PHYSICS SSS1 FIRST TERM COMPRESSED NOTE

PHYSICS SS 1 FIRST TERM

                                                             

WEEK 1

TOPIC: INTRODUCTION TO PHYSICS

REFERENCE BOOK: NEW SCHOOL PHYSICS FOR SENIOR SECONDARY SCHOOL BY M.W. AYANKOHA

LEARNING OBJECTIVES: by the end of the lesson, learners should be able to 

1. Explain the concept of physics, states the importance of physics and state the branches of physics.

2. Differentiate between fundamental and derived quantities and state their examples.

3. Able to use various instruments to measure physical quantities.

4. Explain the concept of time

WHAT IS PHYSICS?

Physics is the branch of science concerned with the nature and properties of matter and energy. The subject matter of physics includes mechanics, heat, light and other radiation, sound, electricity, magnetism, and the structure of atoms. Physics can therefore be defined as a branch of science that deals with the properties of matter and energy and the relationship between them. It also tries to explain the material world and the natural

Phenomena of the universe. A person who studies and deals with physics is known as a physicist.

IMPORTANCE OF STUDYING PHYSICS

1. Physics helps us to understand how the world around us works, from bottle openers, light bulbs and cell phones to muscles, lungs and brains; from paints, musical instruments and movements, to cameras, cars and buildings; from earthquakes, tsunamis and hurricanes to thunder and lightning, and from our DNA genes to the earth formation.

2. Physics helps us to organize the universe. It deals with fundamentals and helps us see the connections between seemly disparate phenomena. It gives us powerful tools to help us express our creativity, to see the world in new ways and then to change it.

Physics provides quantitative and analytical skills needed for analyzing data and solving problems in science, engineering and medicine, as well as in economics, finance, management, law and policy.

3. Physics is the basis for most modern technology and the tools and instruments used in scientific, engineering, medical research and development. Manufacturing is dominated by physics-based technology.

4. Physics helps you to help others: Physics is an important part of the Medical Field. Medicine without Physics technology would be impossible.

IMPORTANCE OF PHYSICS IN OUR DAILY LIFE

1. In our daily life, we hardly find a device in which laws of physics are not involved. For examples

2. Air Conditioning and refrigeration: This is based on Physics concepts of cooling by rapid evaporation, conducting properties of materials and convention.

3. Medical Diagnosis: Modern-day medical workers would not be effective if not for some applications of Physics. X-rays, ultrasound, microscopes, Electro-cardiogram, pacemaker, radiotherapy equipment etc. are designed based on the principles of Physics.

4. Communications: Radio, television and other electronic communication have made a tremendous impact in making the world a better place to live in. This would not have been possible without principles and concepts discovered and developed by physicists.

5. Space exploration: Today we know more about the universe, through space exploration, many of these explorers are Physicists.

6.  Generation and Distribution of Electricity: No major business outfit can function without electricity. No factory or workshop can function without electricity. Industries, Hospitals, Educational and research institutes, etc. will close down if electricity supply is cut off. Thought about how electricity is generated and transmitted shows reveal Physics is as the backbone.

BRANCHES OF PHYSICS AND THEIR DEFINITION

Atomic Physics: It is the study of the structure and properties of atoms.

Astrophysics: The branch of physics which deals with the study of universes such as stars, planets and galaxies, etc.

Cosmology: The study of the universe as a whole, including its origins and evolution, including the Big Bang and how the universe will continue to change.

Crystallography: The study of crystals and crystalline structures.

Electricity and Magnetism: It is the study of the charges at rest and in motion, their effects and their relationship with magnetism.

Electronics: The branch of physics in which motion of an electron is controlled by using semiconductor devices.

Geophysics: It is the study of the internal structure of the earth.

Light (optic): It is the study of physical aspects of light, its properties and use of optical instruments.

Mechanics: It is the study of the motion of objects, its causes, and effects.

Modern physics: It is the branch of physics which deals with the theory of relativity and quantum mechanics. Max plank and Einstein are considered the father of modern physics.

Nuclear physics: It is the study of properties and behaviour of nuclei and the particles.

Sound (acoustic): It is the study of physical aspects of sound waves, their production, properties, and applications.

Thermodynamics (Heat): It is the study of nature of heat, modes of transfer and effects of heat.

Quantum Mechanics: The study of how electrons and photons interact at the quantum mechanical level.

Relativity: The study of systems displaying the properties of Einstein's theory of relativity, which generally involves moving at speeds very close to the speed of light.

FIRMS/INDUSTRIES WHERE PHYSICISTS CAN WORK

1. The Physicist by his training can work in so many industries with little retraining to suit the particular industry. Specifically, a physicist can work in the following areas:

2. Telecommunication: As Telecom experts

Aviation: They are required as pilots or air-traffic control Officers

3. Energy company e.g. Power Holding, Enron, etc.

4. Electronic Manufacturing Company e.g. Sony, Philips etc.

5. Information Technology Outfits

6 Radio/Television Broadcasting Station.

7. Iron and Steel Industries.

8. Educational Research Institutions

9. Space Technology

10. Medical Diagnostic Industries: As Medical Physicist and Manufacturer of Medical Equipment

EVALUATION

1. Explain the meaning of physics.

2. State 10 branches of physics.

3. State the importance of physics.

4. State the various feed relevant to physics.

PERIOD 2

UNITS AND DIMENSIONS PHYSICAL QUANTITY

All quantities in terms of which laws of Physics are described and which can be measured directly or indirectly are called quantities. For examples mass, length, time, speed, force etc.

TYPES OF A PHYSICAL QUANTITY

Fundamental Quantities: The physical quantities which do not depend upon other physical quantities are called fundamental or base physical quantities. e.g., mass, length, time, temperature electric current, luminous intensity and amount of substance. However, there are three important fundamental quantities in physics. These are length, mass and time.

Derived Quantities: The physical quantities which depend on fundamental quantities are called derived quantities e.g. speed, acceleration, force, etc.

DIFFERENCES BETWEEN FUNDAMENTAL AND DERIVED QUANTITIES

Fundamental Quantities                                                            Derived Quantities

1. They are based on an international system              They are formulated from the international system

2. They are basic units of measurement                       They are not basic units of measurement

3. They have direct calculations                                   Their calculations are derived

 

4. They are generally acceptable quantities                  They are just accepted

5. They can stand alone                                                They cannot stand alone

                                                                            UNIT

The process of measurement is a comparison process. Unit is the standard quantity used for comparison. The chosen standard for measurement of a physical quantity, which has the same nature as that of the quantity, is called the unit of that quantity.

Choice of a unit (characteristics of a unit)

1. It should be suitable in size (suitable to use)

2. It should be accurately defined (so that everybody understands the unit in the same way)

3. It should be easily reproducible.

4. It should not change with time.

5. It should be universally acceptable

Fundamental (or base) Units: These are units which are independent of the unit of other physical quantity and cannot be further resolved into any other units. The units of fundamental physical quantities are called fundamental or base units. e.g, kilogram, metre, second etc.

Derived Units: All units other than fundamental units are derived units (which are dependent on fundamental units) e.g., unit of speed (ms-1) which depends on the unit of length (metre) and unit of time (second), unit of momentum (Kgms-1) depends on the unit of mass, length and time etc.

                                                                    SYSTEM OF UNITS

A system of units is a complete set of fundamental and derived units for all physical quantities. Different types of system of units

F.P.S. (Foot Pound Second) System (British Engineering system of units): In this system the unit of length is foot, mass is pound and time is second.

C.G.S. (Centimeter Gram - Second) System: In this system the unit of length is a centimeter, mass is gram and time is second.

M.K.S (Metre Kilogram Second) System: This system is related to mechanics only. In this system the unit of length is metre, mass is kilogram and time is second.

                            S.I. (INTERNATIONAL SYSTEM) UNITS

(Introduced in 1971) Different countries use a different set of units. To avoid complexity, by international agreement, seven physical quantities have been chosen as fundamental or base physical quantities and two as supplementary. These quantities are

                                            FUNDAMENTAL QUANTITIES

Base Physical quantity             Fundamental Unit                    Symbol

Mass                                               Kilogram                                   Kg

Length                                                Metre                                      m

Time                                                   Second                                    s

Temperature                                        Kelvin                                    K

Electric current                                   Ampere                                    A

Luminous intensity                            Candela                                   cd

Amount of substance                            Mole                                    mol

SUPPLEMENTARY QUANTITIES

Supplementary Physical Quantity        Supplementary Unit               Symbol

    Plane angle                                                    Radian                                Rad

    Solid angle                                                    Steradian                              Sr

Below is the table of some derived quantities and their units.

Conventions of writing of units and their symbols

1. Unit is never written with capital initial letter.
2. For a unit named after a scientist, the symbol is a capital letter otherwise not.
3. The unit or symbol is never written in plural form.
4. Punctuation marks are not written after the symbol.

S.I. Prefixes

The magnitudes of physical quantities vary over a wide range. For example, the atomic radius is equal to 10-10 m, the radius of the earth is 6.4 x 106 m and the mass of an electron is 9.1 x 10-31 kg. The internationally recommended standard prefixes for certain powers of 10 are given in the table:

 DIMENSIONS 

The powers to which the fundamental units of mass, length and time must be raised to represent the physical quantity are called the dimensions of that physical quantity. For example:

Force = mass x acceleration = [MLT–2]. Hence the dimensions of force are 1 in mass 1 in length and (-2) in time.

DIMENSIONAL FORMULA

Unit of a physical quantity expressed in terms of M, L and T is called dimensional formula. It shows how and which of the fundamental quantities represent the dimensions. The Dimensional equation of a physical quantity Y is given by:

Y= [M^aLbTc]. For example, the dimensional formula of work is  [ML2T–2]

EVALUATION

1. Distinguish between fundamental and derived quantities and units.
2. Give the examples of fundamental and derived quantities and units.
3. What is dimension? 
4. Give the dimensions of the following physical quantities: velocity, acceleration, momentum, work, impulse, force, etc.

POSITION: Position is the location of a point in space.

LOCATION OF A POINT: Rectangular coordinate is used to locate the position of a point in space.

RECTANGULAR COORDINATE: The rectangular coordinate contains positive and negative x- axis and positive and negative y-axis. The axes are calibrated based on the size of quantity that are to be plotted on the graph. The rectangular coordinate system is as shown in the figure below:

                        

                        

    

COORDINATE OF A POINT: The coordinate of a point is always generally stated in the form A(x, y). Where A is the name of the point, x represents a value or number on x – axis and y also represents a value or number on y – axis.

EXPLANATION:

For example, if the coordinate of a point is given as D (2 , - 5).

That is point D. 2 is to be marked on the positive x – axis while – 5 is to be marked on the y – axis.

