following text books.
i. Senior Secondary School Physics by P.N. Okeke et al.
ii. New School Physics for Senior Secondary Schools by Anyakoha, M.W.

TOPIC: FUNDAMENTAL QUANTITIES AND UNITS:
CONTENT:
1. Fundamental quantities: mass, length, time and electric charge
2. Simple measurement of current and temperature.

Meaning of Measurement
Measurement is the process of observing and recording the observations that are collected as part of a research effort. To get the exact measurement of an object we make use of tools used in the field of science, especially in physics called measuring instrument. Examples of such instrument are chemical balance, lever balance, spring balance,steel rule, tape rule, meter rule, venier calliper, caliper, micometer screw guage, stopwatch/clock, thermomerter, voltmeter,ammeter,burette, pipette, beaker etc.

CONCEPT OF FUNDAMENTAL QUANTITIES
Fundamental quantities are physical quantities whose dimensions and units are not usually derived from other physical quantities. Basically, there are three fundamental quantities in mechanics. They include:
• Mass
• Length and
• Time.

i) Mass: This is a fundamental quantity with dimension ‘M’, usually written in capital letter. The S.I. unit of mass is kilogramme (kg). Mass can also be measured in gramme (g), tonne (t), etc.

Measurement of Mass
Mass is simply the quantity of matter contained in the body. It also refers to the intrinsic property of all material objects to resist changes in their momentum.The instrument used in measuring mass is chemical/beam balance. Other instruments include lever balance, direct reading balance etc.It is a scalar quantity & measured in kilogram(kg).Mass is a basic/fundamental quantity & is constant from place to place.


ii) Length: This is another fundamental quantity with dimension ‘L’, written in capital letter. The S.I. unit of length is metre (m). Length can also be measured in kilometre (km), centimetre (cm), inches (inch), feet (ft), etc.

Measurement of Length
Length is simply distance between two points. It is a fundamental quantity & measured in meters(m).Length can be measured using the following
(a) Tape rule or steel rule: for measuring large distances e.g length of a playing ground etc.
(b) Meter rule: for measuring short distances e.g length of a tables etc.
(c) Caliper : for measuring cylindrical objects with the aid of a meter rule
(d) Venier calliper : for shorter length where meter rule cannot be used such as internal & external diameter of a tube, diameter of a rod, depth of cavity & thickness of a plate or meter rule we make use of venier calliper. It has two scales main scale & venier scale. The main scale is graduated in centimeters and millimeters. The vernier division has a length of 0.9mm or 0.09cm. The difference in length between vernier scale divisions is 0.1mm or 0.01cm.
(e) Micrometer screw guage : where higher accuracy for measurement is required such as the length of the diameter of a thin wire, diameter of small ball (pendulum bob) & thickness of a paper we make use of micrometer screw guage.

iii) Time: Time is a fundamental quantity with dimension ‘T’, also written in capital letter. The S.I. unit of time is second (s). Time can also be measured in minutes and hours.

Measurement of Time
Time can be defined as the interval between an event. It is a fundamental quantity & measured in seconds(s).Time can be measured using the following :
(a) Ticker tape timer :for measuring short interval of time accurately.
(b) Stop watch/clock : used in the laboratory and also on the field for sporting activities
(c) Sand-clock/Hour glass : for measuring time per hour
(d) Simple pendulum : can measure time in seconds, minutes & hours
(e) Heart beat: It is a natural wayof counting. It is mostly used in medical line.

iv) Measurement of Weight
Weight is the earth pull on a body or the downward force produced when a mass is in a gravitational field.The instrument used in measuring weight is spring balance. It is a vector quantity & measured in newton(N). Weight is a derived quantity & varies from place to place.

Relationship Between mass & weight
W=mg
Where, W = weight(N) m=mass(kg) g= acceleration due to gravity(m/s2)


Fundamental & Derived Quantity
Fundamental quantities are the basic quantities that are independent of others e.g. length (m), mass (kg) and Time (s). Other fundamental quantities are electric current (A), temperature (k), amount of substance (moles) and luminous intensity (candela)
Derived quantities are those obtained by simple combination of basic quantities e.g. Area, Volume, Density, Velocity, Acceleration, Force, energy, work, power, momentum, pressure, electric charge, electric potential etc.

https://youtu.be/oAtDAoqdExw

The below table summarized the dimensions and units of the basic fundamental quantities.
S/N Quantity Dimension S.I. Unit
1. Mass M Kilogramme (kg)
2. Length L Metre (m)
3. Time T Second (s)





https://youtu.be/VV2_gyCG48k

Evaluation:
1. List the three basic fundamental quantities.
2. What are their dimensions and SI units?


OTHER FUNDAMENTAL QUANTITIES
S/N Quantity S.I. Unit
1. Temperature Kelvin (K)
2. Current Ampere (A)
3. Amount of substance Mole (mol)
4 Luminous intensity Candela (cd)

Activity Work - Practical:
a) Measuring the temperature of boiled water in a specific interval of time say, 2mins as it cools down.
b) Measuring the current value in a simple electric circuit.


Evaluation:
1. Mention the three other fundamental quantities and their SI units.
2. How many fundamental quantities are there altogether?
https://youtu.be/qEOKCaXbM0E
https://youtu.be/oAtDAoqdExw

GENERAL EVALUATION:
1. Enumerate all the fundamental quantities with their SI units.
2. Write down the dimension of the three basic fundamental quantities.
3. Why are the above quantities called fundamental quantities?

ASSIGNMENT:
Objective
1. The dimension for mass is ---
A. m
B. L
C. M
D. kg
2. ‘T’ is the dimension for ---
A. length
B. time
C. mass
D. current
3. The dimension for length is ---
A. l
B. t
C. L
D. M
4. The following are fundamental quantities. Except---
A. Temperature
B. Mass
C. Time
D. Length
5. The SI unit of current is---
A. Coulomb
B. Ampere
C. Volt
D. Kelvin

6. The following are the fundamental quantities except (a) Length (b) weight (c) mass (d) time
7. The reading accuracy of meter rule is (a) 0.01cm (b)0.1cm (c) 10.005cm (d) 0.004cm
8. The best instrument for measuring the diameter of a thin wire is (a) vernier caliper (b) steel rule (c) micrometer screw gauge (d) meter rule
9. The SI unit of weight is (a) N (b) m (c) mls2 (d) kg
10. Hour glass measures time in (a) seconds (b) minutes (c) hour (d) micro-seconds

Essay
In Activity Work (a) above, plot a graph of temperature against time as the temperature of the water cools.
1. Differentiate between mass & weight
2. The weight of an object of mass 5000g is ……. (take g = 10m/s2)


READING ASSIGNMENT
Study the derivation of dimensions and SI units of the derived quantities in the following text books.
i. Senior Secondary School Physics by P.N. Okeke et al.
ii. New school physics by M.W.Anyakoha, Prof. Pg 3-11




TOPIC: DERIVED QUANTITIES AND UNITS (CONT):
CONTENT:
Concept of derived quantities.
Derivation of their dimensions and SI units.

CONCEPT OF DERIVED QUANTITIES
Derived quantities are physical quantities whose dimensions and units are usually derived from the fundamental quantities. E.g, force, speed, etc.
Other physical quantities apart from the fundamental quantities are derived quantities. This is because their dimensions and units are usually derived from the fundamental ones.
Derived quantities include:
Work
Energy
Momentum
Impulse
Volume
Area
Pressure
Power
Density
Moment
Torque, etc.
https://youtu.be/pm1uG2Rqnfo

Evaluation:
What are derived quantities?
Mention five examples of derived quantities.


DIMENSIONS AND UNITS OF DERIVED QUANTITIES
1. Derive the dimensions and the S.I. units of i) speed ii) acceleration iii) Force.

SOLUTION


2. Show that the dimension of pressure is ML^(-1) T^(-2). Hence, derive the S.I. unit.
SOLUTION


3. Derive the dimension for work. What is the S.I. unit?
SOLUTION:


https://youtu.be/DTv_eI9Hlro

Evaluation:
1. Derive the dimensions of
i) volume ii) power iii) density.
2. State their SI units.

GENERAL EVALUATION:
Differentiate between fundamental and derived quantities.
List ten examples of derived quantities and explain why they are called derived quantities.
Write down the SI unit of i) acceleration ii) force iii) momentum iv) density

ASSIGNMENT:
Objective
1. The following are derived quantities. Except ---
Current
Force
Speed
Impulse
2. The SI unit of force is ---
kgm/s
N
Ns
J
3. Joule (J) is the SI unit of ---
Force
Work
Momentum
Velocity
4. The dimension for pressure is ---

ML-1 T-2

ML2 T-3

ML-3

ML2 T-2

5. The dimension for energy is

ML-3

ML2 T-1

ML2 T-2

MLT-1

Essay
Show that the dimension of momentum is MLT^(-1). Hence, write down the S.I. unit.
Derive the dimensions and SI units of i) Mechanical power ii) Impulse.

