Physics Notes Form 2

Free KCSE Mocks - KCSE Questions and Answers - Download Free KCSE Marking Schemes - KCSE Revision - KCSE Results
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 artificia l 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.

Examples of field patterns.

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.

a) 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.

b) 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.

c) Magnetizing using an electric current – this is the use of magnetic effect of an electric current through a solenoid (insulated wire of many turns).

Demagnetizing

Demagnetizing is the process of removing magnetic properties of a magnet .

The following methods are which a magnet can lose its magnetism;

a) Hammering them hard with their poles facing E-W direction

b) Heating them strongly

c) Placing a magnet inside a solenoid and passing an a.c. current through it for a short time.

Caring for magnets

a) Magnets should be stored in pairs with unlike poles adjacent to each other attached to pieces of soft iron called keepers.

b) Magnets should not be hammered especially with their poles facing E-W direction.

c) Magnets should not be heated strongly or dropped roughly on hard surfaces.

d) Magnets should not be placed near alternating currents.

e) Magnets should be kept dry and clean since rust can make them lose their magnetism.

Uses of magnets

1. Used in making other magnets

2. Used in making loud speakers

3. Used in making moving coil meters

4. Used in making telephone speakers.

Domain theory of magnetism.

In ferromagnetic substances small atomic magnets form large groups called domains.

These atomic magnets face one direction where the direction varies from one domain to another.

In an un-magnetized crystal the directions of these domains are different hence their resultant magnetism is zero.

When a magnetic material is placed in a magnetic field the atomic magnets rotate and eventually all domains face the same direction.

When this happens then the material becomes magnetized.

When a material is magnetized we say it is saturated.

This means that the magnetism of the material cannot be increased by any other method and this is the domain theory of magnetism.

Chapter Two

Measurement II

Measuring length using vernier callipers.

Vernier callipers is used when higher accuracy in measurement is required and this cannot be done using a metre rule.

Vernier callipers has two scales; main scale and vernier scale. Outside jaws are used to measure both lengths and external diameters, inside jaws for measuring internal diameters while the tail is used for measuring depths of cavities .

The main scale is divided into cm and mm. The vernier scale is divided into 10 equal divisions of 0.9 mm each. The accuracy of vernier callipers is 0.10 mm.

The reading is taken in two steps;

a) The main scale is read at zero mark of the vernier scale. The values given in cm.

b) The vernier is read at the position where a mark on the vernier scale is exactly lined up with a mark on the main scale. The values are given as a two decimal of a cm.

Examples

1. Give the reading in the following diagram.

Solution

Main scale reading: - 2.7 cm

Vernier scale reading: - 0.04 cm

Adding both we get 2.74 cm.

2. What is the reading of the vernier callipers shown below?

Solution

Main scale reading - 7.6 cm Vernier scale reading - 0.04 cm Adding both readings we get 7.64 cm.

Micrometer screw gauge

It is a device used to measure small lengths.

It has an accuracy of 0.01 mm. It has two scales; the sleeve scale and thimble scale.

The sleeve scale is divided into upper and lower scales with the upper division in mm and lower divisions in 0.5 mm.

Thimble scale is divided into 50 equal divisions each division consisting of 0.01 mm.

The reading is taken in two steps;

a) The reading on the sleeve scale is read ta the point where it touches the edge of the thimble in mm and half mm.

b) The thimble scale is read at the point where the centre line of the sleeve is parallel to the thimble scale division.

Examples

1. Give the reading in the following.

Solution Sleeve reading – 3.5 mm Thimble reading – 0.45 mm Adding up we get 3.95 mm.

2. What is the reading in the following micrometer screw gauge?

Solution

Sleeve scale reading – 4.0 mm Thimble scale reading - 0. 32 mm Adding up the two we get 4.32 mm.

Calculating the size of a molecule.

Both the volume and area of a drop can be calculated using the following formulas Volume = 4/3 πr3 and Area = πr2h.

