Physics Notes

PHYSICS FORM 4 NOTES

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PHYSICS FORM FOUR

CHAPTER ONE

THIN LENSES.

A lens is conventionally defined as a piece of glass which is used to focus or change the direction of a beam of light passing through it. They are mainly made of glass or plastic. Lens are used in making spectacles, cameras, cinema projectors, microscopes and telescopes.

 

Types of thin lenses.

A lens which is thicker at its centre than at its edges converges light and is called convex or converging lens. A lens which is thicker at its edges than at its centre diverges light and is known as concave or diverging lens.

Properties of lenses.

1. Optical centre – this is the geometric centre of a lens which is usually shown using a black dot in ray diagrams. A ray travelling through the optical centre passes through in a straight line.
2. Centre of curvature – this is the geometric centre of the circle of which the lens surface is part of. Since lenses have two surfaces there are two centres of curvature. C is used to denote one centre while the other is denoted by C1.
3. Principal axis – this is an imaginary line which passes through the optical centre at right angle to the lens.
4. Principal focus – this is a point through which all rays travelling parallel to the principal axis pass after refraction through the lens. A lens has a principal focus on both its sides. F is used to denote the principal focus
5. Focal length – this is the distance between the optical centre and the principal focus. It is denoted by ‘f’.

The principal focus for a converging lens is real and virtual for a diverging lens. It is important to note that the principal focus is not always halfway between the optical centre and the centre of curvature as it is in mirrors.

 

Images formed by thin lenses

The nature, size and position of the image formed by a particular lens depends on the position of the object in relation to the lens.
Construction of ray diagrams
Three rays are of particular importance in the construction of ray diagrams.

1. A ray of light travelling parallel to the principal axis passes through the principal focus on refraction through the lens. In case of a concave lens the ray is diverged in a way that it appears to come from the principal focus.
2. A ray of light travelling through the optical centre goes un-deviated along the same path.
3. A ray of light travelling through the principal focus is refracted parallel to the principal axis on passing through the lens. The construction of the rays is illustrated below.

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PHYSICS FORM THREE
CHAPTER ONE
 LINEAR MOTION
Introduction
Study of motion is divided into two;

1. Kinematics
2. Dynamics

In kinematics forces causing motion are disregarded while dynamics deals with motion of objects and the forces causing them.

1. Displacement

Distance moved by a body in a specified direction is called displacement. It is denoted by letter‘s’ and has both magnitude and direction. Distance is the movement from one point to another. The Si unit for displacement is the metre (m).

1. Speed

This is the distance covered per unit time.
Speed= distance covered/ time taken. Distance is a scalar quantity since it has magnitude only. The SI unit for speed is metres per second(m/s or ms-1)
Average speed= total distance covered/total time taken
Other units for speed used are Km/h.
Examples

1. A body covers a distance of 10m in 4 seconds. It rests for 10 seconds and finally covers a distance of 90m in 60 seconds. Calculate the average speed.

Solution
Total distance covered=10+90=100m
Total time taken=4+10+6=20 seconds
Therefore average speed=100/20=5m/s

1. Calculate the distance in metres covered by a body moving with a uniform speed of 180 km/h in 30 seconds.

Solution
Distance covered=speed*time
=180*1000/60*60=50m/s
=50*30
=1,500m

1. Calculate the time in seconds taken a by body moving with a uniform speed of 360km/h to cover a distance of 3,000 km?

Solution
Speed:360km/h=360*1000/60*60=100m/s
Time=distance/speed
3000*1000/100
=30,000 seconds.

1. Velocity

This is the change of displacement per unit time. It is a vector quantity.
Velocity=change in displacement/total time taken
The SI units for velocity are m/s
Examples

1. A man runs 800m due North in 100 seconds, followed by 400m due South in 80 seconds. Calculate,
2. His average speed
3. His average velocity
4. His change in velocity for the whole journey

Solution

1. Average speed: total distance travelled/total time taken

=800+400/100+80
=1200/180
=6.67m/s

1. Average velocity: total displacement/total time

=800-400/180
=400/180
=2.22 m/s due North

1. Change in velocity=final-initial velocity

= (800/100)-(400-80)
=8-5
=3m/s due North

1. A tennis ball hits a vertical wall at a velocity of 10m/s and bounces off at the same velocity. Determine the change in velocity.