USING RECTANGULAR COORDINATE TO LOCATE POINTS: Rectangular coordinate system is used to locate the position of a point as illustrated in the worked example below:

            

Worked Examples:

Use rectangular coordinate to locate the position of the points whose coordinate are given below: I) A(-5 , 3). II) B( 1 , 4 ). III). C(-3, -2)

                                       

            

DISTANCE: Distance is the space or gap or length between two points. The S.I unit of distance is meter and symbol of meter is (m).

DISPLACEMENT: Displacement is a distance travelled in a specified direction. Its unit is meter. Displacement is a vector quantity because it has magnitude and direction.

CALCULATION OF DISPLACEMENT

Example: A man walked 30km due East. He then moved 40km due North. What is the displacement of the man?                                                                 

        

 

Therefore, displacement = 50km N36.88°E or 50 km

PERIOD 3 AND 4

MEASUREMENTS

Measurement is the determination of the amount or size or numerical value of a physical quantity using an instrument. Measurements play a crucial role in Physics, but they can never be perfectly precise. We usually note the reading accuracy of the measuring instrument and specify the measurement only in the correct number of significant figures.

LENGTH

a. The metre rule

                              

The metre rule is graduated in cm and m. The smallest graduation is 1 mm or 0.1 cm. This is its reading accuracy. Measurements can be estimated up to half this smallest graduation. i.e. 0.5 mm or 0.05 cm. This is the estimated uncertainty. Thus, we can record a length as 21.55 ± 0.05 cm.

b. CALLIPERS: Callipers are not used to measure distance or length directly as the case is in meter rule. The claws of the callipers are adjusted to touch the edges of the object that is being measured. The span of the jaws of the callipers is then measured against a calibrated scale or meter rule to determine or estimate the size of the measured distance or length.

c. THE VERNIER CALLIPERS: The accuracy is 0.1 mm or 0.01 cm. The instrument has two sets of jaws and scales, the smaller vernier scale, slides on the main scale. The main scale is graduated in mm and cm. The vernier scale is constructed by dividing 9 mm length into 10 equal intervals such that each vernier division has a length of 0.9 mm or 0.09 cm. It is used to measure the thickness of a metre rule, internal and external diameters of test tubes, or diameter of a rod. 

            

TAKING READINGS WITH THE VERNIER CALLIPERS

Use the following formula:

Obtained reading = Main scale reading + Vernier scale reading. 

In the diagram above, 

Main scale reading: 10.0 cm (Immediate left of zero)

Vernier scale reading: 0.02 cm (Alignment of scale lines)

Measurement reading: 10.02 cm

WORKED EXAMPLE 

Estimate the reading of the vernier calliper as shown in the figure below:

            

SOLUTION

Main Scale Reading = 4.3 cm

Vernier Scale Reading = 5 x 0.01 cm = 0.05 cm

Vernier Calliper Reading= 4.3 cm + 0.05 = 4.35 cm.   

MICROMETER SCREW GAUGE: The accuracy of micrometer screw gauge is 0.01 mm or 0.001 cm. It is used to measure the thickness of a small ball, thickness of paper, etc. Micrometer is used to measure the thickness of paper, thickness of a small ball, thickness of I tiny wire. 

Using a Micrometer Screw-Gauge: Close the jaws of the micrometer and check for a zero error. Place the wire between the anvil and spindle end as indicated in the diagram.

Rotate the thimble until the wire is firmly held between the anvil and the spindle.

The ratchet is provided to avoid excessive pressure on the wire. It prevents the spindle from further movement - squashing the wire.

 To take a reading:

On the main scale, there is a linear scale reading on it. The long lines are every millimetre, the shorter ones denote half a millimetre in between. On the diagram this reading is 2.5 mm

Now look at the rotating scale. That denotes 46 divisions - each division is 0.01mm so we have 0.46mm from this scale. The diameter of the wire is the sum of these readings: 2.5 + 0.46 = 2.96 mm The beam balance is a device used for the determination of the mass of a body under gravitation.  

MEASUREMENT OF MASS (BEAM OR CHEMICAL BALANCE): It consists of a beam supported at the centre by a knife edge resting on a support moving inside a vertical pillar. The beam carries a light pointer which moves over a scale. There are two stirrups at the ends of the beam which carry two scale pans of equal masses along with adjusting nuts. These can be adjusted to make the pointer oscillate within the scale when the balance is raised. The balance is mounted on a platform provided with three leveling screws which make the pillar vertical. There is a plumb line which shows whether the pillar is vertical or not. The balance is enclosed in a glass case in order to avoid disturbances due to air.

MEASUREMENT OF WEIGHT (SPRING BALANCE): Weight is measured with a spring balance which uses Hooke's Law of Elasticity. The spring balance is graduated in newtons. 

MEASUREMENT OF VOLUMES OF OBJECTS

REGULAR SOLIDS: These are objects that have definite shapes. Their volumes can be determined by the use formulae. For example, volumes of objects such as box, sphere, cylinder, cone, etc. 

Volume of cube = s³ 

Volume of cuboid = lbh 

Volume of cylinder = πr²h

Volume of sphere = (4/3)πr³ 

IRREGULAR SOLIDS: These are objects that do not have definite shapes. Volumes of these types of objects cannot be calculated by the use of formulae. Their volumes can only be calculated or determined by the following steps:

Step I: tie the object to one end of a rope

Step II: fill an over flow can or eureka with water

Step III: immerse the object into the water in the over flow can.

Step IV: use a measuring cylinder and measure the volume of the liquid displaced.

Step V: The volume of the liquid displaced is the volume of the object.

MEASUREMENT OF TIME: Time is defined as the period in which a process, action or an event takes place. Time is also called the Point or Period when something occurs. Time is an integral part of Physics and every single quantity in the physical world relies on it. Time has made the universe function in a simple and routine way. If time wouldn't have existed, there would be many irregularities in the schedule and timing of people. It is quite difficult to think of life when there is no time. There won't be any physical quantities like acceleration, velocity and electromagnetic waves which depend on time for their existence. The most natural time unit is the solar day which is manifested by the passing of day and night. 

It takes the earth one solar day to complete one revolution about its axis.

1 day = 24 hours 

1 hour = 60 minutes 

1 minute = 60 seconds 

In the International System of Units (SI), the unit of time is the second (the symbol is s).

TYPE OF CLOCK/WATCH

Ticker-tape timer: This is used to measure short intervals of time accurately. It has a steel strip with a stylus which is controlled by an A.C. it vibrates 50 times in 1 second and makes use of a paper tape which helps in calculating the distance between the dots. The distance between the dots shows the distance travelled by the body pulling the tape in cm. It is commonly used in motion and to practice the third law of motion. i.e., action and reaction are equal and opposite. 

Stopwatch/clock: This is an instrument which is used to determine the time used either in the laboratory or on the field during sporting activities. It calculates both minutes and second. The second's hand makes one revolution in one minute. 

Simple pendulum: A pendulum is an instrument which is mostly used in the laboratory to measure time. The pendulum swings right to left. The time taken or the time of oscillation is determined through this instrument. Pendulum clock has second hand made in the form of a pendulum. It oscillates in order to tick the minute's hand and 60 oscillations of the second-hand make 1 minute. 

Heart-beat: Heartbeat is a natural way of counting. It is mostly used in medical line. The heartbeat gives the pressure and the rate of pumping of blood in the body. An increase in heart-beat is an increase in blood pressure and vice versa. 

Sand-clock: Sand-clock is an instrument used in measuring time per hour. The instrument could still be designed to measure smaller intervals. The sand in the glass is made to run from the top bulb to the lower bulb through a small neck. It takes exactly one hour to complete one run. It is also called hourglass. 

REPETITIVE EVENT

A repetitive event is an event which keeps recurring every time. Example of a repetitive event is time. There are 24hours in a day. This means that, after 24 hours which is a day, there is a reoccurrence of the event (time) in order to determine another day. The continuous counting of time makes a day, a month and a year. 

EVALUATION

1. Define position, distance and displacement.
2. State the instruments for measuring length, mass, weight, volume and time.

ASSESSMENT

Reference: New School Physics, unit 1 page 3. Exercise 1  

TICKET OUT

Reference: New School Physics, unit 1 page 3. Exercise 1  

WEEK 2

TOPIC: MOTION

REFERENCE BOOK: NEW SCHOOL PHYSICS FOR SENIOR SECONDARY SCHOOL BY M.W. AYANKOHA

LEARNING OBJECTIVES: by the end of the lesson, learners should be able to:

1. Explain the meaning of motion
2. State and explain the types of motion
3. Explain relative motion.

Period 1 and 2

Introduction to motion

Motion plays important roles in our daily lives. We move from one place to another either by walking or by moving in cars, aircraft, etc. Videos tapes and tape recorders can only operate when in motion; the air around us is in constant motion; the earth is also moving by rotating about it axis around the sun; electrons must be in motion in a wire for electric current to exist. This gives us an idea of what motion is. Let us now attempt a definition for it.

KINEMATICS is the branch of mechanics that deals with the motion of an object without reference to the force that caused the motion.

WHAT IS MOTION?

In all the examples given above, one will notice that a change of position is involved in motion. Whenever a body changes its position, it covers some distance and sometime interval elapsed. We can thus define Motion as the change in position of a body over some time interval.

TYPES OF MOTION

Referring to some of the motions mentioned earlier, one observes that theses motions are not of the same nature. For the motion of a car is different from that of the videotape operation. Likewise, the motion of the earth about its own axis is different from the motion of air molecules. Hence we categorize motion into the following types:

• Translational/Linear Motion
• Random motion
• Oscillatory/Vibratory/Periodic Motion
• Rotational Motion

Translational motion: "In translational motion, a body moves along a line without any rotation. The line may be straight or curved." Watch how various objects are moving. Do they move along a straight line? Do they move along a circle? A car moving in a straight line has transnational motion. Similarly, an aeroplane moving straight is in translational motion. Translatory motion is further divided into: 

1. Linear motion 
2. Circular motion and; 
3. Random motion. 

Examples of translatory motion 

1. Motion of train 
2. Motion of earth 
3. Motion of birds 
4. Motion of insects 
5. Motion of aeroplane flyng from one airport to another 
6. The motion of gas molecules 

Linear (rectilinear) motion: Straight-line motion of a body is known as its linear motion. In linear motion, the particles move from one point to another in either a straight line or a curved path. The linear motion depending on the path of motion and is further divided as follows 

Rectilinear Motion — The path of the motion is a straight line.  

Curvilinear Motion — The path of the motion is curved. 

Linear Motion: Linear motion examples in daily life 

1. The motion of the car on the road 
2. Motion of football 
3. Sliding a boy in a straight line is the example of linear motion 
4. The motion of the train, etc. 

Circular motion: The motion of an object in a circular path is known as circular motion. 

1. A toy train moving on a circular track
2. Earth revolving around the sun is an example of circular motion. 
3. Bicycle or a car moving along a circular track possesses circular motion. 
4. The motion of the moon around the earth is also an example of circular motion. 