READING ASSIGNMENT
Read up the topic: ‘’Measurement of length, mass and weight’’ in the following text books.
Senior Secondary School Physics by P.N. Okeke et al.
New School Physics for Senior Secondary Schools by Anyakoha, M.W.

TOPIC: MEASUREMENT IN PHYSICS
CONTENT:
1. Measurement of length
2. Measurement of mass & weight

MEASUREMENT OF LENGTH/DISTANCE
Length is measured using the following instruments.
(a). Metre Rule: A metre rule is a measuring device calibrated in centimetres (cm) with a range of 0 – 100cm. In using the metre rule, the eye must be fixed vertically on the calibration to avoid parallax errors. The smallest reading that can be obtained on a metre rule is 0.1cm (0.01cm).


(b). Callipers: these are used in conjunction with metre rule for measuring diameter of tubes, thickness of sheet, etc. The callipers are of two types –
- The external calliper and
- The internal calliper.
The external calliper is used to measure the external diameters of solid objects; while the internal calliper is used to measure the internal diameters of solid objects.


(c) Vernier calliper
The vernier calliper can be used for measuring small linear length and diameters of objects within the range of 0-12cm at least. It is calibrated in centimetres (cm). It has a reading accuracy of 0.1mm (0.01cm)


(c). The micrometer screw gauge: It is used to measure the thickness of a round objects E.g, the diameter of a wire. The micrometer screw guage gives a more accurate reading than the vernier calliper. It is calibrated in millimetre (mm). It has a reading accuracy of 0.01mm (0.001cm)
Other instruments for measuring length include: measuring tape, ruler, etc. The S.I. unit of length is metre (m).


Evaluation:
1. Mention any three instrument used in measuring length.
2. Which of the above instrument could give the highest degree of accuracy?


MEASUREMENT OF MASS/WEIGHT
Mass is defined as the quantity of matter a body contains; while Weight is the amount of gravitational force acting on a body or the force with which a body is attracted towards the centre of the earth. The weight of a substance varies from place to place due to variation in acceleration due to gravity, ‘g’ over places but mass remains constant from place to place.
Mass and weight of objects are measured using instrument such as spring balance, beam balance, chemical balance, scale balance, etc.
However, the difference between mass and weight is shown below.


Evaluation:
1. State three instruments used in measuring mass and weight.
2. State two differences between mass and weight.

GENERAL EVALUATION:
1. Differentiate between mass and weight in four ways.
2. Why is weight a vector quantity?

ASSIGNMENT:
Objective
1. Which of the following physical quantities is regarded as the amount of stuff contained in a body?
A. Weight
B. Force
C. Mass
D. Speed
2. The SI unit of weight is ---
A. kg
B. N
C. A
D. m/s
3. Which of the following quantities varies with the acceleration due to gravity, ‘g’?
A. mass
B. velocity
C. weight
D. momentum
4. The following are instruments used in measuring length. Except ---
A. micrometer screw gauge
B. vernier calliper
C. rule
D. spring balance
5. Chemical balance is suitable for measuring ---
A. mass
B. length
C. weight
D. non of the above

Essay
1. Differentiate mass from weight in four ways.
2. Draw the following measuring instruments i). Beam balance ii). Spring balance

READING ASSIGNMENT
Read up the topic: ‘’Measurement of Area, Volume and Time’’ in the following text books.
i. Senior Secondary School Physics by P.N. Okeke et al.
ii. New School Physics for Senior Secondary Schools by Anyakoha, M.W.





TOPIC: MEASUREMENT IN PHYSICS (CONT)
CONTENT:
Measurement of area and volume
Concept & measurement of time and ways of measuring time.

MEASUREMENT OF VOLUME
Volume of liquid objects is measured using instruments such as cylinder, burette, pipette, eureka can, etc. For regular solid objects, their volume could be determined using their mathematical formula.


MEASUREMENT OF AREA.
The area of a solid object could be determined using mathematical formulae after determining the two dimensions of the object.

https://youtu.be/qJwecTgce6c

WORKED EXAMPLES
1. Find the volume of a cylinder of diameter 12cm and height 15cm.
Solution:
d=12cm

∴ r = 12/2 = 6cm

h=15cm, π=22/7

Now,

v=πr2 h

∴v = 22/7×62×15

∴v=(22×36×15)/7=11880/7

∴v=1697.14cm3

2.What is area of a triangular card board of base 6cm and height 4cm?
Solution:
b=6cm and h=4cm

Now,A=1/2bh

∴A=(6×4)/2=24/2

∴A=12cm2
https://youtu.be/BZky8A4MTC4

Evaluation:
1. Calculate the volume of a rectangular prism of dimension 7cm by 3.5cm by 1.5cm.
2. A cube has an edge of 0.8cm. Find its volume.


CONCEPT & MEASUREMENT OF TIME, AND WAYS OF MEASURING TIME.
You must have heard the following statements made about time:
“Time and tide waits for no man”
“Time is business”
“There is time for everything: time to sow and time to reap, time to laugh and time to cry, time to go to bed and time to wake up” and so on
Time is very important in our daily activities. Many people have failed in one area or the other because of mismanagement of time. In Physics time is very important. Wrong timing can lead to wrong observations, results and wrong conclusions.
What then is time. Time may be considered as the interval between two successive events. It is a fundamental quantity. Its S.I unit is seconds.

Ways of measuring time.

Time as mentioned earlier is very important. That is why early men developed various means of measuring time. They used the sun to tell time. Even today people still use the position of the sun to determine time. Other devices they developed and used are:
The water clock
The sand clock
The primitive Sundials
Today, we have better time-measuring devices that measure time more accurately than the above mentioned devices. Some of them are:
The stop watch which is the standard instrument for measuring time in the laboratory
The wrist watch
The modern pendulum clock
The wall clock
It is worthy of note that:
60 seconds makes one minute
60 minutes makes one hour
24 hours makes one day
365/366 days makes one year
10 years makes a decade
100 years makes a century/centenary
1000 years makes a millennium
https://youtu.be/JErOPF2danc

Calculations on time
Example 1
How many seconds are there in 2 hours 15 minutes?

Solution
Since 60 seconds makes 1 minute and 60 minutes makes 1 hour, 1 hour will have 60 x 60 seconds. 2 hours will have 60 x 60 x2 seconds = 7200seconds.
15 minutes will have 60 x 15 seconds = 900 seconds
Therefore 2 hours 15 minutes will have (7200 + 900) seconds = 8100 seconds

Example 2
If it takes a pendulum bob 32 seconds to complete 20 oscillations, what is the period of oscillation of the bob?

Solution
Period ( T ) is time ( t ) taken for the bob to complete an oscillation.
i.e T = t/number of oscillations

T = 32/20

= 1.6 seconds
Evaluation
What is the standard instrument for measuring time in the laboratory?
Mention 2 examples each of modern and olden days time-measuring devices you know.

GENERAL EVALUATION:
1. Discuss the significance of time to the study of science.
2. Highlight the various instrument for measuring time.

ASSIGNMENT:
1. How many hours are there in a year ?
8760hrs
8660hrs
8890hrs
8784hrs
2. How many hours are there in a leap year?
8890hrs
8784hrs
8770hrs
8800hrs
3. How many minutes are there in a year?
525,600mins
1440mins
8784mins
8760mins
4. What is the SI unit of time?
Minute
Second
Hour
Kilometre
5. Which of the is the formula for calculating the volume of a cone?
l×b×h
πr² h
1/3 πr² h
4/3 πr³

Essay
1. What is an eureka can?
2. Explain how the volume of an irregular object can be measured.

READING ASSIGNMENT
Read up the topic: ‘’ Position, Distance and Displacement ’’ in the following text books.
Senior Secondary School Physics by P.N. Okeke et al.
New School Physics for Senior Secondary Schools by Anyakoha, M.W.

TOPIC: MOTION
CONTENTS
Types of motion: (a) Random motion (b) Translational motion (c). Rotational motion (d). Oscillatory motion (e). Relative motion
Causes and effects of motion.