Solution
Initial velocity(u)=-10m/s
Final velocity (v) = 10m/s
Therefore change in velocity= v-u
=10- (-10)
=20m/s

1. Acceleration

This is the change of velocity per unit time. It is a vector quantity symbolized by ‘a’.
Acceleration ‘a’=change in velocity/time taken= v-u/t
The SI units for acceleration are m/s2
Examples

1. The velocity of a body increases from 72 km/h to 144 km/h in 10 seconds. Calculate its acceleration.

Solution
Initial velocity= 72 km/h=20m/s
Final velocity= 144 km/h=40m/s
Therefore ‘a’ =v-u/t
= 40-20/10
2m/s2

1. A car is brought to rest from 180km/h in 20 seconds. What is its retardation?

Solution
Initial velocity=180km/h=50m/s
Final velocity= 0 m/s
A = v-u/t=0-50/20
= -2.5 m/s2
Hence retardation is 2.5 m/s2

Motion graphs
Distance-time graphs

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Chemistry Notes

PHYSICS FORM TWO NOTES

CHAPTER ONE

MAGNETISM

Introduction

Magnets are substances that are able to attract and hold items. Lodestone is the only known natural magnet which was discovered by the Chinese 2,000 years ago. Other magnets produced artificially by man are called artificial magnets.

 

Magnets and non-magnetic materials

Magnetic materials are those that are strongly attracted by magnets while non-magnetic ones are those that are not affected by magnets. Iron, steel, cobalt and nickel are magnetic substances, while wood, glass and copper are examples of non-magnetic substances.Substances that are repelled by magnets are said to be diamagnetic whereas those which are strongly attracted i.e. iron, nickel, cobalt are called ferromagnetic materials. The materials that are so lightly attracted such that the magnet seems to have no effect on them are called paramagnetic materials (mostly non-magnetic materials). Ferrites are a mixture of iron oxide and barium oxide are the most newly developed magnetic materials. Ceramic magnets or magnadur magnets are made from ferrites and are very strong.

 

Properties of magnets

1. They are double poled substances with both the North and South poles.
2. Like poles repel and unlike poles attract. Repulsion is a sure method of determining whether two substances are magnets.
3. The greatest magnetic force is concentrated around the poles of a magnet.

Magnetic field patterns.

Magnetic field is the space around a magnet where magnetic field (force) is observed.

Plotting field patterns

A line of force gives the direction of the magnetic field at each point along it. Their closeness is a measure of the strength of the magnetic field or of the force that would be exerted by the bar magnet.

The points marked ‘X’ are called neutral points where there is no magnetic field at such points. Watches (non-digital), electron beams in cathode ray tubes and TV sets are shielded from external magnetic fields by placing a soft-iron cylinder around the neck of the tube or watch.

 

Making magnets

The following are methods used to make magnets.

1. Magnetic induction– this is a process by which magnets are made by placing ferromagnetic materials in a magnetic field. Materials like iron lose their magnetism easily and are said to be soft while others like steel gain magnetism slowly but retain it longer and are therefore said to be hard and are used to make permanent magnets.
2. Magnetizing by stroking– the object to be magnetized is placed on a bench then a bar magnet is dragged along the length of the bar from one end to the other. This is repeated several times and the object becomes magnetized. This method is known as single-stroke method.

PHYSICS FORM ONE
CHAPTER ONE
INTRODUCTION TO PHYSICS
Science in our lives
Scientists are people trained in science and who practice the knowledge of science. We require people in industries to work as engineers, technicians, researchers, in hospitals as doctors, nurses and technologists. Science gives us powerful ideas, instruments and methods which affect us in our daily lives.

Scientific methods

• A laboratory is a building specifically designed for scientific work and may contain many pieces of apparatus and materials for use.
• A hypothesis is a scientific fact or statement that has not been proven or experimented.
• A law or principle is a scientific fact or statement that has been proven and experimented to be true for all conditions.
• A theorem is a fact or statement that is true and proven but applicable under specific conditions.

What is physics?
Physics is a Greek word meaning nature hence it deals with natural phenomena. Physics is therefore a science whose objective is the study of components of matter and their mutual interactions. Physics is also defined as the study of matter and its relation to energy.A physicist is able to explain bulk properties of matter as well as other phenomena observed.

Branches of physics

• Mechanics – the study of motion of bodies under the influence of force.
• Electricity – this deals with the movement of charge from one point to another through a conductor.
• Magnetism – the study of magnets and magnetic fields and their extensive applications.
• Thermodynamics / heat – this is the study of the transformation of heat from one form to another.
• Optics –the study of light as it travels from one media to another
• Waves – the study of disturbances which travel through mediums or a vacuum.
• Particle physics
• Nuclear physics
• Plasma physics

Relation of physics to other subjects
Since physics enables us to understand basic components of matter and their mutual interactions it forms the base of natural science. Biology and chemistry borrow from physics in explaining processes occurring in living things and organisms. Physics also provides techniques which are applied almost every area of pure and applied science i.e. meteorology, astronomy etc.
Career opportunities in physics

• Engineering – civil
• Electrical
• Mechanical
• Agricultural
• Environmental
• Chemical
• Computer
• Meteorology
• Surveying
• Geology
• Astronomy

NOTE: – all science based careers i.e. doctors, nurses, technologists, engineers, pharmacists etc. need physics as a true foundation.