Examples of circular motion in daily life 

1. The motion of the electron around the nucleus 
2. The motion of toy car on the circular track 
3. The motion of planets around the sun 

Random motion: The disordered or irregular or zig-zag motion of a body is called random motion. Have you noticed the type of motion of insects and birds? Their movements are irregular and disorder.

Examples of Random motion

1. The motion of insects and birds is random motion. 
2. The motion of dust or smoke particles in the air. 
3. The Brownian motion of pollen grains suspended in water.
4. The random motion of gas molecules.

Rotatory (Rotational) motion: The spinning motion of a body about its axis is called its rotatory motion. Rotatory motion is the motion that occurs when a body rotates on its own axis. A few examples of the rotatory motion are as follows: 

1. The motion of the earth about its own axis. 
2. The motion of wheels and the steering wheel of vehicles.

                             

Rotational motion

Oscillatory periodic or vibratory motion: Periodic motion is a motion that repeats itself after an equal interval of time. Oscillatory motion is the motion of a body to and fro about a fixed point. E.g. A swinging pendulum, balance wheel of a watch, a moving church bell, etc.

                             

Some examples of periodic motion include: 

1. The motion of the earth in its orbit around the sun which repeats itself after a time period of one year. 
2. Movement of a clock’s pendulum which repeats itself after a fixed time period. 
3. The motion of rocking chair.
4. The motion of a vibrating tuning fork.
5. A swing in motion.
6. The motion of string of a guitar when struck.

EVALUATION

Explain the meaning of motion

State and explain the types of motion

Period 3 and 4

Relative Motion: This is the motion of a moving object in relation to a static object or another moving object e.g. A moving car and a tree, A car overtaking another car.

Example

Two cars A and B travelling in opposite directions along the same highway at uniform velocities 200 kmh-1and 50 kmh-1 respectively pass each other at a certain point. The velocity of A relative to B at the time they pass each other is?

Solution

If they pass head on in opposite direction, their velocity will be 

200 kmh-1 + 50 kmh-1 = 250 kmh-1

If both cars are travelling in the same direction, their relative velocity will be 

= 200 kmh-1 - 50 kmh-1 = 150 kmh-1

EVALUATION

Explain Relative motion

ASSESSMENT: 

Reference: New School Physics, unit 1 page 3. Exercise 1  

TICKET OUT:

Reference: New School Physics, unit 1 page 3. Exercise 1  

WEEK 3

TOPIC: CAUSES OF MOTION

REFERENCE BOOK: NEW SCHOOL PHYSICS FOR SENIOR SECONDARY SCHOOL BY M.W. AYANKOHA

LEARNING OBJECTIVES: by the end of the lesson, learners should be able to:

Define force.

State, explain the types of forces and give their examples.

Explain the meaning friction.

State laws of solid friction 

Solve problems relating to friction.

CAUSES OF MOTION 

If you pull or push a body, any of the following can happen: 

1. The body can start moving if it was initially stationary. 
2. The speed of motion can increase or decrease depending on the direction of push or pull.
3. The body, if already moving, can come to a stop. 
4. The direction of motion of the body can change. 
5. The body can be deformed. 

Force is either a push or a pull. It is that agency that causes motion. We can thus define force as that which alters the state of rest or motion of a body in a straight line. Note that the force that moves a body can be external or internal. For example, when one hits a ball, that is an external force. On the other hand, for a car to move, the force required is derived from the energy generated within the car. That is, the burning fuel inside the engine of the car generates energy from which the motive force is derived. 

Types of force 

There are two types of force in nature. These are: 

• Contact force and 
• Non-contact force (Force field)

Contact force: This is a force that acts in direct physical contact with a body. For instance, when one pulls or pushes a box, the force is in physical contact with the box. Another is the force between two rough surfaces in contact, which prevents one from sliding on the other (friction), Normal force, Spring force, Tension, etc. 

Non-contact force: There are situations where a force acts on a body without the force actually being in contact with the body. The force act at a distance or through a region around the body. This is called a non-contact force of force field. Examples are gravitational force, magnetic force and electrostatic (electric) force.

 FRICTION

Friction is the opposing force between two surfaces in contact when they move over one another. 

There are two types of friction namely: 

1. Static or Limiting Friction: This is the maximum force that must be overcome before a body can just start to move over another. 
2. Dynamic or Kinetic Friction: This is the force needed to keep an object moving at uniform speed. 

A larger force is always required to move a static object than to keep an object moving, hence static friction is greater than kinetic friction. 

          Laws of Solid Friction 

1. Friction opposes motion 
2. Friction is directly proportional to the normal frictional force 
3. Frictional force is directly proportional and perpendicular to the normal reaction. 
4. Friction is independent of the area of surfaces in contact 
5. Friction depends on the nature of surfaces in contact.

Advantages of Friction 

1. It protects us from sliding when walking 
2. It assists in the braking system of a car (to stop) 
3. It helps in sharpening an object  
4. It also assists in grinding 
5. It assists in holding belts firmly in machines. 
6. It makes it possible for nails and screws to hold pieces of wood firmly together. 

Disadvantages of Friction 

1. It generates unwanted heat 
2. It reduces
3. It causes wear and tear in moving parts of a machine 
4. It reduces the efficiency of a machine 

Ways of Reducing Friction 

1. By lubrication 
2. By smoothening 
3. By streamlining 
4. Use of ball bearing or rollers
5. By providing air between the two surfaces. 

Coefficient of friction

The coefficient of friction is the ratio of the frictional force resisting the motion of two surfaces in contact to the normal reaction pressing the two surfaces together. It is usually symbolized by the Greek letter mu (µ). 

Relationship between Friction Force, Normal Reaction and Coefficient of Friction: 

                                  

F α R

 F = μ R

μ = F

      R

Where,

F= Frictional Force, 

R = Normal reaction 

μ = Coefficient of friction

F and R are measured in units of force (such as newtons), the coefficient of friction is dimensionless. 

Worked Examples 

1. A box is placed on an inclined plane such that the frictional force opposing its motion is 60 N. If the normal reaction of the plane on the box is 80 N , calculate the coefficient of friction. Solution 

Frictional force = 60 N 

Normal reaction force = 80 N 

Coefficient of friction =μ

F= uR Substituting the values 

60 = μ x 80 

μ = 60 = 0.75

      80

2. A wooden block of mass 10 kg rests on a rough horizontal surface. If the limiting frictional force between the block and the surface is 12 N, calculate the coefficient of friction (g = 10 m/s²)

                    

         Frictional force, F = 12 N 

         Normal reaction, R = W= mg = 10 x 10 = 100N  

         μ = 12  = 0.12

               100 

3. A cement block of mass 30 kg rests on a horizontal floor. If the coefficient of friction, μ, is 0.15, determine the minimum force required to move the cement block when pulled horizontally.

R = W = mg = 30 x 10 = 300 N   

μ = 0.15 

F= μR 

F = 0.15 x 300 = 45 N 

The minimum force required to move the cement block = 45 N

For an object on a horizontal surface

   

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.

 

 

W = mg

At equilibrium, R = mg, this implies that, 

R = W [g is acceleration due to gravity = 10m/s2]

R = mg

F = μ mg      

Fr = μmg…………………… 2

         

Case one: if the force P is applied, and the object is stationary.

P – Fr = ma

Since no motion, a = 0

P – F_r = 0

P = F_r …………………….. 3

Case two: when the force P is applied and the body moves.

 P – F_r = ma

P = F_r + ma

But F_r = μmg 

P = μmg + ma

P = m [ μg + a ] …………………………….. 4

For an object on a smooth inclined plane

Case one: if the body moves upward, a > 0

P – mg sin ø = ma

P = mg sin ø + ma …………………………. 5

Case two: if the body is stationary a = 0

P – mg sin ø = ma

P – mg sin ø = 0

P = mg sin ø ……………………………… 6

 Case three: if the body slides down the plane , a >0

• for a smooth plane

mg sin ø – P = ma

P = ma + mg sin ø ………………………… 7

•  For a body on a rough inclined plane

 P – mg sin ø - F_r = ma

But F_r = μR

P - mg sin ø - μmg = ma ………………………. 8

Also, R = mg cos ø

P - mg sin ø - μ mg cos ø = ma ...……………… 9

If the body moves upward the incline plane 

μ = tan Ө    .........……………………………... 10

EVALUATION

Define force.

State, explain the types of forces and give their examples.

Explain the meaning friction.

State laws of solid friction 

Solve problems relating to friction.

ASSESSMENT: 

Reference: New School Physics, unit page . Exercise 1  

TICKET OUT:

Reference: New School Physics, unit page . Exercise 1  

WEEK 4

TOPIC: SPEED AND VELOCITY, RECTILINEAR ACCELERATION -Velocity-time graph REFERENCE BOOK: NEW SCHOOL PHYSICS FOR SENIOR SECONDARY SCHOOL BY M.W. AYANKOHA

LEARNING OBJECTIVES: by the end of the lesson, learners should be able to:

Define distance and displacement

Differentiate between speed and velocity.

Explain acceleration

Draw and use velocity time graph to solve problems.

DISTANCE AND DISPLACEMENT

Distance: This is the gap between any two positions in space. It is denoted by S and measured in metre (m) it is a scalar quantity and is calculated as the product of average speed and time.

Thus, distance = average speed X time.  

Displacement: This is the distance covered in a specific direction. it is a vector quantity measured in metre(m). The direction of motion of bodies can be found by using the compass.

Displacement = average velocity X time. It is denoted by X 

The Use of Bearing to Indicate Direction and Displacement

The bearing of an object from the origin is the angle which it makes with the north pole in the clockwise sense. It is specified in two ways:

• The use of cardinal points: N – North, S – South, W – West, and E – East
• The use of three digit notation. Students should note that bearing which are located by cardinal points are with respect or reference to the North and South.

                                                Cardinal points and their directions 

SPEED AND VELOCITY

Speed: Speed is defined as the rate of change of distance moved in an unspecified direction or the rate of change of distance per unit time in an unspecified direction. It is measured in metre per second (m/s). It is a scalar quantity.

The mathematical expression of speed is 

                   v = s 

                         t

Average Speed: Average speed is defined as the ratio of the total distance travelled to the total time taken. It is a scalar quantity and measured in m/s or ms-1

average speed = total distance travelled

                                 total time taken

Uniform or Constant Speed

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: Velocity is defined as the rate of change of distance moved in a specific direction or the rate of change of displacement. Velocity is a vector quantity. For instance, it would be easy and correct to say that a car travelling at a steady speed of 50km/h in a direction of N400E has a velocity of 50km/h, N400E.

 velocity =   displacement

                          time

Uniform velocity

Uniform (constant) velocity: An object is said to undergo (constant) velocity, if the rate of change of displacement is constant, no matter how small the interval may be.

Example 1:

A train moves with a speed of 54km/h for one quarter minute. Find the distance travelled by the train.