Examples

1. A drop of olive oil, whose volume is 0.12 mm 3, was placed on a surface of clean water.

The oil spread and formed a patch of area 6.0 × 104 mm2. Estimate the size of the olive oil.

Solution

Volume = 0.12 mm2. Area of the oil patch = 6.0 × 104 mm2. Volume = area × thickness of the patch, therefore Thickness of the oil patch = volume / area = 0.12 / 6.0 × 104 = 2.0 × 10-6 mm or 2.0 × 10-9 m.

2. Suppose an oil drop has a volume of 0.10 mm 3 and forms a film with a radius of 10 cm.

Calculate, the thickness of the oil film. Solution

Area of the film = πr2 = 3.14 × 10 × 10 = 314 cm2 = 31,400 mm2.

Thickness of the oil film = volume / area, hence 0.10 / 31,400 = 3.0 × 10-6 mm.

(The thickness of the oil film is called upper limit to the size of molecule because the molecule cannot be bigger than the thickness of the oil film)

Chapter Three

Turning Effect of a Force

Turning effects

The turning effect of a body is called the moment of that force.

The turning effect produced depends on both the size of the force and the distance from the pivot.

The moment of a force about a point is the product of the force applied and the perpendicular distance from the pivot (or turning point) to the line of action of the force.

Hence, Moments of a force = Force × perpendicular distance from pivot.

The law of moments

The law of moments states that “when a body is in balance or in equilibrium, the sum of the clockwise moments equals the sum of anti-clockwise moments”.

The SI units of the moments of a force is Newton metre (Nm).

Examples

1. A uniform rod of negligible mass balances when a weight of 3 N is at A, weight of 3 N is at B and a weight of W is at C. What is the value of weight W?

2. The following bar is of negligible weight. Determine the value of ‘ x’ if the bar is balanced.

Solution

The distance from the turning point to the line of action can be determined as,

Clockwise moments = 10 × 30 = 300 N cm, Anticlockwise moments = 10 × ‘x’ = 10 x. N cm. Using the principle of moments

Anti-clockwise moments = clockwise moments

10 x = 300, hence x = 30 cm.

3. Study the diagram below and determine the value of X and hence the length of the bar.

Solution

Clockwise moments = 15x N + 5(X × 20) N

Anticlockwise moments = (20 × 10) + (60 × 10) N cm, = 800 N cm.

Anti-clockwise moments = clockwise moments

800 N cm = 15X + 5X + 100

800 n cm = 20X + 100

20X = 700

X = 35 cm.

Therefore, the length of the bar = 40 + 20 + 35 + 20 = 115 cm.

The lever

A lever is any device which can turn about a pivot or fulcrum .

The applied force is called the effort and is used to overcome the resisting force called the load. We use the law of moments in the operation of levers.

Example

Consider the following diagram. (The bar is of negligible mass). Determine the effort applied.

Solution

Taking moments about O. Then, clockwise moments = effort × 200 cm. Anticlockwise moments = 200 × 30 cm.

Effort = (200 × 30)/ 200 = 30 N.

Chapter Four

Equilibrium and Centre of Gravity.

Centre of gravity

Centre of gravity or C.G is the point of balance of a body in which the total weight of the body seems to act through.

For regular shaped bodies the C.G is at the geometric centre of the body. For irregular bodies their weight still acts at the centre of the gravity and the law of moments can be used to determine the weight of the body.

Example

The figure below shows a uniform bar of weight ‘W’ and length 80 cm. If a force of 20 N keeps it in balance, determine the weight ‘W’ of the bar.

Solution

Taking moments about the pivot, clockwise moments = W × 20 N cm.

Anticlockwise moments = 20 × 30 N cm. Clockwise moments = anticlockwise moments 20 W = 600, therefore W = 30 N.

Parallel forces and equilibrium

For a body to be in equilibrium (neither moving nor rotating), under the action of parallel forces, the following conditions will be satisfied;

a) The sum of upward forces must be equal to the sum of downward forces.

b) The sum of clockwise moments equals the sum of anticlockwise moments.

The two are called the first and second condition of equilibrium respectively.