Basic laboratory safety rules

• Proper dressing must be observed, no loose clothing, hair and closed shoes must be worn.
• Identify the location of electricity switches, fire-fighting equipment, first aid kit, gas and water supply systems.
• Keep all windows open whenever working in the laboratory.
• Follow all instructions carefully and never attempt anything in doubt.
• No eating or drinking allowed in the laboratory.
• Ensure that all electrical switches, gas and water taps are turned off when not in use.
• Keep floors and working surfaces dry. Any spillage must be wiped off immediately.
• All apparatus must be cleaned and returned in the correct location of storage after use.
• Hands must be washed before leaving the laboratory.
• Any accidents must be reported to the teacher immediately.

 

 

 

 

 

 

 

 

CHAPTER TWO
MEASUREMENT I
In order to measure we need to know or define the quantity to be measured and the units for measuring it. In 1971 a system known as the International System of Units (Systeme’ International- SI units) and seven basic units were agreed upon as follows. Other quantities can be/derived obtained from these basic quantities and are referred to as derived quantities.

Basic quantity	SI units	Symbols
Length	Metre	m
Mass	Kilogram	kg
Time	Second	s
Electric current	Ampere	A
Thermodynamic temperature	Kelvin	K
Luminous intensity	Candela	Cd
Amount of substance	Mole	mol

Length
This is the measure of distance between two points in space. The SI unit for length is the metre (m).Therefore 1 km = 1000 m
1 Hm = 100 m
1 Dm= 10 m
1 mm = 0.001 m
Length is measured using a metre rule (100 cm), tape measure (100 m, 300 m, 500 m)

Area
This is the measure of the extent of a surface. It is a derived quantity of length. Its SI units are square metres (m2).  Other units are cm2, km2, etc. Formulas are used to determine areas of regular bodies while for irregular bodies an approximation of area is used.

Volume
This is the amount of space occupied by matter. The SI units for volume are cubic metre (m3). Other sub-multiples are cm3, mm3 and l. Hence 1 m3 = 1,000,000 cm3 and 1l= 1,000 cm3. Volume can be measured using a measuring cylinder, eureka can, pipette, burette, volumetric flask, beaker, etc.

Mass
This is the quantity of matter contained in a substance. Matter is anything that occupies space and has weight. The SI unit for mass is the Kilogram (kg). Other sub-multiples used are grams (g), milligrams (mg) and tonnes (t). 1 kg = 1,000 g = 1,000,000 mg=100 tonnes. A beam balance is used to measure mass.

Density
This is mass per unit volume of a substance. It is symbolized by rho (ρ) and its SI unit are kg/m3. Density = mass / volume.

Examples

• A block of glass of mass 187.5 g is 5.0 cm long, 2.0 cm thick and 7.5 cm high. Calculate the density of the glass in kgm-3.

Solution
Density = mass / volume = (187.5 /1000) /(2.0 × 7.5 × 5.0 /1,000,000) = 2,500 kgm-3.

• The density of concentrated sulphuric acid is 1.8 g/cm3. Calculate the volume of 3.1 kg of the acid.

Solution
Volume = mass / density = 3,100 / 1.8 = 1,722 cm3 or 0.001722 m3.

The following is a list of densities of some common substances

Substance	Density (g/cm3)	Density (kg/m3)
Platinum	21.4	21,400
Gold	19.3	19,300
Lead	11.3	11,300
Silver	10.5	10,500
Copper	8.93	8,930
Iron	7.86	7,860
Aluminium	2.7	2,700
Glass	2.5	2,500
Ice	0.92	920
Mercury	13.6	13,600
Sea water	1.03	1,030
Water	1.0	1,000
Kerosene	0.80	800
Alcohol	0.79	790
Carbon (iv) oxide	0.00197	1.97
Air	0.00131	1.31
Hydrogen	0.000089	0.089

 