Types of motion
Definition of motion: Motion by definition is a change in the position of a body with time. Motion exists in various forms and occurs in the three states of matter (solids, liquids and gases). These various forms are; random, translational, rotational and oscillatory motion.
Some examples of motion are;
The movement of the earth round the sun
The rotation of the earth about its axis
An aero plane flying in the sky
A boy walking or running
https://youtu.be/8qh--3X6E5w

https://youtu.be/I6CVEphVZvY

https://youtu.be/1U8a4_1q9bo

Random motion.
Random motion is the movement of a body in a zigzag or disorderly manner with no specific direction as shown in the diagram below. Some examples of this kind of motion are; the motion of dust particles in the air, the motion of smoke particles, the motion of butterfly e.t.c.


https://youtu.be/gtvBorXF4gc

Translational motion
This is motion performed by a body in a straight line from point ‘P’ to another point ‘Q’. if you walk from one end of the classroom to the other, you have performed translational motion. Translational motion can also be called rectilinear motion. Another example of translational motion is the dropping of a fruit from a tree to the ground. A car moving in one direction from one town to another, movement of a man etc. Rectilinear motion is similar to translational motion. In this type of motion, the body moves in a straight line e.g. light ray traveling from a point A to another point B in a straight line.



https://youtu.be/HbavPdQ_2EU

Rotational motion
When a body moves in a circular path about an axis, it has performed rotational motion. In other words, rotational motion is the motion a body performs in a circular path about an axis. The rotation of the blades of a fan, the rotation of a wheel about an axis, the rotation of the earth about its axis, the motion of a moving vehicle wheel are all examples of rotational motion. See diagrams below.


https://youtu.be/fmXFWi-WfyU

Oscillatory motion
This is the motion of a body in a to and fro manner about a fixed point. When a body moves to and fro about a fixed point, we say, the body is oscillating. One complete oscillation is a circle. Examples of oscillatory motion include, the motion of the balanced wheel of a wrist watch, the motion of a simple pendulum, the motion of a loaded test tube inside water, e.t.c.



https://youtu.be/Hx1s2uaApZY

Note: it is possible for a body to perform two types of motion at the same time. For example a rolling football performs both rotational and translational motion at the same time.

Class activity
Set up a simple pendulum as shown above
For a length (L) of the pendulum say, 80.0cm, push the bob through a small angle to oscillate to and fro
Using a stop watch, determine and record down the time (t) it will take the bob to complete 20 oscillations

Calculate the period (T) of oscillation of the bob i.e t/20

Repeat the experiment for four other values of L= 70.0cm, 60.0cm, 50.0cm and 40.0cm. in each case determine the period (T) and its square.
Tabulate your results. Plot a graph of T2 on the vertical axis against L on the horizontal axis
Determine the slope S of the graph

Given that 4π2/g = S, calculate the value of g.

https://youtu.be/7J_Pi4Xuk7Y

Relative motion
Relative motion is the motion of a body with respect to another. Put in another way, it is the motion of a body with respect to a reference point. All motions are relative.
If two bodies, A and B are moving on a straight line, the velocity of A relative to B is found by adding the Velocity of B revered to the velocity of A. For instance, if a car traveling on a straight road at 100km/hr passes a bus going in the same direction at 60km/hr, the velocity of the car relative to the bus is (-60+100) = 40km/hr. If the car and the bus are traveling in opposite direction with the same velocities of 100km/r and 60km/hr respectively, the velocity of the car relative to the bus is ( -(-60) + 100) = (60 +100) = 160 km/hr.
NB: When the velocities are not in the same straight line, the parallelograms law should be used to add this since velocities are vectors, and their magnitudes and direction must be taken into consideration.

https://youtu.be/pygnrS75HLs

Evaluation
Mention 2 other examples each of random motion, translational motion, rotational motion and oscillatory motion apart from the ones in this e-note.
Mention two examples of bodies that perform two motions at the same time. State the two motions.


Causes and effects of motion
Sir Isaac Newton’s works on motion reveals that an object will remain in its state of rest(inertia) unless an external force acts on it. This means that if an object is kept on a table, the object will remain in that state of rest or on the table unless something touches it. This leads to the conclusion that the cause of motion is force which can either be a push or a pull. Consider the diagram below.


If an object (e.g. a book) is placed on a table, it will continue to be at rest. Only the application of a force can make it move visibly. Hence, force causes motion. There are two types of force (a) Contact force (b) Field force

(a) Contact Force: They are forces that are in contact with the body they affect e.g. tension, reaction frictional forces, forces of pull & push, viscous force etc.

(b) Field Force: They are forces whose sources do not require contact with the body on which they act. The effect of such forces is felt at a distance or in a field of the force e.g. electrical force, magnetic, gravitational pull etc.

https://youtu.be/xMmFTA9AThw

A pull or push will make the object to move to point B from point A. this means that force is a vector quantity because it has both magnitude and direction.

https://youtu.be/joVOE3sLeGI

Class activity
Tap a stationary ball on the table or ask your classmate to hold your hand and pull you towards his or her side. What is your observation? What can you conclude from this?

Assignment
Reading assignment: Read on types of forces, and friction
The students should be grouped in fours or fives or as may be suitable in your campus and carry out this activity on 100m race. The time taken for a member of the group to run 100m should be noted and recorded. All members of the group should take turns. Tabulate your readings. Now answer the following questions
Who was the fastest runner in the group?
Who was the slowest runner in the group?
Who is the overall fastest runner in the class?
Who is the overall slowest runner in the class?

Objective questions
A loaded test tube in water is carefully and slightly depressed and then released. Which of the following best describes the subsequent motion of the test tube?
Random B. Oscillatory
C. Linear D. Circular

The motion of the prongs of a sounding turning fork is
A. random.
B. translational.
C. rotational
D. vibratory

`Which of the following phenomena is the practical evidence for the existence of the continual motion of molecules?
A. Translational motion
B. Rotational motion
C. Brownian motion
D. Oscillatory motion

When a cylinder rolls down an inclined plane, it has one or more of the following types of motion:
i. oscillatory ii. Random iii. Rotational iv. Translational.
A. i and iv B. ii and iii. C. iii and iv D. iv only E. iii only

Which of the followings cannot not perform motion? A. tree B. bird C. helicopter D. snail E. man

READING ASSIGNMENT
Read up the topic: ‘’Force and types of force’’ in the following text books.
Senior Secondary School Physics by P.N. Okeke et al.
New school physics by M.W.Anyakoha,Phd. Pg 12-27

TOPIC: MOTION

CONTENT: 1. Force
2. Types of forces.
3. Friction and types.
4. Calculations on friction.
5. Advantages and disadvantages of friction.
6. Ways of reducing friction.

Force and the types, Friction and types
Force can be defined as that which changes or tends to change the state of rest or uniform motion of a body. Force is a vector quantity and the S.I unit is Newton.
Force can cause a body at rest to move, it causes a moving object to accelerate, change direction, move in a curved path e.t.c.

Types of forces: There are two types of forces, namely contact force and force field.
Contact force is a force that exists between bodies by virtue of their contact. They are push, pull, normal reaction, tension in strings, wires or frictional force.

Force field/Non-contact force is the force that exists within a vector field such as gravitational field, magnetic field, Electric field, nuclear field. The forces are gravitational force, magnetic force, electrostatic force and nuclear force.
https://youtu.be/7_Uo7RufH4c

Gravitational force: This is the force of attraction of a planet on any object in it field. It can also be defined as the force of attraction between two masses. The earth is a gravitational field.

Electrostatic force: This is the force that acts between electrical charges, namely positive and negative charges. The law of electrostatics states that unlike charges attract while like charges repel.

Magnetic force: This is the force that exists between two magnets. There is the North pole and the south pole. The law of magnetism states that unlike poles attract while like poles repel.


Nuclear force: This is the force of attraction which holds the protons and neutrons in the nucleus of an atom.


FRICTION
Definition of friction
Friction can be defined as the force that opposes the relative motion between any two surfaces in contact. There can be solid friction or fluid friction. Fluid friction is also called viscosity.
It acts whenever there is motion or tendency for something to move. i.e friction (or frictional force) is absent if there is no motion or if there is no force intending to cause motion. It stops your car when the brake is applied. It prevents your foot from slipping backward when you walk.


Types of friction
There are two types of frictional force
1. Static friction. This is the frictional force that exists between two surfaces relatively at rest and preventing the motion of one surface over the other.

2. Dynamic/kinetic friction: This is the frictional force that exists between the two objects that are in relative motion to each other.
https://youtu.be/R10tuvCdl8c

EVALUATION:
1. What is force?
2. List the two types of forces and differentiate between the two.
3. What is friction?
4. Differentiate between static friction and dynamic friction.



Laws of solid friction, Calculations on friction.

LAWS OF SOLID FRICTION
 It always opposes motion
 It depends on the nature of surfaces in contact. Friction between rough surfaces is greater than the frictional force between smooth surfaces.
 It does not depend on the relative speed between the two surfaces.
 It does not depend on the area of the surface in contact.
 It is directly proportional to the perpendicular force (normal reaction) between the two surfaces.(R is the perpendicular force between the two surfaces in contact)


https://youtu.be/XYAy6KhYzcg

Coefficient of friction: it is defined as the ratio of the frictional force to the normal reaction force between two surfaces. A high coefficient of friction implies that a large force is required to cause movement.
https://youtu.be/RIBeeW1DSZg

The weight ( W) of an object is acting vertically downward.. the normal reaction (R ) is always acting perpendicular to the plane.. the normal reaction is equal to the weight.