Examples 1. A uniform rod of length 1.0 m is hung from a spring balance as shown and balanced in horizontal position by a force of 1.6 N. Determine; a) The weight of the rod

b) Reading of the spring balance.

Solution

a) Let the weight of the rod be ‘W’. W acts at 50 cm mark, therefore taking moments about point of suspension, clockwise moments = W × 0.2 Nm = 0.2W Nm.

Anticlockwise moments = 1.6 × 0.3 = 0.48 Nm.

Using the law of moments, then

Anticlockwise moments = clockwise moments

0.48 = 0.2 W, hence W = 2.4 N

b) Upward forces = downward forces

Downward force = W + 1.6 N

= 2.4 + 1.6

= 4.0 N

Upward force = reading of the spring balance = 4.0 N

2. A uniform rod is 1.0 m long weighs 5 N. It is supported horizontally at one end by a spring and the other end rests on a table as shown below. A mass of 2kg is hung from the rod as shown; determine,

a) Reading of the spring balance

b) Reaction force, F, from the table.

Solution

a) The 2kg mass and the weight of the rod (5 N) gives clockwise moment while the spring balance provides anticlockwise moments.

Clockwise moments = (2 × 10) × 0.4 + (5 × 0.5) = 10.5 Nm. Anticlockwise moments = S × 1 (reading of the spring balance)

1S = 10.5, hence S = 10.5 N. b) Upward forces = downward forces

Downward forces = (2 × 10) + 5 = 25 N Therefore F+ 10.5 = 25, hence F = 14.5 N.

Stability

This is a term which explains how easy or difficult it is for an object to topple over when a force is applied to it. Factors affecting stability,

a) Base area – the bigger the base area the more the stability.

b) Position of the centre of gravity – the higher the centre of gravity the less stable the body will be.

States of equilibrium

1. Stable equilibrium – if a body is displaced by a small amount of force it returns to its original position.

2. Unstable equilibrium – if a body is displaced by a small amount of force it toppled over and does not return to its original position.

3. Neutral equilibrium – a body is at rest in whichever position it is placed in i.e. it does not rise or fall when displaced.

Applications of stability

Neutral equilibrium It is used mainly in the design of motor vehicles i.e.

a) Racing cars – they have a low and wide wheelbase to increase their base area.

b) Double decker buses – they are manufactured with a low centre of gravity by mounting their chassis and engines as low as possible.

Chapter Five

Reflection at Curved Surfaces

Concave and convex mirrors

They are also known as spherical mirrors and are formed when a spherical glass is silvered .

If the inside is silvered a convex or diverging is formed while a concave or converging mirror is formed when the outside is silvered.

Parts of a spherical mirror.

1. Centre of curvature (C) – this is the centre of the sphere of which the mirror is part of. The centre itself is called the pole (P).

2. Principal axis – this is the line joining the centre of curvature (C) to the pole (P).3. Principal focus (F) – is a point on the principal axis through which a ray is reflected when it hits a concave mirror.

In a convex mirror the ray is reflected and appears to originate from the point. F is virtual for a convex mirror while it is real for a concave mirror.

4. Radius of curvature (r) - this is the distance from the pole to the centre of curvature. The distance from the pole to the principal focus is called the focal length (f).

Parabolic mirrors.

They produce a wide parallel beam or converge a large beam of light to a point. They are widely used in making car headlights or in spotlights.

Images formed by spherical mirrors.

Location of images using ray diagrams.

When drawing ray diagrams the following symbols are used to represent the mirrors.

The image is located by drawing any two of the following rays:

i) A ray parallel to the principal axis which is reflected through the principal focus.

ii) A ray through the centre of curvature which is reflected along its own path since it hits the mirror normally.

iii) A ray through the principal focus which is reflected parallel to the principal axis.

Virtual images are formed when rays diverge and as such the rays are extended backwards using dotted line till they meet.

The image formed is also dotted since it is not formed by an intersection of real rays.

A real image is formed by intersection of real rays.