Solution:

 Speed = 54km/h = 15m/s

 Time = ¼ min = ¼ × 60 = 15s

 Distance = speed (m/s) × time (s)

         = 15(m/s) × 15(s)  

       = 225m

ACCELERATION & RETARDATION

Acceleration is defined as the increasing rate of change of velocity. It is measured in ms-2.

Acceleration (a) = Increasing Velocity change   . ……………………………………5.

                                             Time taken 

Uniform Acceleration.

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/s-2. It is also known as deceleration or negative acceleration

Retardation (a) = Decreasing Velocity Change

                                     Time Taken               

EQUATION OF UNIFORMLY ACCELERATED MOTION

S = (v+u) t ………………………………………………………7

          2

v = u + at ……………………………………………………….8

v2 = u2 + 2 aS ……………………………………………………….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 (ms2), s – distance covered and t – time (m).  

                                                                               

Example 2

A car moves from rest with an acceleration of 0.2mls2 . Find its velocity when it has moved a distance of 50m.

Solution:

a = 0.2 ms2 , S = 50 m, u = 0m/s , v = ?

v2 = u2 + 2 as

v2 = 02 + 2 x 0.2 x 50 = 20

v = √20 m/s

EVALUATION

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?

GRAPHS

The motion of an object is best represented or described with graphs. These graphs are 

Distance- time

Displacement – time

Velocity – time

Distance – time

In a distance-time graph, its slope or gradient gives the speed.

 (i) Uniform speed (ii) Non-uniform speed

Fig. 6: Distance-time graph

Gradient/slope = speed =    

Displacement – time graph

A displacement-time graph could be linear or curved. For a linear graph, the gradient gives the velocity.

a) Non-uniform velocity

Fig. 6.4 Displacement-time graph

Gradients/slope = velocity (v) =     

Velocity – time graph

The velocity-time graph is more useful than any of the two graphs described above because it gives more useful information concerning the motion of objects. The following information can be obtained from the graphs (i) acceleration (ii) retardation (iii) distance (iv) average speed.

The motion of objects can form shapes such as square, triangle, trapezium, rectangle or a combination of two or more shapes. Thus, the sum of the areas of the shapes formed corresponds to the distance moved, covered or travelled by the objects.

Example 3

A motor car accelerates for 10secs to attain a velocity of 20m/s. It continues with uniform velocity for a further 20 seconds and then decelerates so that it stops in 20 seconds. Calculate (i) Acceleration (ii) Deceleration (iii) The distance travelled.

i) 

  or 

20 = 

A = 

ii) Deceleration = 

iii) Using area of trapezium

 ½ × (AB + OC) h = ½ × (20 + 50) 20  

        = ½ × (70) × 20 = 700m

Example 4

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

Total distance covered = area of the trapezium OABC

= ½ (AB + OC) AE

= ½ (15 + 30) 30

= 675m.

Using equations of motion.

U = O, V = 3, t = 5

V = u + t

a = v-u/t = 30 – 0 / 5

a = 30/5 = 6ms-2 

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

Define distance and displacement

Differentiate between speed and velocity.

Explain acceleration

Draw and use velocity time graph to solve problems.

ASSESSMENT: 

Reference: New School Physics, unit page. Exercise 1  

TICKET OUT:

Reference: New School Physics, unit page. Exercise 1  

WEEK 5

TOPIC: SCALARS AND VECTORS 

REFERENCE BOOK: NEW SCHOOL PHYSICS FOR SENIOR SECONDARY SCHOOL BY M.W. AYANKOHA

LEARNING OBJECTIVES: by the end of the lesson, learners should be able to:

Explain concept of scalar and vector quantities

Show Vector representation, addition of vectors

Resolve of vectors and resultant

CONCEPT OF SCALAR AND VECTOR QUANTITIES

Physical quantities are divided into scalar and vector quantities.

A scalar is one which has only magnitude (size) e.g. distance, speed, temperature, volume, work, energy, power, mass etc.

A vector quantity has both magnitude and direction e.g. force, weight, magnetic flux, electric fields, gravitational fields etc.

VECTOR REPRESENTATION

A vector quantity can be graphically represented by a line drawn so that the length of the line denotes the magnitude of the quantity. The direction of the vector is shown by the arrow head.

ADDITION AND SUBTRACTION OF VECTORS

Two or more vectors acting on a body in a specified direction can be combined to produce a single vector having the same effect. The single vector is called the resultant.

For example: 

(a) Two forces Y and X with magnitude of 3N and 4N respectively acting along the same direction will produce a resultant of 7N (algebraic sum of the two vectors).

(b) If Y and X act in opposite direction, the resultant will be 1N.

(c) If the two vectors are inclined at 900 to each other, Pythagoras theorem is used.

                                  

           

R2 = X2 + Y2

R2 = 42 + 32

R2 =16 + 9 

R2 = 25 

R = 25 

R = 5 N

Tan θ = FyFx

θ = tan-1 FyFx

θ = tan-1 34 

θ = tan-1(0.75)

θ = 36.90

(d) If the two vectors are inclined at an angle less than 900 or more than 900, the resultant is obtained by using Parallelogram law of vector addition. 

Parallelogram law of vector addition states that if two vectors are represented in magnitude and direction by adjacent sides of a parallelogram , the resultant is represented in magnitude and direction by the diagonal of the parallelogram drawn from the common point 

RESOLUTION OF VECTORS

A single vector can be resolved into two vectors called components. A vector F represented as the diagonal of the parallelogram can be resolved into its component later taken as the adjacent sides of the parallelogram.  

 

VERTICAL COMPONENT

Fy=F Sinθ  

HORIZONTAL COMPONENT

Fx=F cosθ  

THE RESULATNT OF MORE THAN TWO VECTORS

To find the resultant of more than two vectors, we resolve each vector in two perpendicular direction s add all the horizontal components X, and all the vertical components, Y. 

For example, consider four forces acting on a body as shown below

Figure 1

Figure 2:

   

Add all the resolved horizontal components  

Figure 1:

Fx = F1 Cosθ1 + (-F2 Cosθ2) + (-F3 Cosθ3) + F4 Cosθ4

Fy= F1 Sinθ1 + F2 Sinθ2 + (-F3 Sinθ3) + (-F4 Sinθ4)

R = Fx2+ Fy2

And the direction is given by  

  = tan-1 FyFx

EVALUATION

Explain concept of scalar and vector quantities

Show Vector representation, addition of vectors

Resolve of vectors and resultant

ASSESSMENT: 

Reference: New School Physics, unit page. Exercise 1  

TICKET OUT:

Reference: New School Physics, unit page. Exercise 1  

WEEK 6

TOPIC: CONCEPT OF WORK, ENERGY AND POWER

REFERENCE BOOK: NEW SCHOOL PHYSICS FOR SENIOR SECONDARY SCHOOL BY M.W. AYANKOHA

LEARNING OBJECTIVES: by the end of the lesson, learners should be able to:

Define work, energy and power

 State the principle of conservation of energy

 Differentiate between kinetic and potential energy. 

 Derive the equations for kinetic and potential energies. 

CONCEPT OF WORK 

Work is said to be done whenever a force moves a body through a distance in the direction of the force, and is equal to the product of the force and the distance moved. 

For example, work is done when you drag a crate of soft drink through a distance or when a car moves a certain distance, or when a boy climbs a staircase, and so on.  

Thus, 

Work = force x distance in the direction of force. 

W = F x s 

If the force is applied at angle θ to the horizontal as shown below, then 

W = F x s Cos θ

  

   

The SI unit of work is the joule (J).

1 joule is the work done when a force of 1 Newton moves a distance of 1 metre. 

 1 J = 1 Nm

Larger units are the kilojoule (kJ) and the megajoule (MJ). 

1 kJ = 10³ J

1 MJ = 10⁶ J

II. CONCEPT OF ENERGY 

Energy can be defined as the capacity to do work. 

Thus the unit of energy is the same as that of work, i.e. the Sl unit of energy is the joule, J. 

Energy can appear in any form.

III. WORK DONE IN A FORCE FIELD 

In the gravitational field, there is always a force pulling a body towards the Earth’s centre. 

The weight of a body is the force of attraction on a body as a result of the Earth’s gravity acting on its. 

The magnitude of the work done is given by: 

Work = force x distance 

W = mg × h 

W= mgh 

Where,

m = mass of the body (kg), 

g = aceleration due to gravity g (10 ms⁻²) 

h = height (m), and 

W = work done in joules (J)

MECHANICAL ENERGY 

There are two kinds of mechanical energy: 

Kinetic and potential energy: Kinetic energy is the energy a body possesses because it is in motion. The symbol for kinetic energy is EK. Kinetic energy is the energy due to motion.

Examples of kinetic energy are; 

A rolling ball

An object falling under gravity 

Wind or air in motion 

An athlete running a race 

A bullet movement 

A plane flying, etc. 

The work done in bringing the body to rest (zero speed) from initial speed v, is equal to the kinetic energy of the body when its speed is v. 

Work done = force × distance 

Work done = F × s

But distance = average speed x time  

                                   

      s=v +0 ×t2 i.e., s = ½vt 

But force = mass × acceleration 

So, F = ma and also, 

a = v/t

Therefore, 

F = mv t 

Work done = ½ v t x mv t (because w = F × s)

 = ½ mv² 

 Ek = ½ mv²

Where m is the mass of the object in kg, v is the speed in ms-1.

i.e. 

Work done = change in kinetic energy of the body. 

POTENTIAL ENERGY 

Potential energy is the energy a body possesses because of its position. 

The symbol for potential energy is Ep. 

Potential energy = work done 

Ep = force × distance

Ep = mg × h

Ep = mg h

LAW OF CONSERVATION OF MECHANICAL ENERGY 

Energy can be transformed from one form to another, the total energy of the system remains the same.

Potential energy can be transformed to kinetic energy and vice versa but in all cases the sum remains constant. 

Let the Kinetic Energy be Ek and Potential Energy be Ep 

Ek + Ep = constant 

Or Ek + Ep at any point = Ek + Ep at another point.

Typical examples of alternating potential and kinetic energy are those of simple pendulum, the motion of a loaded spring and an object falling from a height 

NOTE:

Ep at furthest point = Ek at rest (equilibrium) position. 

Vmax = 2gh

      

Power

Power is the quantity of energy converted or transferred per unit time. It is also expressed as the work done divided by the time taken, t.

In the International System of Units, power is measured in watts, w.

Power can be found by dividing work done by time. The formula for power is:

P = Wt or P = Et

P is the power, W is the work done by the body, E is the energy expended and t is the time taken.

EVALUATION

Define work, energy and power

 State the principle of conservation of energy

 Differentiate between kinetic and potential energy. 

 Derive the equations for kinetic and potential energies. 