Case two: if the body is stationary a = 0
P – mgsinø = ma
P – mgsinø = 0
P = mgsinø ……………………………… 6
Case three: if the body slides down the plane, a >0
mgsinø – P = ma
P = ma + mgsinø ………………………… 7
For a body on a rough inclined plane.
P – mgsinø - Fr = ma
But Fr = μmg
P - mgsinø - μmg = ma ………………………. 8
Also, R = mg cosø
P - mgsinø - μ mg cosø = ma …………………………… 9

If the body moves upward the incline plane
μ = tanӨ………………………………….. 10


Questions A: A crate slid down an inclined plane such that the frictional force opposing its motion is 40N. If the normal reaction of the plane on the crate is 50N, calculate the coefficient of dynamic friction.

Solution:
Frictional force F = 40N
Normal reaction R = 50N
Coefficient of friction µ= ?
F=µR
40 = µ x 50 (dividing both sides by 50)
40/50 = µµ = 0.8


Question B. A block of mass 12kg rests on a horizontal floor, coefficient of friction is 0.35. Determine the minimum force required to move the block when pulling horizontally. ( g = 10m/s2)


SOLUTION
W =mg= 12 x10 =120N, W=R=120N
Where W – weight of the body, m – mass of the body, g is acceleration due to gravity and R is the normal reaction
F = µR
F=P= µR=120 X 0.35= 42.0N

Question C. A metal block of mass 5kg lies on a rough horizontal platform. If a horizontal force of 8N applied to the block through its center of mass just slides the block on the platform. Calculate the coefficient of limiting friction between the block and the platform. ( g = 10m/s2).

Question D. A wooden block whose weight is 50N rests on a rough horizontal plane surface. If the limiting friction is 20N. Calculate the coefficient of static friction.

EVALUATION
1. Mention at least four characteristics/laws of solid friction.
2. A body of mass 40kg is given an acceleration of 10ms-2 on a horizontal ground for which coefficient of friction is 0.5. Calculate the force required to accelerate the body. ( g = 10m/s2).



Advantages and disadvantages of friction, Ways of reducing friction
Advantages of friction (or desirable effects of friction)
I. Locomotion: when we walk, friction between our shoes and the ground prevents our shoes from slipping backward.

II. Enhances fastening: friction between the bolt and the nut enhances their fastening ability. The friction between nails and wood also help the nail to hold woods together in firm position.

III. Blending: friction between the grinding stones helps in grinding pepper, tomatoes, this is also true of the friction between the two rough discs of the grinding machine.

IV. Stops motion: friction between the car tyre and the road helps to stop the motion of a moving car when the brake is applied.

V. Production of electric charge: when certain materials are robbed against each other, static electric charges is produced. This principle is applied in the Van de Graff generator.

VI. Ladder: when a ladder to be used to climb over a wall rest on the wall, friction between the foot of the ladder and floor prevent the foot of the ladder from slipping.

VII. Making of fire: matches sticks are ignited when they are robbed against the side of the matches’ box. Fire can also be made by striking two stones together.
https://youtu.be/5dXojGLpyCo

Disadvantages of friction (or undesirable effects of friction)
- Wearing: The thread pattern under your footwear soon wear out after a prolong use due to friction. This is also true of the thread on the tyre of cars and other automobile.

- Tearing/cutting: you can easily cut a piece of rope or cloth by robbing it repeatedly against the edge of the wall.

- Reduces efficiency of machines: all machines have efficiency less than 100% due to friction between their moving parts. Friction causes waste of useful energy, therefore it reduces the output of the machine.

- Generation of undesirable heat and noise: moving machine parts/machine itself soon becomes hot due friction and this may necessitate cooling of machine parts.
https://youtu.be/Gxjoy4Sj58E

Methods of reducing friction
Due to the disadvantages of friction mentioned above, it is often necessary to reduce friction in machines. This is possible through any of the following methods:
1. Lubrication: this is the use of certain substances (called lubricants) to reduce the effects of friction. Examples of lubricants includes, grease, oil,… many of which are petroleum products.

2. Streamlining: This involves shaping an object in such a way that when the object is moving against direction of the wind or liquid, the surface in contact is minimal. That is the reason why ships, aircraft and submarines are made or designed after that of fish.

3. Use of rollers/ball bearings: This involves the use of rollers , ball bearings, wheels to reduce the surface area in contact between two surfaces.

4. Use of belt/chain drive: This can also be used to prevent two surfaces in contact.

5. Smoothing/polishing: This reduces projections on the surface thus reducing friction.
https://youtu.be/M0W04bUSvAc

GENERAL EVALUATION:
1a. State three: (i) Laws of solid friction (ii) Advantages of friction (iii)
Disadvantages of friction (iv) methods of reducing friction

ASSIGNMENT:
1. Which of these is not a consequence of a force field?
A. weight B. magnetic force C. Reaction D. Electric force
2. The following are contact forces Except
A. tension B. reaction C. Friction D. Electric force
3. Which of the following about solid friction is/are correct?
i. Friction depends on the nature of the surfaces in contact.
ii. Friction depends on the area in contact
iii. Friction always acts in the direction of motion
A. i only B. i and ii only C. iii only D. i and iii only
4. Which of the following are contact forces?
i. force of tension ii. Force of friction iii. Magnetic force iv. Force of reaction
A. i, ii and iv B. i, ii and iii C. i, iii and iv D. ii, iii and iv
5. A wooden block of mass 1.6kg rests on a rough horizontal surface. If the limiting
frictional force between the block and the surface is 8N, calculate coefficient of friction
( g = 10m/s2). A. 0.6 B. 0.5 C. 0.3 D. 0.2

Essay
1. Explain the following terms (i) Force (ii) contact force (iii) force field

2. Define friction and state the laws governing solid friction

3. A body of weight 6N rest on a plane inclined at an angle of 300 to the horizontal (a) what force keeps it sliding down the plane? (b) what is the coefficient of friction

4. A 5kg mass on a horizontal platform accelerated at the rate of 0.1m/s2, when a horizontal
force of 10N is applied to it. Calculate the coefficient of friction between it and the platform
(g = 10m/s2).
5. A metal box of mass 4kg rests on the top of a metal surface. What force applied parallel to the
surface is required to
(i) just move the box?
(ii) move the box with an acceleration of 2m/s2?
Take the coefficient of friction between the box and the surface as 0.25 and
g = 10m/s2.
6. A force of 20N applied parallel to the surface of a horizontal table is just sufficient
to make a block of mass 4kg move on the table, calculate the coefficient of friction
between the block and the table ( g = 10m/s2).

PRE-READING ASSIGNMENT:
Senior secondary physics Bk 1 by Ndupu, okeke , ladipo. Topic circular motion.

ACTIVITY:
Differentiate between circular motion and rotational motion.

VECTOR & SCALAR QUANTITY, DISTANCE/DISPLACEMENT, SPEED/VELOCITY, ACCELERATION, DISTANCE/DISPLACEMENT –TIME GRAPH, SPEED/VELOCITY–TIME GRAPH
CONTENT:
 Scalar & Vector Quantity
 Distance & Displacement
 Speed & Velocity
 Acceleration & Retardation
 Distance/Displacement - Time Graph
 Speed/Velocity - Time Graph

https://youtu.be/Ix3htsNmSZY

SCALAR & VECTOR QUANTITY
A scalar quantity is defined as a quantity that has magnitude only but no direction. Typical examples of scalar quantities are time, distance, speed, temperature, volume, work, power, electric potential etc. A scalar quantity or parameter has no directional component, only magnitude. For example, the units for time (minutes, days, hours, etc.) represent an amount of time only and tell nothing of direction. Additional examples of scalar quantities are density, mass, and energy.

A vector quantity is defined as a quantity that has both magnitude and direction. Typical examples of vector quantities are velocity, displacement, acceleration, force, momentum, moment, electric field intensity etc. To work with vector quantities, one must know the method for representing these quantities. Magnitude, or “size” of a vector, is also referred to as the vector's "displacement." It can be thought of as the scalar portion of the vector and is represented by the length of the vector. By definition, a vector has both magnitude and direction. Direction indicates how the vector is oriented relative to some reference axis, as shown in Figure 1. Using north/south and east/west reference axes, vector "A" is oriented in the NE quadrant with a direction of 45 north of the o EW axis. Giving direction to scalar “A" makes it a vector. The length of “A” is representative of its magnitude or displacement.



https://youtu.be/Pj8Zh0A-uLU

https://youtu.be/iLB_4Wu2QOg

Distance & Displacement
Distance is the gap or space between two points, measured in meters (m).It is a scalar quantity & can be calculated mathematically as;
Distance = Average speed x time taken ……………………………………..1.

Displacement is distance in a specified direction, measured in meters (m). It is a vector quantity & can be calculated mathematically as;
Displacement = Average x time taken ………………………………………..2.

Speed & velocity
Speed :the rate at which a body covers a distance is called the speed of the body. Thus

Speed = distance/Time ………………………………….3.

The S.1 unit of speed is meter per second (ms-1)
When a body covers equal distance in equal time intervals, no matter how small the time interval may be, it is said to be a uniform speed or constant speed
Velocity is defined as the rate of change of displacement with time. It is also the rate of change of distance in a specified direction. The S.1 unit of velocity is meter per second (ms-1). In everyday language, the words velocity and speed are often used interchangeably. In the study of motion it is necessary to distinguish between the two. In speed, no direction is specified, but in velocity it is necessary to specify direction.
When a body moves with equal displacement in equal time interval, no matter how small the time interval may be, the velocity is said to be a uniform velocity or constant velocity.