Example
The mass of an empty density bottle is 20 g. Its mass when filled with water is 40.0 g and 50.0 g when filled with liquid X. Calculate the density of liquid X if the density of water is 1,000 kgm-3.
Solution
Mass of water = 40 – 20 = 20 g = 0.02 kg.
Volume of water = 0.02 / 1,000 = 0.00002 m3. Volume of liquid = volume of bottle
Mass of liquid = 50 – 20 = 30 g = 0.03 kg
Therefore density of liquid = 0.03 / 0.00002 = 1,500 kgm-3

Relative density
This is the density of a substance compared to the density of water.
It is symbolized by (d) and has no units since it’s a ratio.
Relative density (d) = density of substance / density of water.
It is measured using a relative density bottle
Example
The relative density of some type of wood is 0.8. Find the density of the wood in kg/m3.
Solution
Density of substance = d × density of water
Density of substance = 0.8 × 1,000 = 800 kgm-3

Densities of mixtures
We use the following formula to calculate densities of mixtures
Density of the mixture = mass of the mixture / volume of the mixture

Example
100 cm3 of fresh water of density 1,000 kgm-3 is mixed with 100 cm3 of sea water of density 1030 kgm-3. Calculate the density of the mixture.
Solution
Mass = density × volume
Mass of fresh water = 1,000 × 0.0001 = 0.1 kg
Mass of sea water = 1030 × 0.0001 = 0.103 kg
Mass of mixture = 0.1 + 0.103 = 0.203 kg
Volume of mixture = 100 + 100 = 200 cm3 = 0.0002 m3
Therefore density = mass / volume = 0.203 / 0.0002 =1,015 kg/m3.

Time
This is a measure of duration of an event. The SI unit for time is the second (s). Sub-multiples of the second are milliseconds, microseconds, minute, hour, day, week and year. It is measured using clocks, stop watches, wrist watches, and digital watches.

Accuracy and errors
Accuracy is the closeness of a measurement to the correct value of the quantity being measured. It is expressed as an error. An error is therefore the deviation of measurement to the correct value being measured. The smaller the error the accurate the measurement.
% error = (sensitivity / size measured) × 100.

 

 

 

 

 

 

 

CHAPTER THREE
FORCES.
Force is a push or a pull. Force is therefore that which changes a body’s state of motion or shape. The SI unit for force is Newton (N). It is a vector quantity. It is represented by the following symbol.

 

 

Types of forces

• Gravitational force –this is the force of attraction between two bodies of given masses.
• Earth’s gravitational force is the force which pulls a body towards its center. This pull of gravity is called weight.
• Force of friction – this is a force which opposes the relative motion of two surfaces in contact with each other. Friction in fluids is known as viscosity.
• Tension force – this is the pull or compression of a string or spring at both its ends.
• Upthrust force – this is the upward force acting on an object immersed in a fluid.
• Cohesive and adhesive forces – cohesive is the force of attraction of molecules of the same kind while adhesive is the force of attraction of molecules of different kinds.
• Magnetic force – this is a force which causes attraction or repulsion in a magnet.
• Electrostatic force – this is the force of attraction or repulsion of static charges.
• Centripetal force – this is a force which constrains a body to move in a circular orbit or path.
• Surface tension – this is the force which causes the surface of a liquid to behave like a stretched skin. This force is cohesive.

Factors affecting surface tension

• Impurities – they reduce the surface tension of a liquid e.g. addition of detergent
• Temperature – rise in temperature reduces tension by weakening inter-molecular forces.

Mass and weight.
Mass is the amount of matter contained in a substance while weight is the pull of gravity on an object. The SI unit for mass is the Kg while weight is the newton (N).  Mass is constant regardless of place while weight changes with place. The relationship between mass and weight is given by the following formula, W = mg where g = gravitational force.

Differences between mass and weight

Mass	Weight
It is the quantity of matter in a body	It is the pull of gravity on a body
It is measured in kilograms	It is measured in newton’s
It is the same everywhere	It changes from place to place
It is measured using a beam balance	Measured using a spring balance
Has magnitude only	Has both magnitude and direction

Example
An astronaut weighs 900 N on earth. On the moon he weighs 150 N. Calculate the moons’ gravitational strength. (Take g = 10 N/kg).
Solution
Moons’ gravitational strength = weight of astronaut on the moon / mass of astronaut.
= 150 / 90 = 1.67 Nkg-1.

 

Measuring force
We use a spring balance to measure force. A spring balance is an instrument that uses the extension of a spring to measure forces.

Example
The length of a spring is 16.0 cm. its length becomes 20.0 cm when supporting a weight of 5.0 N. calculate the length of the spring when supporting a weight of:

1. 2.5 N      b) 6.0 N          c) 200 N

Solution
5N causes an extension of 4.0 cm, therefore 1.0 cm causes an extension of 4 /5 = 0.8 cm.