ASSESSMENT: 

Reference: New School Physics, unit page. Exercise 1  

TICKET OUT:

Reference: New School Physics, unit page. Exercise 1  

WEEK 7

TOPIC: CONCEPT OF WORK, ENERGY AND POWER

REFERENCE BOOK: NEW SCHOOL PHYSICS FOR SENIOR SECONDARY SCHOOL BY M.W. AYANKOHA

LEARNING OBJECTIVES: by the end of the lesson, learners should be able to: 

1 differentiate between heat and temperature. 

2. state and explain the effects of heat energy. 

3. state the consequences and application of thermal expansion. 

4. explain the applications of bimetallic strip. 

DEFINITION OF HEAT

Heat is the total internal energy of the molecules of a body. Heat is transferred from one object or source to another due to the differences in their temperature. It flows from a hotter object to the cooler one. It is measured in joules. 

DEFINITION OF TEMPERATURE

Temperature is defined as the average kinetic energy of the molecules of an object. It is the degree of hotness or coldness of an object.

It can be measured in various scales, which are – Kelvin, Celsius and Fahrenheit. The thermometer is used to gauge the temperature of the object.

DIFFERENCE BETWEEN HEAT AND TEMPERATURE        

EFFECTS OF HEAT OR THERMAL ENERGY

The effects of heat energy are:

1. Change In Temperature: When heated there is increase in kinetic energy and particles move at higher speed. Since temperature is a measure of average Kinetic Energy, the temperature increases.

2. Expansion of the body: Addition of heat usually cause the body to expand. During expansion, the dimension of the body increases. 

3. Change of State: On heating, change of state may occur, i.e. a solid may change into a liquid and a liquid may change into a gas. e.g. if ice (solid) is heated it changes its state to water (liquid) and if this water is further heated it becomes water vapour (gas). Conversely when a gas loses heat energy it changes into a liquid and on further cooling it freezes into a solid.

4. Chemical Change: When we heat substances, it may bring about change in its chemical properties. 

5. Change in Physical Properties: Heating can change the physical properties, such as colour, texture, density, electrical resistance, magnetic properties, conductivy, elasticity of substance. 

6. Chage in pressure: when a gas is heated, its pressure and volume increase. 

7. Thermionic emission: hearing a metal results in the emission of electrons in a process known as thermionic emission. 

KINETIC MOLECULAR THEORY

The molecular theory assumes that matter is made up of atoms that aggregate in molecules. 

The atom is the smallest particle of an element can exist separately and still retain the chemical properties of that element. 

The molecule is a group of atoms of the same or different elements joined together in simple proportion. 

Kinetic molecular theory assumes that 

1. Every substance is made up of tiny particles called molecules. 

2. The molecules are in constant state of random motion, colliding elastically with one another and changing their direction as a result. 

3. There's always an attractive force between the molecules. 

4. The volume of gas molecules is negligible compared with the volume of the gas container. 

 

PERIOD 3 AND 4

LEARNING OBJECTIVES: by the end of the lesson, learners should be able to: 

1 explain linear, area and volume expansivity. 

2 solve simple problems on linear, area and volume expansivity

3 explain the anomalous expansion of water and it application to marine lives. 

EXPANSION

Most substances (whether solid, liquid or gas) expand when heated and contracts when their temperature fall. When a body is heated, it gains some energy as a result of the fast movement of its molecules, hence an increase on their kinetic energy. This result in an increase in the speed and vibration of the molecules of the system. When the system is cooled after being heated, there is a decrease in the speed of molecules and also their kinetic energy. Thus, they are said to be contracting. 

Thermal expansion of solids can be demonstrated using ball and ring apparatus as well as a steel rod apparatus. 

At room temperature, that ball is just able to pass through the ring. If however, the ball is heated it will no longer pass through the ring because its size has increased (expansion).

Application of expansion

Railway tracks: The Rail-line expands during hot weather and contracts when the temperature falls. For this reason, the rails are

not laid as one continuous line, rather a small gap is allowed between successive rails to allow for expansion. If this is not done, the rail will buckle and be damaged.

Bimetal strip: A bimetal strip is made of two strips of different metals laid side by side and joined together to become one strip. The two metals have a different rate of expansion when heated.

If a bimetal shown above is heated, since brass expands more than iron, the strip will bend as shown below. On cooling, the strip returns to its original shape.  

                     

Bimetal finds application in a thermostat. A thermostat is a device used in regulating temperature. It is used in pressing Iron, water heater, etc to ensure that the desired temperature is maintained. Bimetal is also used in automatic fire alarm and in the balance wheel of a watch to prevent the watch from losing time when the temperature rises.

Removing tight stopper of a bottle: The phenomenon of thermal expansion can be employed in removing the tight stopper of a bottle. If the bottle is slightly heated, its neck expands, allowing the stopper to be removed easily.

Advantages of expansion of solid 

For making bimetallic strip used in a thermostat 

Removal of tight glass stopper by careful and gentle heating 

Red-hot rivets in ship buildings 

Expansion of metals is used in bi metallic thermometer 

Fitting of wheels in rims 

Fire-alarms e.g. electric bell 

Disadvantages of expansion of solid 

Expansion of metal or concrete bridges.

Cracking of glass when hot water is poured into it 

Expansion of balance wheel or wristwatch, leading to loss of time.

Expansion of railway lines.

Bursting of water pipes 

Sagging of overhead wire.

Linear (coefficient of linear) expansivity

Different solids expand by different amounts when heated over the same temperature range. Copper for instants will expands more than steel when both are heated through the same rise in temperature. This is because they have a different coefficient of linear expansion or linear expansivity.

Linear expansivity is defined as the increase in length per unit length per degree rise in temperature or it is the fractional increase in length per degrees rise in temperature. 

If a substance increases its length from l₁ to l₂ when its temperature is raised θ°, then the expansivity (α) is given by:

α = l2-l1l1= el1 

       

 l₂ = l₁ (1 + αθ)

Where, 

l₂ = final length. 

l₁ = original length. 

θ = θ₂ - θ₁ = temperature rise or increase in temperature

e = expansion or increase in length. 

α = coefficient of linear expansivity. 

The unit of is per °C or per K (K-1).

The statement that the linear expansivity of glass is 0.0000085 K-1 or 0.0000085/0C means that a unit length of glass expands by 0.0000085 units when it is heated through 1 K (1°rise in temperature).

Area (superficial) expansivity

When a solid is heated, it expands in all directions -in length and breadth. Hence there is an increase in the area of the solid. The increase in the area when a body is heated is known as area or superficial expansion. 

Therefore superficial expansion is defined as the increase in area per unit area per degree rise in temperature or is the fractional increase in area per degree rise in temperature.

β = A2-A1A1= ΔAl1 

       

A₂ = A₁ (1 + βθ), 

β = 2α.

Hence, 

A₂ = A₁ (1 + 2αθ)

Where,

β = area or superficial expansivity.  

A₂ = final area. 

A₁ = original area. 

θ = θ₂ - θ₁ = temperature rise or increase in temperature

α = coefficient of linear expansivity. 

Volume (cubic) expansivity

The Volume or Cubic expansivity is the increase in volume per unit volume per degree rise in temperature or it is the fractional increase in volume per degree rise in temperature.

γ = V2-V1V1= ΔVl1 

      

V2 = V1 (1 + γθ),  

γ = 3α

Hence, 

V₂ = V₁ (1 + 3αθ)

Where,

γ = Cubic expansivity.  

V₂ = final volume. 

V₁ = original volume. 

θ = θ₂ - θ₁ = temperature rise or increase in temperature

α = coefficient of linear expansivity 

Example 

The linear expansivity of the material of a cube is 12 x 10-6 K. If the length of each side of the cube is 10 cm, find the area of one face of the cube and the volume of the cube when its temperature is raised by 30 K.

Expansion in liquids 

Like solids, liquids expand on heating and contract on cooling. Because liguids are always held in a container, the expansion of liquids is often complicated by the expansion of the containers.

Real and Apparent Expansivity 

Because the expansion of liquids is complicated by the expansion of their containers, it is necessary to distinguish between the real and the apparent cubic expansivity of a liquid.

Real expansion = Apparent expansion + expansion of the container.

The real (or absolute) cubic expansivity (Yr) of a liquid is the increase in volume per unit volume per degree rise in temperature.

The apparent cubic expansivity (Ya) of a liquid is the increase in volume per unit volume per degree rise in temperature when the liquid is heated in an expansible vessel.

Because the apparent expansivity depends also on the cubic expansivity of the vessel, the real expansivity of a liquid (Yr) is always more than its apparent expansivity (Ya). 

Yr = Ya + Y

Where 

Yr = real (absolute) cubic expansivity 

Ya = apparent cubic expansivity 

Y = cubic expansionist of the vessel 

To determine the apparent cubic expansivity (Ya) of a liquid 

Ya. = volume of liquid expelled 

           Volume of remaining liquid × temp rise 

Ya. = mass of liquid expelled 

           mass of remaining liquid × temp rise 

Example 

A density bottle holds 250 g of liquid at 30'C and only 248.5 g at 60'C. Find

the apparent and 

the real cubic expansivity of the liquid, if the linear expansivity of the material of the bottle is αg = 0.000006 K-1 

Solution 

Ya = mass of liquid expelled mass of remaining liquid × temp rise    

    

Ya = 250.0 - 248.5 248.5 × (60 - 30) = 0.0002012 K-1 

         Yr = Ya + Y = 0.0002012 + 3 × 0.000006 = 0.0002192 K-1 

Variation of density with temperature 

d1 = d2 (1 + γθ)

 

Where d1 is the density at a lower temperature and d1 is the density at a higher temperature.

The anomalous expansion of water 

Most liquids expand when heated and contract when cooled. Water is an exception to this rule as it behaves in an anomalous way when cooled. It contracts on cooling from any temperature until at 4'C when it starts to expand if cooled below this temperature. Thus water expands (rather than contracts) when cooled from 4°C to °C. Hence a given mass of water has its least volume (and hence its highest density) at 4°C.

This is of utmost importance in nature. It makes ponds, lakes or rivers to freeze from the top surface rather than from the bottom. Thus marine lives can survive during winter and since ice forms at the surface of the water while the bottom of the lake remains at 4°C, a temperature warm enough for aquatic life. 

EVALUATION

Differentiate between heat and temperature. 

State and explain the effects of heat energy. 

State the consequences and application of thermal expansion. 

 Explain the applications of bimetallic strip. 

 

ASSESSMENT: 

Reference: New School Physics, unit page. Exercise 1  

TICKET OUT:

Reference: New School Physics, unit page. Exercise 1  

EVALUATION

WEEK 8

TOPIC: HEAT TRANSFER

REFERENCE BOOK: NEW SCHOOL PHYSICS FOR SENIOR SECONDARY SCHOOL BY M.W. AYANKOHA

LEARNING OBJECTIVES: by the end of the lesson, learners should be able to:

State and explain the three modes of heat transfer

Differentiate between good and poor conductors of heat and their examples. 