Velocity = Displacement/Time……………………………………….4

Acceleration & Retardation
Acceleration is defined as the increasing rate of change of velocity. It is measured in m/s2.

Acceleration (a) = Increasing Velocity change/Time taken ……………………………………5.

When the velocity of a moving body increases by equal amount in equal intervals of time, no matter how small the time intervals may be, it is said to move with uniform acceleration.

Retardation is defined as the decreasing rate of change of velocity. It is measured in m/s2.It is also known as deceleration or negative acceleration

Retardation (ar) = Decreasing Velocity Change/Time Taken ………………………………6.

https://youtu.be/un2BJgVL2-I

EQUATION OF UNIFORMLY ACCELERATED MOTION

S = (v+u)/2t ………………………………………………………7

v = u + at ……………………………………………………….8

v² = u²+ 2aS ……………………………………………………….9

S = ut + ½ at² ……………………………………………………….10

Equations (7) to (10) are called equations of uniformly accelerated motion and could be used to solve problems associated with uniformly accelerated motion
where u- initial velocity( m/s), v – final velocity (m/s), a – acceleration (m/s2), s – distance covered and t – time (m)

Example - A car moves from rest with an acceleration of 0.2mls2 . Find its velocity when it has moved a distance of 50m
Solution:
a = 0.2mls² , S = 50m, u = 0m/s , v = ?
v² = u² + 2 as
v² = 0² + (2x0.2x50) = 20
v = √20 m/s


https://youtu.be/UYS5fFMd8cM

EVALUATION
1. State the differences & similarity between speed & velocity 2.A car has a uniform velocity of 108km/hr. How far does it travel in ½ minute?


Distance/Displacement- Time Graph
If the body is moving with uniform velocity, the velocity is equal to the slope or gradient of the straight line graph.


If the velocity is non – uniform, the velocity at a point is the gradient or slope of the tangent at that point.


Speed/Velocity - Time Graph
Speed/velocity–graph is more useful than distance/displacement-time graph because it gives additional information about the motion performed by the body. Such information include acceleration, retardation, total distance covered & average speed or velocity
Example - A car starts from rest and accelerates uniformly until it reaches a velocity of 30mls after 5 seconds. It travels with uniform velocity for 15 seconds and is then brought to rest in 10s with a uniform retardation. Determine (a) the acceleration of the car (b) The retardation (c) The distance covered after 5s (d) The total distance covered (use both graphical and analytical method)
The velocity – time diagram for the journey is shown above, from this diagram


b. the retardation = slope of BC = CB / CD
= (0-30) / (30-20) = -30/10
= -3mls2 (the negative sign indicate that the body is retarding)

c. Distance traveled after 5s = area of A E O
= ½ x b x h
= ½ x 5 x 30
= 75m
d. Total distance covered = area of the trapezium OABC
= ½ (AB + OC) AE
= ½ (15 + 30) 30
= 675m.
Using equations of motion.
a) U = O, V = 3, t = 5
V = u + t
a = v-u/t = 30 – 0 / 5
a = 30/5 = 6ms-2
b) a o in
a = v – u / t = 0-30 / 10
a = -3 mls2

(c) S = ( u + v) 5
2
= 30 / 2 x 5
= 75m
(d) To determine the total distance travelled we need to find the various distance for the three stages of the journey and then add them.
for the 1st part S= 75m from (c)
for the 2nd stage where it moves with uniform velocity.
S = vt
= 30 x 15
= 450m
for the last stage S = ½ (u + v) t
= ½ (30 + 0) 10
= 150m.
Total distance = 75 + 450 + 100 = 675m.

EVALUATION
1. A train slows from 108km/hr with uniform retardation of 5mls2. How long will it take to reach 18km/hr and what is the distance covered.
2. Why is velocity – time more useful than displacement time graph?

Reading Assignment - www.google.com (click on google search, type “ distance & displacement ”, click on search) & New school physics by M.W.Anyakoha,Ph D Pg 14 – 18

ASSIGNMENT
1. A body accelerates uniformly from rest at the rate of 3ms-2 for 8 seconds. Calculate the distance covered. (a) 12m (b) 24m (c) 48m (d) 96m
2 A particle starts from rest and moves with a constant acceleration of 0.5 ms-2 . The distance covered by the particle in 105s is (a) 2.5m (b) 5.0m (c) 25.0m (d) 50.0m
3.A car moving with speed 90kmh-1 was brought uniformly to rest by the application of brakes in 10s. How far did the car travel after brakes were applied (a)120m(b) 150m (c) 125m(d)15km
4. A body starts from rest and accelerates uniformly at 5mls2 until it attains a velocity of 25mls. Calculate the time taken to attain this velocity. (A) 2.5s (b) 5.0s (c) 10s (d) 125s
5. The distance traveled by a particle starting from rest is plotted against the square of the time elapsed from the commencement of motion. The resulting graph is linear. The slope of this graph is a measure of (a) initial displacement (b) initial velocity (c) acceleration (d) half of acceleration

THEORY
1. When is a body said to be moving with uniform speed?
2. A motor car accelerates uniformly from rest at 5mls2 until it reaches a speed of 20ms-1.zbdgv It travels at this speed for 4 seconds. The brakes are then applied and the car comes to rest with uniform retardation in a further 8 seconds. Draw a sketch showing a graph of speed against time. Use your graph to determine
(a)How far the car travels after the brakes are applied?
(b)The time during which the car accelerated
(c)Total distance covered
(d) Average speed



Concept of distance, speed, velocity and uniform speed/velocity
https://youtu.be/Jyiw6KkedDY

i. DISTANCE: This is the separation or space between two points. It is measured in meters and it is a scalar quantity.

ii. DISPLACEMENT: It is distance in a specified direction. It is a vector quantity and it is measured in meters.

iii. SPEED: It is the rate of change of distance moved with time. The unit is m/s and it is a scalar quantity.

Speed = distance/time

(a) UNIFORM SPEED: It is obtained if the rate of change of distance with time is constant or when a body travels equal distances in equal time intervals.

(b) AVERAGE SPEED: If the speed is not constant, The average speed is taken. Average speed is the total distance travelled divided by the total time taken.

Average speed = (Total distance covered)/(Total time taken)

(c) INSTANTANEOUS SPEED: It is the actual speed of a body at any instant.

iv. VELOCITY: It is the rate of change of displacement with time. The unit is m/s. It is a vector quantity.

Velocity = displacement/time

UNIFORM VELOCITY: It occurs when the rate of change of displacement with time is constant or when a body travels equal displacement in equal time interval.

https://youtu.be/Xo3KBoEMDEo

https://youtu.be/QaU9jMHh7gE

EVALUATION:
1. Define speed, velocity and uniform velocity.
2. Differentiate between velocity and speed.


Calculations on speed and velocity
https://youtu.be/EGqpLug-sDk

1. A car covers a distance of 60km in half an hour. What is the average speed of the car in
(a). km/hr (b) m/s
Solution:
(a) time = ½ hour = 0.5 hour

Average speed = (Total distance covered)/(Total time taken) = 60/0.5 = 120km/h

(b) convert km/hr to m/s

1 km/h = 1000/(60×60) m/s

1km = 1000m
1hr = 3600s

120km/h = 120×1000/(60×60) = 3.33m/s


2. A car travelled to Lagos a distance of 150m in 100 seconds. Calculate his average speed.

Average speed = (Total distance covered)/(Total time taken)=150/100=1.5m/s

3. A car covers 1500m in 10 secs. What is the speed in km/hr?

Speed = distance/time=1500/10=150m/s

Convert to km/hr

1 km/h = 1000/(60×60) m/s

1 m/s =(60×60)/1000 km/h

150m/s = (150×60×60)/1000=540km/h
https://youtu.be/P0UYC8S4kUI

EVALUATION:
1. Convert 144km/h to m/s.
2. A car covers a distance of 40m in 2 sec. What is his speed in km/h?



Distance-time graph, Displacement-time graph
If the body is moving with uniform velocity, the velocity is equal to the slope or gradient of the straight line graph.


If the velocity is non – uniform, the velocity at a point is the gradient or slope of the tangent at that point.


TRAVEL GRAPH: It is the graphical representation of the motion of a body. There are Distance-time graph, Displacement-time graph and Velocity-time graph.


(a) DISTANCE-TIME GRAPH FOR UNIFORM MOTION




(b) DISTANCE-TIME GRAPH FOR NON UNIFORM MOTION


(c) DISPLACEMENT-TIME GRAPH FOR UNIFORM VELOCITY


(d) DISPLACEMENT-TIME GRAPH FOR NON UNIFORM VELOCITY




Position, Distance and Displacement
1. Concept of position, Concept of distance and displacement
2. Distinction between distance and displacement.