1. 2.5 N => 2.5 × 0.8 = 2.0 cm therefore length becomes = 16.0 + 2.0 = 18.0 cm.
2. 6.0 N => 6.0 × 0.8 = 4.8 cm therefore length becomes = 16.0 + 4.8 = 20.8 cm.
3. 200 N => 200 × 0.8 = 160.0 cm therefore length becomes = 16.0 + 160.0 = 176.0 cm.

Vector and scalar quantities
A scalar quantity is a quantity which has magnitude (size) only. Examples are distance, mass, speed
A vector quantity is a quantity which has both magnitude and direction. Examples are displacement, weight, velocity.

 

CHAPTER FOUR
PRESSURE
Pressure is defined as the force acting normally (perpendicularly) per unit area. The SI units for pressure is newton per metre squared (N/m2). One Nm-2 is known as one Pascal (Pa).
Pressure = normal force / area or pressure = thrust / area. Another unit for measuring pressure is the bar. 1 bar = 105 N/m2. 1millibar = 100 N/m2.
Calculating pressure
Examples

1. A rectangular brick of weight 10 N, measures 50 cm × 30 cm × 10 cm. calculate the values of the maximum and minimum pressures which the block exert when resting on a horizontal table.

Solution
Area of the smallest face = 0.3 × 0.1 = 0.03 m2.
Area of the largest face = 0.5 × 0.3 = 0.15 m2.
Maximum pressure = 10 N / 0.03 = 3.3 × 102 N/m2.
Minimum pressure = 10 N / 0.15 = 67 N/m2.

1. A man of mass 84 kg stands upright on a floor. If the area of contact of his shoes and the floor is 420 cm2, determine the average pressure he exerts on the floor. (Take g = 10 N/Kg)

Solution
Pressure = force / area = 840 / 0.042 = 20,000 Nm-2.

Pressure in liquids.
The following formula is used to determine pressure in liquids.
Pressure = h ρ g, where h – height of the liquid, ρ – density and g – is force of gravity.
Examples

1. A diver is 10 m below the surface of water in a dam. If the density of water is 1,000 kgm-3, determine the pressure due to the water on the diver. (Take g = 10 Nkg-1)

Solution
Pressure = h ρ g = 10 × 1000 × 10 = 100,000 Nm-2.

1. The density of mercury is 13,600 kgm-3. Determine the liquid pressure at a point 76 cm below the surface of mercury. (Take g = 10 Nkg-1)

Solution
Pressure = h ρ g = 0.76 × 13,600 × 10 = 103,360 Nm-2.

1. The height of the mercury column in a barometer is found to be 67.0 cm at a certain place. What would be the height of a water barometer at the same place? (Densities of mercury and water are 1.36 × 104 kg/m3 and 1.0 × 103 kg/m3 respectively.)

Solution
Let the pressure due to water be h1ρ1g1 = h ρ g, hence;
h1 = h ρ / ρ1= (6.7 × 10-1) × (1.36 × 104) = 911.2 cm or 9.11 m.

 

U-tube manometer
It is a transparent tube bent into U-shape. When a liquid is poured into a u-tube it settles at equal level since pressure depends on height and they share the same bottom. Consider the following diagrams;

For the levels to differ the pressure P1 must be greater than P2, hence
P1 = P2 + hρg.
If P1 is the lung pressure, P0 is the atmospheric pressure, then if the difference is‘h’ then lung pressure can calculated as follows.
P1 = P0 + hρg.
Example
A man blows into one end of a U-tube containing water until the levels differ by 40.0 cm. if the atmospheric pressure is 1.01 × 105 N/m2 and the density of water is 1000 kg/m3, calculate his lung pressure.
Solution
Lung pressure = atmospheric Pressure + liquid pressure
P1 = P0 + hρg. Hence P1 = (1.01 × 105) + (0.4 × 10 × 1000) = 1.05 × 105 N/m2.

Measuring pressure

1. Simple mercury barometer– it is constructed using a thick walled glass tube of length 1 m and is closed at one end. Mercury is added into the tube then inverted and dipped into a dish containing more mercury. The space above the mercury column is called torricellian vacuum. The height ‘h’ (if it is at sea level) would be found to be 760 mm. Atmospheric pressure can be calculated as,

P = ρ g h =>where ρ (mercury)- 1.36 × 104 kg/m3, g– 9.81 N/kg, h– 0.76 m.
Then P = (1.36 × 104) × 9.81 × 0.76 = 1.014 × 105 Pa.
NOTE– this is the standard atmospheric pressure, sometimes called one atmosphere. It is approximately one bar.

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