State the applications of conduction, convection and radiation

Explain how the thermos flask minimize heat loss

HEAT TRANSFER

The modes of heat transfer are:

1. Conduction

2. Convention 

3. Radiation

CONDUCTION

Conduction is the method of transfer of heat within a body or from one body to the other due to the transfer of heat by molecules vibrating at their mean positions. The bodies through which the heat transfer must be in contact with each other. There is no actual movement of matter while transferring heat from one location to the other.

 

Good Conductors

Materials that allow heat to pass through them easily are called good conductors of heat. Metals are good conductors of heat. 

Poor Conductors or Insulators

Materials that do not allow heat to pass through them easily are called poor conductors or insulators. 

         

Applications of conduction of heat in our daily life

1. Heat conduction is applied in cooking with metal pot e.g. Aluminum pots. 

2. Ironing of clothes with pressing iron 

3. Welding of two iron metals together. 

4. The handles of the cooking utensils are made of materials like plastic and sometimes wood which cannot conduct heat when carried by the Cook; 

5. Woolen clothes which prevent body from losing heat to the surrounding are worn during cold; 

6 Thatch-roofed homes feel cooler inside than houses covered with metal sheets because metals conduct heat.

Water is poor conductor of heat

Materials Needed:

Test tube

Water

Ice

Bunsen burner

Thin Wire

Procedure:

Fill the test tube with water and put a small ice cube (wrapped in a wire) in it

Make sure that the ice cube is at the bottom of the test tube

Heat the test tube from the top using a Bunsen burner. The water will boil at the top of test-tube while the water at the bottom will be cold. This shows that water is poor conductor of heat.

             

CONVECTION

Convection is the mode of heat transfer which occurs mostly in liquids and gases. In this method, heat transfer takes place with the actual motion of matter from one place within the body to the other. Often when we boil water we have seen bubbles and currents develop in the water on careful observation

Applications of Convection in everyday Life

Ventilation: Household ventilation can make our house cool. The air which we breathe out is warmer and lighter. It moves up in the room to go out of the ventilators near the top side of the walls. Fresh and cool air enters the room through windows and doors.

Chimney used in hotels or kitchens of the houses: Winds are convective air currents. Monsoon clouds move inland from the oceanic mass riding on the convective currents and also based on pressure differentials. But, the monsoon currents bring cold air towards the hot air of the land.

Air Conditioners: Air conditioners are installed near the ceiling of the room, to allow the setting up of convection currents. The air-conditioner releases cool dry air into the room. As cool air is denser, it sinks. The warm air, being less dense, will rise. The air circulated and the temperature of the air will eventually fall to the desired value.

 

LAND AND SEA BREEZES

Sea breeze

On a sunny day the land heats up more quickly than the sea because land absorbs heat faster than water. Hence, air over the land surface becomes more heated than air above the sea. So the hot air over the land being lighter moves up and the cooler air from the sea takes its place. Thus a cool and comforting breeze blows from the sea to the land. Therefore, it is called sea breeze.

   

  

Land breeze

The situation during the night is opposite. The sun is not there to heat and the cooling process has started. The land gives up heat more quickly than water. Thus, the air above the sea remains warmer and moves up while its place is filled up by the cool breeze blowing from the land. Therefore, this breeze from land to sea is called the land breeze.

   

   

RADIATION

Radiation is another form of heat transfer. It does not require any medium and can be used for transfer of heat in a vacuum as well. This method uses electromagnetic waves which transfer heat from one place to the other. The heat and light from the sun in our solar system reach our planet using radiation only. The rate at which radiations are emitted depends upon various factors such as:

Colour and texture of the surface

Surface temperature

Surface area

Why does a cup of hot tea become cold after sometime?

All the objects, lying inside a room including the walls, roof, and floor of the room are radiating heat. However, they are also absorbing heat at the same time. When the temperature of an object is higher than its surroundings then it radiating more heat than it is absorbing. As a result, its temperature goes on decreasing until it becomes equal to its surroundings. At this stage, the body is giving out the amount of heat equal to the amount of heat it is absorbing.

When the temperature of an object is lower than its surroundings, then it is radiating less heat than it is absorbing. As a result, its temperature goes on increasing until it becomes equal to its surroundings. 

The rate at which various surfaces absorb heat also depends upon the nature of those surfaces. For example, take two surfaces, one is dull black and the other is a silver polished surface with a candle at the middle of the surface.

It is found that a dull black surface is a good absorber of heat as its temperature rises rapidly. A polished surface is a poor absorber of heat as its temperature rises very slowly.

It is also found that the transfer of heat by radiation is also affected by the surface area of the body emitting or absorbing heat. Larger is the area, greater will be the transfer of heat. It is due to this reason that large numbers of slots are made in radiators to increase their surface area.

APPLICATION OF RADIATION

We wear white or light-coloured clothes in summer because they are poor absorbers and good reflectors of heat. This way they keep us cool. On the contrary, we prefer to wear dark-coloured clothes in winters because they absorb most of the heat of sun and keep our body warm.

Radiators of heat in cars, machines and air conditioners are painted black so as to have cooling effect by radiating most heat.

Room (electric) heaters have bright polished surfaces which act as good reflectors of heat. Such surfaces absorb very little heat and reflect towards us most of the heat radiations. These surfaces remain cool even after continuous use of heaters. The highly polished surfaces of spacecraft reflect most of the heat radiated from the sun.

Base of cooking utensils is made black. Such a black surface absorbs more heat from the surroundings. This is because conduction, convection and radiation of heat are minimum

Thermos or Vacuum Flask

It is device is used to prevent loss of heat energy from its content

The three modes of heat transfer are prevented in the thermos flask in the following ways:

The vacuum between the double walled glasses prevents loss of heat by conduction and convection.

The silver colour of the inside of the double walls prevents heat loss by radiation.

The cork support, or plastic prevents heat loss by conduction.

The cork stopper prevents heat loss by conduction, evaporation and convection.

                       

   The thermos flask 

ASSESSMENT: 

Reference: New School Physics, unit page. Exercise 1  

TICKET OUT: 

Reference: New School Physics, unit page. Exercise 1  

EVALUATION

State and explain the three modes of heat transfer

Differentiate between good and poor conductors of heat and their examples. 

State the applications of conduction, convection and radiation

Explain how the thermos flask minimize heat loss

WEEK 9

TOPIC: ELECTRIC CHARGES

REFERENCE BOOK: NEW SCHOOL PHYSICS FOR SENIOR SECONDARY SCHOOL BY M.W. AYANKOHA

LEARNING OBJECTIVES: by the end of the lesson, learners should be able to: 

Define electric charges 

Explain how charges are produced 

State the law of electrostatics 

Distinguish between conductors and insulators with examples 

Describe gold leaf electroscope 

Describe ways of charging gold leaf electroscope

Electric charge is the physical property of matter that causes it to experience a force when placed in an electromagnetic field. 

Electrostatics is the study of charges at rest while the study of charges in motion is current electricity. 

Types of Charges

There are two types of charges; Positive & Negative charges. 

A body becomes positively charged if it loses electrons while it becomes negatively charged if it gains electrons.

PRODUCTION OF CHARGES

These charges are produced in three ways namely: 

1. By Friction: This is when two uncharged bodies are rubbed against each other which allows electrons moving from one surface to another. eg when an ebonite rod is rubbed with fur, negative charges are produced. 

Ebonite rod + fur = Negative charge 

If a glass rod is rubbed with silk = Positive charge

2. Induction: This occurs when a charged body is brought near a neutral body without contact, charges are produced and these charges are called induced charges. 

3. By Contact: This occurs when a charged body is in contact with an uncharged, charges are transferred to the uncharged body as a result of contact between the two. 

Like Charges: When positively charged glass rods are brought near each other, repulsion takes place

Unlike Charges: When a positively charged rod is brought near an ebonite rod, there is an attraction between them.

Law of Electrostatics Like charges repel, unlike charges attract 

Conductors are materials that allow electrons (charged) to flow through them easily e.g. air, acids, salt solution, earth, human body. 

Insulators are materials that do not allow electrons to flow through them easily e.g. wood, paper, plastic, ebonite, silk, glass, etc.

THE GOLD LEAF ELECTROSCOPE

This is an instrument for the detection and testing of small electric charges. This is a metal disc connected to a narrow metal plate and a thin piece of gold leaf is fixed to the plate. The electroscope is insulated; a glass in front prevents air draught but the behaviour of the leaf can be seen. 

When a charge is placed on the disc/cap, the charge spread down to the plate and leaf. Like charges repel each other and make the leaf to discharge from the plate, the bigger the charge, the more the divergence. If the charges are opposite to each other, the leaf collapses.

Distribution of Charges

When a conductor is charged by electrostatic induction, the distribution of charge along the conductor can be determined using a proof plane. 

A proof plane is a small conductor attached to an insulated handle used to transfer charges. Charges are not uniformly distributed always on the surface of a conductor except a spherical surface. They are always concentrated at curved or sharp points.

Investigation shows that charges are always it concentrated at sharp points and charge per area or charge density is highest at sharpest point on the conductor and the greater the charge on the proof plane, the greater the charge density on the surface where the proof plane made contact.

                                       

STORAGE OF CHARGES - THE. ELECTROPHORUS.  

An electrophorus is a simple device for storing and transferring charges. It consists of a disc that is given a negative charge by friction and a metal plate that is given a net positive charge by induction when in contact with the disc. The positive charges are stored in the disc when the handle is lifted from the ebonite rod/handle.

LIGHTING AND LIGHTNING CONDUCTOR

The basic idea of a lightning conductor is to provide a direct and easy path for lightning to reach the ground. A lightning conductor is made up of material of more conductive properties than a building, it has a metal rod that is buried deep into the ground. 

Copper and its alloys are mostly used in lightning protection. Lightning rods are pointed so a charge will be concentrated at the end. If the rod has a round end, the charges would spread equally around its surface. As long as air is prevented from ionizing, it would not conduct the lightning bolt. The purpose of the rod is to prevent ionization by discharging the ions into the dir. If the cloud were negatively charged, positive ions are attracted to the cloud, the negative charge flows to the earth as electrons, the ions neutralize the charge on the cloud so that it loses its charge without any lightning effect taking place.