CONCEPT OF POSITION
The position of an object is its location in space. It is usually expressed in relation to a reference point. To locate an object in space, a co-ordinate system is needed. It is usually a mathematical construct with co-ordinates.
A coordinate system could be two-dimensional as in P(x,y) or three dimensional as in P(x,y,z).

CONCEPT OF DISTANCE & MEASUREMENT
Distance can be define as a physical measurement of length between two points. It does not take into consideration the direction between the two points it measures; hence, it is a scalar quantity. This therefore means that distance has only magnitude but no direction. E.g, 10km.
Distance could be measured using instruments like measuring tape, ruler, venier calliper, micrometer screw gauge, etc.

CONCEPT OF DISPLACEMENT
Displacement is defined as the distance travelled or moved in a specific direction. It takes into consideration the direction between the different points it seeks to measure; hence, displacement is a vector quantity. Thus, it has both magnitude and direction. E.g, 10km due east. The ‘10km’ is the magnitude (or value), while ‘due east’ is the direction.
Both distance and displacement have the same S.I. unit, metre (m). They could also be expressed in kilometre (km), miles, etc.


https://youtu.be/o1NEJRf2zng

Evaluation:
1. Define distance.
2. What is displacement?
3. State the SI unit of distance.


Distinction between distance and displacement
We need to understand the concepts of distance and displacement. Distance is the gap between two points with no regard to direction. On the other hand, displacement is distance covered in a particular direction. Therefore distance is a scalar quantity while displacement is a vector quantity. The only similarity between distance and displacement is that they have the same unit. Let us consider a girl who walked and covered a distance of 20m between two points A and B as shown in fig 1 and fig 2 below


The two activities of the girl are not exactly the same. In both figs. 1 and 2, she covered a distance of 20m. If we are only interested in the distance covered, we can conclude that she did the same thing in fig. 1 and 2 i.e she covered the same distance (20m). If we are interested in both distance and direction, then her displacement in fig. 1 and 2 are not the same. In fig.1 she covered a distance of 20m due east while in fig.2, she covered a distance of 20m due west. From these, we see that distance is a scalar quantity because it has magnitude only while displacement is a vector quantity because it has both magnitude and direction.
https://youtu.be/9z-EIcdJ9VY

Speed/Velocity - Time Graph
Speed/velocity–graph is more useful than distance/displacement-time graph because it gives additional information about the motion performed by the body. Such information include acceleration, retardation, total distance covered & average speed or velocity


Example - A car starts from rest and accelerates uniformly until it reaches a velocity of 30mls after 5 seconds. It travels with uniform velocity for 15 seconds and is then brought to rest in 10s with a uniform retardation. Determine (a) the acceleration of the car (b) The retardation (c) The distance covered after 5s (d) The total distance covered (use both graphical and analytical method)
The velocity – time diagram for the journey is shown above, from this diagram


a. the acceleration = slope of OA
= AE / EO
= (30-0) /(5-0)=30/5
= 6mls2

b. the retardation = slope of BC = CB / CD
= (0-30) / (30-20) = -30/10
= -3mls2 (the negative sign indicate that the body is retarding)
c. Distance traveled after 5s = area of A E O
= ½ x b x h
= ½ x 5 x 30
= 75m
d. Total distance covered = area of the trapezium OABC
= ½ (AB + OC) AE
= ½ (15 + 30) 30
= 675m.
Using equations of motion.
a) U = O, V = 3, t = 5
V = u + t
a = v-u/t = 30 – 0 / 5
a = 30/5 = 6ms-2
b) a o in
a = v – u / t = 0-30 / 10
a = -3 mls2

(c) S = ( u + v) 5
2
= 30 / 2 x 5
= 75m
(d) To determine the total distance travelled we need to find the various distance for the three stages of the journey and then add them.
for the 1st part S= 75m from (c)
for the 2nd stage where it moves with uniform velocity.
S = vt
= 30 x 15
= 450m
for the last stage S = ½ (u + v) t
= ½ (30 + 0) 10
= 150m.
Total distance = 75 + 450 + 100 = 675m.

Using equations of motion.
a) U = O, V = 3, t = 5
V = u + t
a = v-u/t = 30 – 0 / 5
a = 30/5 = 6ms-2
b) a o in
a = v – u / t = 0-30 / 10
a = -3 mls2

(c) S = ( u + v) 5
2
= 30 / 2 x 5
= 75m
(d) To determine the total distance travelled we need to find the various distance for the three stages of the journey and then add them.
for the 1st part S= 75m from (c)
for the 2nd stage where it moves with uniform velocity.
S = vt
= 30 x 15
= 450m
for the last stage S = ½ (u + v) t
= ½ (30 + 0) 10
= 150m.
Total distance = 75 + 450 + 100 = 675m.
https://youtu.be/TG2Y2MDx-zE

EVALUATION
1. A train slows from 108km/hr with uniform retardation of 5mls2. How long will it take to reach 18km/hr and what is the distance covered.
2. Why is velocity – time more useful than displacement time graph?
3. A boy moved continuously for 40secs and covered the following distances in the times stated below:
Distance (m) 200 400 600 800
Time (second) 10 20 30 40
i. Draw the distance-time graph and calculate the speed.
ii. state whether or not the speed is uniform. Give reason(s) for your answer
4. A body accelerates uniformly from rest at the rate of 3ms-2 for 8 seconds. Calculate the distance covered. (a) 12m (b) 24m (c) 48m (d) 96m
5. A particle starts from rest and moves with a constant acceleration of 0.5 ms-2 . The distance covered by the particle in 105s is (a) 2.5m (b) 5.0m (c) 25.0m (d) 50.0m
6.A car moving with speed 90kmh-1 was brought uniformly to rest by the application of brakes in 10s. How far did the car travel after brakes were applied (a)120m(b) 150m (c) 125m(d)15km
7. A body starts from rest and accelerates uniformly at 5mls2 until it attains a velocity of 25mls. Calculate the time taken to attain this velocity. (A) 2.5s (b) 5.0s (c) 10s (d) 125s
8. The distance traveled by a particle starting from rest is plotted against the square of the time elapsed from the commencement of motion. The resulting graph is linear. The slope of this graph is a measure of (a) initial displacement (b) initial velocity (c) acceleration (d) half of acceleration


ASSIGNMENT
1. A body accelerates uniformly from rest at the rate of 3ms-2 for 8 seconds. Calculate the distance covered. (a) 12m (b) 24m (c) 48m (d) 96m
2 A particle starts from rest and moves with a constant acceleration of 0.5 ms-2 . The distance covered by the particle in 105s is (a) 2.5m (b) 5.0m (c) 25.0m (d) 50.0m
3.A car moving with speed 90kmh-1 was brought uniformly to rest by the application of brakes in 10s. How far did the car travel after brakes were applied (a)120m(b) 150m (c) 125m(d)15km
4. A body starts from rest and accelerates uniformly at 5mls2 until it attains a velocity of 25mls. Calculate the time taken to attain this velocity. (A) 2.5s (b) 5.0s (c) 10s (d) 125s
5. The distance traveled by a particle starting from rest is plotted against the square of the time elapsed from the commencement of motion. The resulting graph is linear. The slope of this graph is a measure of (a) initial displacement (b) initial velocity (c) acceleration (d) half of acceleration
6. During the same time interval, it is observed that a train travels the same distance as
does a lorry. The two vehicles therefore have the same
A. uniform acceleration B. instantaneous velocity C. initial velocity D. average speed.
7. The time rate of change of displacement is known as
A. speed. B. velocity C. impulse. D. acceleration.
8. The slope of a straight line displacement-time graph indicates the
A. distance traveled B. uniform velocity
C. uniform acceleration D. acceleration at an instant.
9. A car moves with a speed of 30m/s. Calculate the distance travelled in 30s.
A. 30m B. 60 C. 450m D. 900m
10. The speed of an object in rectilinear motion can be determined from the
A. Area under a velocity-time graph. B. Area under a distance-time graph.
C. Slope of a distance-time graph D. Slope of a velocity-time graph.

THEORY
1. When is a body said to be moving with uniform speed?

2. A motor car accelerates uniformly from rest at 5mls2 until it reaches a speed of 20ms-1.zbdgv It travels at this speed for 4 seconds. The brakes are then applied and the car comes to rest with uniform retardation in a further 8 seconds. Draw a sketch showing a graph of speed against time. Use your graph to determine
(a)How far the car travels after the brakes are applied?
(b)The time during which the car accelerated
(c)Total distance covered
(d) Average speed

3. Using a suitable diagram, explain how the following can be obtained from a Distance-time graph or Displacement-time graph.
i. Speed ii. Velocity iii. Instantaneous speed

4. A Car is travelling with a uniform velocity of 72km/h. What distance does he cover in 20s?

5. A car travels with a constant velocity of 45km/h for 10s. What distance does it cover in this time?

READING ASSIGNMENT:
New school physics by M.W. Anyakoha,Ph D Pg 14 – 18

Evaluation:
1. Differentiate distance from displacement in two ways.
2. Why is 5km due east a displacement?

GENERAL EVALUATION:
1. Discuss the concept of distance and displacement.
2. Enumerate the measuring devices for distance.

ASSIGNMENT:
1. which of the following is displacement?
A. 25cm
B. 43inches
C. 52mm due south
D. 88km
2. One of the following is not a measuring device for distance.
A. Vernier calliper
B. Micrometer screw gauge
C. Rule
D. Spring balance
3. A position in two dimensional co-ordinate system has a value P(-2,5). What is the x –coordinate of the point?
A. 5 unit
B. -2 unit
C. 3 unit
D. 7 unit

Essay:
Explain the distinction between distance and displacement.

READING ASSIGNMENT
Read up the topic: ‘’Motion and types of motion’’ in the following text books.
i. Senior Secondary School Physics by P.N. Okeke et al.
ii. New School Physics for Senior Secondary Schools by Anyakoha, M.W.

TOPIC: CIRCULAR MOTION

CONTENT: 1. Meaning of circular motion
2. Definition of terms
i. Angular velocity ii. Tangential velocity iii. Centripetal acceleration
iv. Centripetal force v. Centrifugal force vi. Period vii. Frequency
3. Calculations on circular motion.

Meaning of circular motion
Circular motion is the motion of a body around a cicle. The simplest form of circular motion is the uniform circular motion, where the speed is constant but the direction is changing.
In physics, circular motion is rotation along a circle: a circular path or a circular orbit. It can be uniform, that is, with constant angular rate of rotation, or non-uniform, that is, with a changing rate of rotation. The rotation around a fixed axis of a three-dimensional body involves circular motion of its parts. We can talk about circular motion of an object if we ignore its size, so that we have the motion of a point mass in a plane. For example, the center of mass of a body can undergo circular motion. Examples of circular motion are: an artificial satellite orbiting the Earth , a stone which is tied to a rope and is being swung in circles (cf. hammer throw), a racecar turning through a curve in a race track, an electron moving perpendicular to a uniform magnetic field, a gear turning inside a mechanism. Circular motion is accelerated even if the angular rate of rotation is constant, because the object's velocity vector is constantly changing direction. Such change in direction of velocity involves acceleration (centripetal acceleration is directed towards the center of the circular path)of the moving object by a Centripetal Force, which pulls the moving object towards the center of the circular orbit or that inward force required to keep an object moving with a constant speed in a circular path. Without this acceleration, the object would move in a straight line.

Centrifugal Force is often confused with centripetal force. Centrifugal force is a force that act in opposite direction to the centripetal force. Centrifugal force is an outward force associated with curved motion, that is, rotation about some (possibly not stationary) center.


https://youtu.be/1cL6pHmbQ2c

Consider a body moving in a circular path center O with a constant speed.
1. The direction at different points are not the same i.e the direction at A is different from the
direction at B. This leads to a change in velocity.
2. This difference in velocity produces an acceleration directed towards the center of the
circle. This acceleration is called centripetal acceleration.
3. Since there is an acceleration, there is a force directed towards the center of the circle
called centripetal force.
4. In addition to the centripetal force, there is an equal and opposite force which acts
outwards from the center called the centrifugal force. These two forces enable the
object to move in the orbit.

Definition of terms used in circular motion.

1. Angular velocity (ω): The ratio of the angle turned through to the elapsed time.


2. Tangential velocity(V): This is the linear velocity in a tangential direction to the
circumference.


3. Centripetal acceleration (a): It is the acceleration of a body moving in a uniform
circular motion and directed towards the center.


https://youtu.be/SQX22VVmRPs

4. Centripetal force (F): It is defined as that inward force that is always directed towards the centre required to keep an object moving with a constant speed in a circular path. The unit is Newton


https://youtu.be/KvCezk9DJfk

5. Centrifugal force: This force is equal in magnitude to the centripetal force but opposite in
direction. (it is always directed away from the centre of the circle)

F=-(mv2)/r or F = - rω2

6. Period (T): This is the time taken for a body to complete one revolution round the circle.

Displacement = 2πr
Time = T
Velocity = v

v = displacement/time=2πr/T

T =2πr/v


7. Frequency (f): It is the number of revolutions in one second.

f =1/T

T =v/2πr

The unit is Hertz or per seconds. (Ie Hz or s-1)

https://youtu.be/y2FmgoOht7Y

Calculations on circular motion

Question 1: A stone of mass 2kg is attached to the end of an inelastic string and whirled round two times in a horizontal circular path of radius 3m in 3 sec, find:
i. Angular velocity
ii. Linear velocity
iii. Centripetal acceleration
iv. Centripetal force
v. Centrifugal force

SOLUTION

1. ω= (Angular displacement)/time = θ/t

Where θ is the angular displacement and ω is the angular velocity

θ = 360 X 2 = 720º (ie two times)
π = 180º
θ = 4π rad

ω= 4π/3 = 1.33πrad/sec

2. v = rω
= 3 x 1.33π = 3.99 π m/s

3.

4. F=ma=2 x 5.31π2=10.62π^2 N

5. F=-(mv2)/r= -10.62π2 N

https://youtu.be/PjfBTPmodvc

GENERAL EVALUATION

1. Explain the following terms (i) Angular velocity (ii) Tangential velocity
(iii) centripetal acceleration
2. A body of mass 10kg is attached to the end of an inelastic thread and whirled round in a
circular path of radius 0.3m, if the body makes a complete revolution in 3 sec find
a. Angular velocity
b. linear velocity
c. centripetal acceleration
d. centripetal force
e. centrifugal force

ASSIGNMENT:
:
1. A body moves with a constant speed but has an acceleration. This is possible if it
A. moves in a straight line.
B. moves in a circle.
C. is oscillating.
D. has a varying acceleration.
2. The angular speed of an object describing a circle of radius 4m with a linear constant speed of
10m/s is
A. 40.0rad/s B. 14.0rad/s C. 2.50rad/s D. 1.58rad/s
3. The relationship between linear velocity and angular velocity is
A. v = rw. B. v = r2w C. v = w2r. D. v = w/r.
4. A stone tied to a string is made to revolve in a horizontal circle of radius 4m with an angular speed
for 2 radians per second. With what tangential velocity will the stone move off the circle if the
string cuts?
A. 16m/s B. 8.0m/s C. 6.0m/s D. 0.5m/s
5. An object of mass 0.40kg attached to the end of a string is whirled round in a horizontal circle of
radius 2.0m and a constant speed of 8m/s. Calculate the angular velocity of the object.
A. 0.8 rad/s B. 16.0 rad/s C. 2.0 rad/s D. 8.0 rad/s
6. A body moving in a circle at constant speed has
i. a velocity tangential to the
circle.
ii. a constant kinetic energy.
iii. an acceleration directed towards the circumference of the circle. Which of the statements
above are correct?
A. i and ii only B. ii and iii only C. i and iii only D. i,ii and iii

ESSAY
Explain the fact that a particle moving along a circular path with uniform speed has an
acceleration.
An object of mass 0.50kg at the end of an inelastic string is whirled in a horizontal circle of radius 2.0m with a constant speed of 10m/s. Determine its angular velocity.
A particle moves in a circular orbit of radius 0.02m, Determine its frequency if its speed is
0.88m/s.
A beam of electrons travelling at 1.0 x 108m/s is caused to describe a circular arc of radius
0.40m by the application of a magnetic field perpendicular to its path. Determine the
acceleration of each electron.

PRE-READING ASSIGNMENT:
Senior secondary physics Bk 1 by Ndupu, okeke , ladipo. Topic linear motion.

ACTIVITY: Differentiate between distance and displacement

TOPIC : DENSITY & RELATIVE DENSITY
CONTENT
 Definition of Density
 Determination of Density
 Relative Density
 Determination of Relative Density of Solids & Liquid

Definition of Density
The density of a substance is the mass per unit volume of the substance.
Density = mass of a given substance/Volume of the substance
Density is scalar quantity& measured in kgm-3 (kilogram per cubic meter)
https://youtu.be/NJhxwlVKong

Determination of Density
The determination of density involves the determination of a mass and a volume. The mass can be found by weighing. The density of a substance can be determined using a graduated density bottle.

Relative Density
Relative density is also known as specific gravity. Relative density of a substance is defined as the density of the substance per density of water.