                

ELECTROSTATICS AND EVERYDAY LIFE 

1. When you take off a pullover over a nylon shirt there is a crackling sound 

2. A pen rubbed with a piece of cloth will pick up small pieces of paper 

3. A television screen collects dust easily 

4. If you roll over in bed you can sometimes see small sparks between the sheets 

5. Sellotape and cling film sticking to everything 

6. Getting a small electric shock from a cat that has rolled on a synthetic carpet 

7. In a thunder storm there are huge flashes of lightning 

8. An electrostatic dust collector in a chimney. 

9. Paint sprays can be charged and the object they are spraying earthed to attract the paint towards it. 

10. Photocopiers use a charged sheet to attract fine carbon powder 

11. Charge build up when emptying oil tankers or refueling planes

ASSESSMENT: 

Reference: New School Physics, unit page. Exercise 1  

TICKET OUT: 

Reference: New School Physics, unit page. Exercise 1  

EVALUATION

Define electric charges 

Explain how charges are produced 

State the law of electrostatics 

Distinguish between conductors and insulators with examples 

Describe gold leaf electroscope 

Describe ways of charging gold leaf electroscope

WEEK 10

TOPIC: DESCRIPTION AND PROPERTIES OF FIELD

REFERENCE BOOK: NEW SCHOOL PHYSICS FOR SENIOR SECONDARY SCHOOL BY M.W. AYANKOHA

LEARNING OBJECTIVES: by the end of the lesson, learners should be able to: 

explain the concept of fields

explain the types of fields 

define gravitational field and force

explain acceleration due to gravity and why it varies on the earth surface

draw magnetic field and force

differentiate between magnets and magnetic lines of force

FIELDS 

A field is described as a region or space under the influence of some physical agency such as gravitational, magnetism and electricity. The field concept is a convenient and informative method of describing the influence of one body over another body separated from the first by some distance.

Force field 

A force field is defined as the force whose sources do not require contact with the body to which they are applied. We identified such force field as a gravitational force field, electric force, magnetic force and electromagnetic force.

Types of force field

There are two classes of force fields:

1. Scalar force field

2. Vector force field 

Scalar force field: A scalar force field is one that has only magnitude but no direction, e.g. Temperature, energy and density.

Vector force field: A vector force filed is the one that has both magnitude and direction, e.g. gravitational, magnetic and electric fields.

GRAVITATIONAL FIELD: Gravitational field is the region or space within which the influence of the force of gravity is felt. In the gravitational field, work is done against the force of gravity. It acts over a distance. It acts around every object that has mass. It is a force field. It influences the motion of objects in the space where they operate.

GRAVITATIONAL ATTRACTION: It is the earth’s attraction on every object that exists in its gravitational field. The effect of gravitational attraction is to change the velocity of an object under its influence. That is to accelerate the object.

ACCELERATION DUE TO GRAVITY: Acceleration due to gravity is the constant downward change in velocity of an object per second. It can also be defined as the acceleration of an object under the influence of gravity whose change velocity per second is 9.8 m/s.

VALUE OF ACCELERATION DUE TO GRAVITY: The value of acceleration due to gravity is 9.8 m/s². It is uniform in a given place and the same for all types of bodies irrespective of their masses. However, the value of acceleration due to gravity varies from place to place. It is minimum at the equator (9.78 m/s²) and increases with increase in latitude to reach a maximum value of 9.83m/s² at the pole of the earth.

ACCELERATION OF DIFFERENT OBJECTS RELEASED FROM THE SAME HEIGHT IN A VACUUM: When different objects of different masses are released from the same height in a vacuum, the objects fall to the ground at the same time because the same amount of acceleration due to gravity act on them all irrespective of their masses.

In the practical sense, when a stone and a feather are dropped from the same height at the same time, the stone fall faster and faster until it reaches the ground ahead of the feather. The feather falls slowly due to air friction or resistance which reduces the motion of the feather than that of the stone. Also, due to the large surface area of the feather, the feather falls more slowly than the stone.

FORCE OF GRAVITATIONAL ATTRACTION: The force of gravitational attraction is the product of the mass of the object and the acceleration due to gravity that acts on the object. It is given by the formula, force = mass × acceleration due to gravity

             Force = mass × acceleration due to gravity.

             Force = m × g

ACCELERATION OF FREE FALL DUE TO GRAVITY: Acceleration of free fall due to gravity is the force of attraction on a unit mass or one kilogram mass of object.

When mass = 1kg, then force = mg = 1× g = g. Force = acceleration due to gravity. 

F = g

Magnetic field: The region or space around a magnet in which the influence of the magnetic force can be felt or detected is called the magnetic field. This space can be mapped out using a magnetic needle. The compass needle when placed in a magnetic field, swings around and settles in a definite direction. The swinging of the needle when in the vicinity of the magnet shows that it has been subjected to a force. This force is known as the magnetic force. Thus magnetic field is a force field. Magnetic force can be felt at Sa distance. It influences an object even when not in contact with it.

A magnetic field is also a vector field, i.e. it has both magnitude and direction.

We can demonstrate the pattern or nature of the magnetic field around a bar magnet by use of Iron filings and Magnetic compass.

ASSESSMENT: 

Reference: New School Physics, unit page. Exercise 1  

TICKET OUT: 

Reference: New School Physics, unit page. Exercise 1  

EVALUATION

explain the concept of fields

explain the types of fields 

define gravitational field and force

explain acceleration due to gravity and why it varies on the earth surface

draw magnetic field and force

differentiate between magnets and magnetic lines of force

WEEK 11

TOPIC: ELECTRIC CHARGES

REFERENCE BOOK: NEW SCHOOL PHYSICS FOR SENIOR SECONDARY SCHOOL BY M.W. AYANKOHA

Explain the types of energy used in generating electricity.

Explain defects of simple cells and their prevention

State the advantages and limitations of hydroelectric power generation

Define electric current and state its formulae 

Define potential difference 

Define resistance 

define electromotive force and internal resistance of a cell

ELECTRIC FIELD 

Definition

The region around the electric charge in which the stress or electric force act is called an electric field or electrostatic field. If the magnitude of the charge is large, then it may create huge stress around the region. The electric field is represented by the symbol E. The SI unit of the electric field is Newton per coulomb which is equal to volts per meter.

Representation of electric field 

The electric field is represented by the imaginary lines of force. For the positive charge, the line of force comes out of the charge and for a negative charge, the line of force will move towards the charge. The electric field for positive and negative charges are shown below.

TYPES OF AN ELECTRIC FIELD 

The electric field is mainly classified into two types. They are the uniform electric field and 

1. The non-uniform

2. Electric field.

Uniform electric field: When the electric field is constant at every point, then the field is called the uniform electric field. The constant field is obtained by placing the two-conductor parallel to each other, and the potential difference between them remains the same at every point.

Non-uniform electric field: The field which is irregular at every point is called the non-uniform electric field. The non-uniform field has a different magnitude and directions.

Properties of an electric field 

The following are the properties of an electric field

1. Field lines never intersect each other.

2. They are perpendicular to the surface charge.

3. The field is strong when the lines are close together, and it is weak when the field lines move apart from each other.

4. The number of field lines is directly proportional to the magnitude of the charge.

5. The electric field line starts from the positive charge and ends from negative charge.

6. If the charge is single, then they start or end at infinity.

7. The line curves are continuous in a charge-free region.

8. When the electric and magnetic field

The electric force around an;

Isolated positive charge and isolated negative charge:

             

Two equal negative charges:

Two equal positive charges:

Two equal but opposite charges:

PRODUCTION OF CONTINUOUS ELECTRIC CURRENT

An electric current or continuous flow of charge can be generated via the following means:

1. Chemical Energy

2. Heat Energy

3. Mechanical Energy

4. Solar Energy

ELECTRICITY FROM CHEMICAL ENERGY 

Electricity is produced from chemical energy through the use of electric cells. A cell is a device for converting chemical energy into electrical energy. A cell consists of two unlike (dissimilar) metals separated by solutions of various acids or salts. The metals are known as the electrodes and the solutions are electrolytes. The positive electrode is known as the anode, the negative electrode is the cathode.

DEFECTS OF SIMPLE CELLS 

Simple cells supply current only for a short time. This is because of chemical processes known as:

1. Polarization: this is due to the formation of hydrogen gas bubbles around the copper plate of the simple cell. Polarization of cells is reduced or prevented by addition of a suitable chemical known as depolarizer, e.g. manganese dioxide, and potassium dichromate. The depolarizer removes the hydrogen by oxidizing it to water.

2. Local action: This is due to impurities in the zinc plate. These impurities (e.g. Iron and carbon) set up tiny cells around the zinc surface, producing bubbles of hydrogen. Local action can be prevented by the process of amalgamation that is the rubbing of mercury over the surface of the zinc plate. The mercury on the zinc plate prevents impurities from coming into contact with the acid. With this local action cannot occur.

ELECTRICITY FROM HEAT ENERGY (THE THERMOELECTRIC EFFECT)

Heat energy can be converted into electric currents by joining two different metallic wires (e.g. Copper and Iron) at one end and connecting the free ends to the terminals of a sensitive current detecting device, e.g. a milli-galvanometer. When the junction of the metals is put in hot water, a current is observed to flow along the wires as indicated by the milli-galvanometer. The junction placed in hot water is known as the hot junction, while the ends connected to the instrument constitute the cold junction.

The greater the difference in temperature between the hot and the cold junctions, the greater the Current flow.

ELECTRICITY FROM MECHANICAL ENERGY 

A great majority of the world's electricity is produced from the conversion of mechanical energy into electric energy. When coils of insulated wire move across the magnetic field between two powerful magnets, the current is induced in the coils because the coils cut across the magnetic lines of force. The current is tapped using split-ring commutators and carbon brushes. The electric generator or dynamo produces electricity in this way. A common example of such a device is the bicycle dynamo used to supply light to the headlamp of a bicycle.

DAMS AND ENERGY PRODUCTION 

Hydroelectric power generation is one of the best methods of electric power generation. This is because it is renewable and does not contaminate the environment. It is also an example of electricity produced by mechanical energy. A dam is a barrier that is built across

a river in order to stop the water from flowing, used especially to make reservoirs (i.e. a lake for storing water) or to generate electricity.

ADVANTAGES OF USING HYDROELECTRIC POWER GENERATION 

1. It does not cause any pollution in the environment

2. The dams constructed over rivers help in irrigation and control of floods 

LIMITATIONS 

1. The flowing water is not always available

2. The ecological balance in the downstream areas of rivers gets disturbed

3. Due to construction of dams over the rivers, plants and animals of that place get destroyed or killed

ELECTRICITY FROM SOLAR 

When sunlight falls on a photosensitive surface (e.g. the surface of potassium, an alkaline metal), electrons are produced whose movements constitute a current. A photoelectric cell or photocell consists of a photosensitive surface as a cathode and a wire ring as the anode. If visible light falls on this surface, electrons are emitted by the photoelectric effect and the flow of these electrons can be detected as current by a micrometre. The electrons are usually accelerated from the cathode to the anode which is at higher potential with respect to the cathode.

Advantages of solar panels 

1. They do not require any maintenance

2. They last over a long period of time

3. Their running cost is almost zero

4. They are most suitable for remote places and do not cause any pollution in the environment

Disadvantages of solar panels 

1. The initial cost of a solar panel is high

2. The efficiency of conversion of solar energy to electricity is low

3. A solar panel produces d.c. electricity which cannot be directly supplied for household purposes

CURRENT ELECTRICITY 

An electric current is the time rate of flow of electric charges along a conductor. An electric current is said to coexist when there is a net flow of electric charge through a region. 