R.D = Density of the substance/Density of water

R.D is also equal to the ratio weight of a substance to weight of an equal volume of water. As weight is proportional to mass

R.D = mass of substance/mass of equal volume of water
https://youtu.be/pgGzVdau1Bw

Determination of R.D of Solid (e.g. Sand)
Mass of empty bottle = m1

Mass of bottle + sand = m2

Mass of bottle + sand + water = m3

Mass of bottle + water only= m4

Mass of sand = m2 – m1

Mass of water added to sand = m3 –m2

Mass of water filling the bottle = m4 – m1

Mass of water having the same volume as sand = (M4-M1) – (M3-M2)

Relative density = Mass of sand/Mass of equal volume of water


https://youtu.be/zs2yEvNsyl8

https://youtu.be/omRMpPYh_vw

EVALUATION
1. Differentiate between density & relative density
2. A glass block of length 100cm width 60cm and thickness 20cm has a mass of 4000g. calculate the density of the glass



Determination of R.D of Liquid
mass of empty density bottle = m1
mass of bottle filled with water = m2
mass of bottle filled with liquid = m3

R.D of liquid = m3 – m1/m2 – m1

Example - A glass block of length 10cm width 8cm and thickness 2cm has a mass of 400g. calculate the density of the glass.
Solution
l = 10cm = 0.1m, b = 8cm = 0.08cm, h = 2cm = 0.02m, m = 400g = 0.4kg

V = lbh = 0.1 x 0.08 x 0.02 = 0.00016m3

Density = Mass (m) /Volume (V) = 0.4/0.00016 = 2500kgm3


'Example - Calculate the volume in m3 of a piece of wood of mass 500g and density 0.76 gcm-3

mass of the wood = 500g

density = 0.76gcm-3

volume = ?

volume = mass / density= 500

0.76

volume = 658cm3 = 6.58 x 10-4 m3

Example - An empty relative density bottle has a mass of 15.0g. when completely filled with water, its mass is 39.0g. what will be its mass if completely filled with acid of relative density 1.20?

NB : The hydrometer is an instrument used to measure the relative density of liquids

https://youtu.be/md-Qk_g9NEo
EVALUATION
1. The volume of an object is 1.5x10m and its mass is 3.0x10 kg. Calculate its density.
2. A relative density bottle weighs 20g when empty, 80g when filled with water & 100g when filled with liquid. Find the relative density of the liquid
Reading Assignment - New school physics by M.W.Anyakoha,Phd.Pg 152 – 157

ASSIGNMENT
1. Find the density of a substance, if the mass of the substance is 150,000g and the dimension is 20m by 10m by 500cm.
a. 0.5kg1m b. 0.24kg1m c. 1.50kg/m.
2. What is the height of a cylindrical iron if the density is 7900kg/m3? The mass is 700kg and the radius is 0.1m.
a. 2.918m b. 2.819m c. 3.418m.
3. Density is defined as the ratio of mass to-------
a. Pressure b. area c. volume
4. Relative density is the ratio of mass of a substance to------
a. Mass of 2an equal volume of water b. volume of a substance c. density
5. The S.I unit of density is ------------- a. g1cm b. kg1m c.kg1m .

Theory
1. Alcohol of mass 33.2g and density 790kg1m is mixed with 9g of water. What is the density of the resulting mixture?(density of water is 1g1cm ).
2. Define relative density of liquid.

TOPIC: PRESSURE , ARCHIMEDES’ PRINCIPLES, UPTHRUST & LAWS OF FLOATATION
CONTENT :
 Pressure
 Archimedes’ Principles & Upthrust
 Laws of Floatation

Pressure
Pressure is defined as the perpendicular force per unit area acting on a surface. It is a scalar quantity & measured in N/m2 or Pascal (pa).It can also be defined as the force per unit area, which is calculated by taking the total force and dividing it by the area over which the force acts. Force and pressure are related but different concepts. A very small pressure, if applied to a large area, can produce a large total force.

P = F/A ……………………………..1.

Where P-pressure, F- force (N) & A-area (m2)

NB: 1 bar = 105 N/m2 = 105 pa

Example – A force of 40N acts on an area of 5m2. What is the pressure exerted on the surface?
Solution
F = 40N, A = 5m2, P = ?
P = F/A = 40/5 = 8pa
https://youtu.be/zlLpKzPz84Q

Pressure in Liquid
Pressure in liquid has the following properties
1. Pressure increases with depth
2. Pressure depend on density
3. Pressure at any point in the liquid acts equally in all direction
4. Pressure at all points at the same level within a liquid is the same
5. It is independent of cross-sectional area
P = hℓg ……………………..2.
where p-pressure, h-height & g-acceleration due to gravity

Pascal's principle : Pressure applied to an enclosed fluid is transmitted undiminished to every part of the fluid, as well as to the walls of the container. The operation of the hydraulic press & the car brakes system is based on this principle.


https://youtu.be/sQ-Kz3xK7ZI

EVALUATION
1. Define pressure
2.State five characteristics of pressure in liquid



Archimedes' Principle & Upthrust
Archimedes’ principle is a law that explains Buoyancy or Upthrust. It states that When a body is completely or partially immersed in a fluid it experiences an Upthrust, or an apparent loss in weight, which is equal to the weight of fluid displaced. According to a tale, Archimedes discovered this law while taking a bath. An object experiences Upthrust due to the fact that the pressure exerted by a fluid on the lower surface of a body being greater than that on the top surface, since pressure increases with depth. Pressure, p is given by p = hρg, where:
h is the height of the fluid column
ρ (rho) is the density of the fluid
g is the acceleration due to gravity

https://youtu.be/_p-hwElkrlk

Let us confirm this principle theoretically. On the figure on the left, a solid block is immersed completely in a fluid with density ρ. The difference in the force exerted, d on the top and bottom surfaces with area a is due to the difference in pressure, given by

d = h2aρg – h1aρg = (h2 – h1)aρg

But (h2– h1) is the height of the wooden block. So, (h2 – h1)a is the volume of the solid block, V.

d = Vρg

Upthrust = Vρg

In any situation, the volume of fluid displaced (or the volume of the object submerged) is considered to calculate Upthrust, because (h2 – h1) is the height of the solid block only when it is completely immersed. Furthermore, the pressure difference of the fluid acts only on the immersed part of an object.
Now, moving back to Vρg. Since V is the volume of fluid displaced, then the product of V, ρ and g is the weight of the fluid displaced. So, we can say that
Upthrust = Weight of the fluid displaced

Compare this conclusion with the statement above summarizing Archimedes' principle. Are they the same? Well, not totally. The “apparent loss in weight” was not mentioned.


In the figure on the left, there are arrows on the top and bottom of the solid block. The downward arrow represent the weight of the block pulling it downwards and the upward arrow represent the Upthrust pushing it upwards. If one were to measure the weight of the solid block when it is immersed in the fluid, he will find that the weight of the block is less than that in air. There is a so-called “apparent loss in weight”, because the buoyant force has supported some of the block’s weight.

NB:
1. When an object is wholly immersed, it displaces its volume of fluid. So up thrust = weight of fluid displaces. = Volume of fluid displaced x its density x g = volume of object x density of fluid x g

2 When the object is partially immersed e.g. if ¼ of its volume (v) is immersed then the up thrust is given by v/4 x density of liquid x g.

Determination of Relative Density by Archimedes’ Principle
1. Relative density of solid
The body is weighed in air w1, and then when completely immersed in water w2



2. Relative density of liquid
A solid is weighed in air (w1), then in water (w2) and finally in the given liquid (w3)



Example - The mass of a stone is 15g when completely immersed in water and 10g when completely immersed in liquid of relative density 2.0 . What is the mass of the stone in air?



Law of Floatation
A floating object displaces its own weight of the fluid in which it floats or an object floats when the upthrust exerted upon it by the fluid is equal to the weight of the body. When an object is floating freely (i.e. neither sinking nor moving vertically upwards), then the upthrust must be fully supporting the object’s weight. We can say
Upthrust on body = Weight of floating body. By Archimedes’ principle,
Upthrust on body = Weight of fluid displaced. Therefore, Weight of floating body = Weight of fluid displaced
This result, sometimes called the “principle of floatation”, is a special case of Archimedes’ principle

https://youtu.be/16HDJNoXQII

https://youtu.be/4tnPfnuY42I

https://youtu.be/ROXYr_SzNW4

EVALUATION
1. State the law of floatation.
2. State Archimedes’ principle.

Reading Assignment - www.google.com (click on google search, type “Archimedes’ principle”, click on search) & New sch. physics by M.W.Anyakoha,Phd. Pg 348 – 358, 150 - 152

https://youtu.be/sKGq-94KMUY

ASSIGNMENT
1. A force of 40N acts on an area of 10m2. What is the pressure exerted on the surface? (a) 8pa (b) 4pa (c) 400pa (d) 10pa
2. What is the height of a cylindrical iron if the density is 7900kglm3 the mass is 700kg and the radius is 0.1m [a) 2.918cm 2.819m © 3.418m
3. Density is defined as the ratio of mass to (a) pressure (b) area (c) volume
4. Relative density is the ratio of mass of a substance to ------------ (A) mass of equal volume of water (b) volume of a substance (c) density
5. Pressure can be measured in the following except (a) bar (b) N/m2 (c) pascal (d) Nm2
Theory
1. Differentiate between force & pressure
2. What is the pressure due to water at the bottom of a tank which is 20cm deep and is half of water? (Density of water = 103kg/m3 and g = 1om/s2 )