Electric current is defined as the time rate of flow of charges along a conductor.

                     

Quantity of charge, Q = Current x time = It. 

The unit of electric current is Ampere (A). 

The current is always measured by an instrument called an ammeter which is placed in series with the circuit.

An idea ammeter has zero assistance. 

    

Potential Difference

The electric potential difference (p.d.) is defined as the work done per unit charge in moving a unit charge from one point to another. It is measured in volts with a voltmeter.

Ohm's law 

This law relates the current flowing through a conductor and the voltage drop across that section of the conductor. 

The law states that the current flowing through a conductor is directly proportional to the potential difference across its ends provided temperature and other physical factors are kept constant. 

The following set-up can be used to investigate Ohm's law:

1. Close the switch and adjust the current flowing through the conductor using the rheostat to the least possible value. Record the corresponding voltmeter reading.

2. Increase the current in steps recording the corresponding voltmeter readings.

3. Plot a graph of voltage against the current. Hence determine the slope of the graph.

The voltage drop across the conductor is directly proportional to the current through it.

This constant is what is regarded or recorded as resistance 

V/I = constant 

The constant is known as resistance R.

Thus, VI = R 

Or V= IR.

Where,

V is the voltage in volts (V)

R is Resistance in ohm (Ω)

I is Current in Ampere (A)

If a substance follows Ohm's law, then a linear relationship exists between V and I. 

These substances are called Ohmic substances e.g. metals and alloys. 

Some substances do not follow Ohm's law, these are called a non-ohmic substance.

Diode valve, rectifier, voltage-dependent resistors, triode valve and electrolytes, are some examples of non-ohmic conductors.

The SI unit of resistance R is volt/ampere = ohm (Ω)

The inverse of resistance is called conductance 

Conductance = 1resistance = 1R which is measured in (Ω)-1.

Applications of Ohm's law 

The main applications of Ohm's law are

(1) To determine the voltage, resistance or current of an electric circuit.

(2) Ohms law is also used in dc ammeter and other dc shunts to divert the current.

Limitations of Ohms law 

Following are the limitations of Ohm's law:

(1) Ohm's law is not applicable for unilateral electrical elements like diodes and transistors as they allow the current to flow through in one direction only.

Examples

(1) If the resistance of an electric iron is 500 Ω and 3.2 A Current flows through the resistance. Find the voltage between two points.

Solution

Given Parameters, 

Resistance (R) = 500 Ω

Current (I) = 3.2 A

Therefore,

Voltage (V) = I x R =3.2 A x 50 Ω = 160 V 

(2) Calculate the current flowing through an 80 Ω device when it is connected to a 12 V supply.

Solution 

I = VR

I = 1280 =1.5 A 

(3) A current of 0.5 A is drawn by a filament of an electric bulb for 10 minutes. Find the amount of electric charge that flows through the circuit.

Solution 

Given parameters;

I = 0.5 A;

t = 10 min = 600s.

Q = lt = 0.5 A x 600 s = 300 C 

Resistance 

Resistance is the amount of opposition given to the flow of electric current through a conductor of electricity. It can also be defined as the ratio of voltage to current.

Resistance is denoted by R, measured in ohm (Ω).

Thus, R = VI

Therefore V = IR 

Factors affecting the resistance of a conductor 

1. Temperature

2. Length of the conductor (L)

3. Cross-section area (A)

4. Resistivity (nature of the material)

Effects of the in temperature on resistance 

1. For Pure metal, the resistance increases.

2. For semiconductors, the resistance decreases with an increase in temperature.

3. For alloys, the resistance is constant and so standard resistors are made of alloys such as constantan.

Resistivity 

The resistivity of a material is a fundamental property of a material that quantifies how strongly a given material opposes the flow of current. The resistivity of a material is highly dependent on temperature. Therefore, at a constant temperature resistance varies directly as the length and inversely as the cross-sectional area of the conductor;

  R LA

  R= LA

Or simply, 

ρ = ARL

The constant is called the resistivity of the material.

Resistivity is measured in ohm-metre (Ωm).

Electrical conductivity 

Electrical conductivity is defined as the reciprocal of resistivity. It is denoted by K and measured in (Ωm)-1

     K=1

Example

A wire of resistance 3.50 Ω has a length of 0.5 m and cross-section area 8.2 x 10-8 m2. Determine its resistivity.

Solution 

ρ = ARL= 8.2 ×10-20.5 m m2  

= 5.74 10-7 Ωm 

Resistors in series and parallel combinations 

A resistor is a passive two-terminal electrical component that implements electrical resistance as a circuit element. Resistors reduce the current flow and lower voltage levels within circuits. It also means a specially designed conductor that offers particular resistance to the flow of electric current. Most circuits often have more than one resistor to limit the flow of charges in a circuit. 

The two simplest combinations of resistors are -series and parallel. 

Also, there are three main groups of resistors:

(1) Fixed resistors: offer fixed values of resistance. They have colour bands around them.

(2) Variable resistors: offer varying resistance e.g rheostat and potentiometer.

(3) Non-linear resistors: the current flowing through these resistors does not change linearly with the voltage applied. Examples include a thermistor and light-dependent resistor 

Circuit 

A circuit is composed of conductors (wire), power source, load, resistor, and switch. 

A circuit starts and ends at the same point. Usually, copper wire with insulation is used as a conductor. A switch is used to make or break a circuit. Resistors control the flow of the electric current in a circuit. A resistor is a passive element which means that it only consumes power but does not generate power. 

A load in a circuit consumes electrical energy and converts it into other forms of energy like light, heat, etc. A load can be a light bulb, fan, etc.

Why do we need a combination circuit?

In an electric circuit, the different components are connected either in series or in parallel to produce different resistive networks. Sometimes, in the same circuit, resistors can be connected in both parallel and series, across different loops to produce a more complex resistive network. These circuits are known as mixed resistor circuits. 

In the end, however, the total resistance should be known. It is important to know how to do this because resistors never exist in isolation. They are always part of a larger circuit that will have many resistors connected in different combinations. 

So how do we calculate this total resistance for resistors in series and parallel circuits? In the next section, let us look at how the total resistance is calculated in a circuit with different resistor combinations.

Resistors in series 

A circuit is said to be connected in series when the same amount of current flows through the resistors. In such circuits, the voltage across each resistor is different. In a series connection, if any resistor is broken or a fault occurs, then the entire circuit is turned off. 

   

From Ohm's law, V = IR.

The voltage drop across R1; V1 = IR1 

The voltage drop across R2; V2 = IR2

The voltage drop across R3; V3 = IR3 

And the total circuit voltage V = V1 + V2 + V3.

Thus V = IR1 + IR2 + IR3 = l (R1+ R2 + R3)

VI = (R1+ R2 + R3)

But VI = R

Thus the combined circuit resistance R = R1+ R2 + R3

Generally, the effective resistance of resistors arranged in series is equal to the sum of the individual resistances.

Resistors in parallel 

A circuit is said to be connected in parallel when the voltage is same across the resistors. In such circuits, the current is branched out and recombines when branches meet at a common point. A resistor or any other component can be connected or disconnected easily without affecting other elements in a parallel circuit.

    

Suppose the current flowing through R1, R2, and R3 are l1, l2 and l3, then:

The voltage drop across R1; V1 = l1 R1 

The voltage drop across R2; V2 = l2R2 

The voltage drop across R3; V3 = l3R3 

But V1 = V2 = V3 = V and I = l1 + l2 + l3 

Therefore, I = VR1+ VR2+ VR3

IV = I1R1+ 1R2+ 1R3

But IV = 1R

Hence, 1R = 1R1+ 1R2+ 1R3 

R is the combined circuit resistance.

A special case of two resistors in parallel 

It follows that 1R = 1R1+ 1R2

R = R1R2R1+ R2

Hence the effective resistance, R = R1R2R1+ R2

Generally, for n resistors arranged in parallel, the effective resistance of the arrangement is given by:

 1R = 1R1+ 1R2+…+ 1Rn   

Note: When a circuit comprises of both series and parallel connections, the arrangement is systematically reduced to a single resistor.

Electromotive force and internal resistance of a cell 

An emf (electromotive force) device has a positive terminal (at high potential) and a negative terminal (at low potential). This device is responsible for moving a positive charge within itself from the negative terminal to the positive terminal.

For this to happen, work is done by some agency in the emf device. The energy required to do this work is chemical energy (as in a battery), mechanical energy (as in an electric generator), and temperature difference (as in a thermopile).

The S.I unit of emf is (V)

Note:

Electromotive force is not a force but a potential difference.

E.m.f. can be defined as the work done in moving a charge once around a closed circuit.

INTERNAL RESISTANCE, r 

The potential difference across a real source of emf is not equal to its emf. The reason is that the charge which is moving inside the emf device also suffers resistance. This resistance is called internal resistance of the end device.

E = IR+ Ir 

= V + Ir 

V = E - Ir 

Note: Emf is the property of a cell but terminal potential difference depends on the current drawn from the cell.

Short-circuiting 

When the terminals of an emf device are connected with a conducting path without any external resistance then 

E = Ir 

Since internal resistance has a very small value, therefore a very high current flows in the circuit producing a large amount of heat. This condition is called short-circuiting.

During short-circuiting, the terminal potential difference is zero.

Combination of cells 

Series combination of cells:

    

Equivalent E.m.f.

E = E1 +E2 + ... + En 

Equivalent internal resistance 

RAB = r1 +r2 + rn 

Parallel combination of cells:

Equivalent e.m.f. = E 

Equivalent internal resistance

 1rT = 1r1+ 1r2+…+ 1rn  

Worked examples 

(1) A resistor having an electrical resistance value of 100 Ω is connected to another resistor with a resistance value of 200 Ω. The two resistances are connected in series. What is the total resistance across the system?

Solution

Here, R1 = 100 Ω and R2= 200 Ω

Rtotal = 100 + 200 = 300 Ω

(2) Three resistors each of resistance 5 Ω are arranged in series in a circuit. What is the equivalent resistance of the circuit?

Solution 

RT = R1 + R2 + R3

RT = 5 + 5 + 5 = 15 Ω

(3) Three resistors of resistance 10, 20 and 4 Ω are connected in series. Find the equivalent resistance of the combination.

Solution 

RT = R1 + R2 + R3

RT = 10 + 20 + 4 = 34 Ω

ASSESSMENT: 

Reference: New School Physics, unit page. Exercise 1  

TICKET OUT: 

Reference: New School Physics, unit page. Exercise 1  

EVALUATION

Explain the types of energy used in generating electricity.

Explain defects of simple cells and their prevention

State the advantages and limitations of hydroelectric power generation

Define electric current and state its formulae 

Define potential difference 

Define resistance 

define electromotive force and internal resistance of a cell