Concave mirror.

a) Object at infinity: image is formed at F. It is real, inverted and diminished.

Convex mirror.

g) Image is always formed behind the mirror. It is virtual, erect and always diminished.

Applications of curved reflectors.

a) They are used in satellite dishes.

b) They are used in making shaving mirrors.

c) They are used in telescopes.

d) They are used in driving mirrors.

Magnification.

Magnification is the ratio of the image size to the object size.

Magnification (M) = height of the image / height of the object.

When the ratio is greater than one we say the image is magnified and when less than one we say it is diminished.

Also magnification = image distance from the mirror / object distance from the mirror.

Examples

1. Determine the size, position and nature of the image of an object 5.0 cm tall, placed on the principal axis of a concave mirror of focal length 15 cm, at a distance 35 cm from the mirror.

Solution

Let 1 cm represent 5 cm. Then the focal length is 3 cm.

Object distance = 7 cm, object height = 1 cm.

From the scale drawing,

Image position = 5.4 cm × 5 = 27 cm in front of the mirror.

Image size = 0.75 cm × 5 = 3.75 cm. Image is real and inverted.

2. A vertical object 5 cm high is placed 10 cm in front of a convex mirror of focal length 15 cm.

find the position, size and nature of image formed. Determine the magnification of the image.

Solution

Let 1 cm represent 5 cm, then the focal length = 3 cm, object size = 1 cm Object distance = 2 cm.

From the scale drawing,

Image position = 1.2 cm × 5 = 6.0 cm behind the mirror. Image size = 0.6 cm × 5 = 3.0 cm.

The image is virtual and erect.

Magnification = image dist. / object dist. Hence 6 /10 = 0.6 (diminished).

Chapter Six

Magnetic Effect of an Electric Current.

Introduction: Oersted’s discovery.

Hans Christian Oersted discovered the magnetic effect of a current in 1819. The direction of the field is dependent on the direction of the current.

This discovery brought about the development of electric bells, electric motors, telephone receivers and radios.

Determining the direction of the lines of force.

The direction of the lines of force can be determined using a simple rule called the right-hand screw rule.

This rule states that “if a right-hand screw advances in the direction of the current , then the rotation of the screw is in the direction of the field”.

Another rule is the right-hand grip rule which states that “if the wire carrying a current is gripped with the right hand, using the thumb along the conductor and pointing in the direction of the current, then the direction of curled fingers is in the direction of the lines of force”.

Magnetic field due to a solenoid. The rule for polarity.

A solenoid is a cylindrical coil of wire acting as a magnet when carrying electric current.

The direction of the field can be determined using a simple rule stated as follows “if the coil (solenoid) is viewed from one end and the current flows in an anticlockwise direction at that end, then that end is the North Pole.

If the current flows in a clockwise direction, then that end is the South Pole”.

Electromagnets.

An electromagnet is a soft metal core made into a magnet by passing an electric current through a coil surrounding it .

They only maintain their magnetism if current continues to flow, if switched off they lose their magnetism.

Factors affecting the strength of an electromagnet.

1. Increasing current through the coil.

2. Increasing the number of turns of the coil.

3. Using iron of C- core shape which brings both magnetic poles together.

Some applications of electromagnets.

a) Electric bell

When the switch is closed the current passing through the solenoids magnetizes them and they pull the soft iron armature which makes the hammer hit the gong therefore producing sound. When the hammer hits the gong the contact between the spring and the screw is broken and then stops the current from flowing.

The soft iron core loses its magnetism and releases the armature which is then pulled back by the screw.

The contact between the spring and the screw is regained and the process repeats itself again and again therefore the gong is struck continuously.

b) Telephone receiver.

It consists of a u-magnet made by attaching two soft-iron bars to the end of a short permanent magnet.

The solenoids are wound in opposite directions around the bars. When the phone is lifted the current flows through the solenoids depending on the microphone on the other end of the line.

These varying current spasms induce magnetism of varying strengths in the iron bars which in turn causes the magnetic alloy diaphragm to vibrate differently producing sound.

Force on a current-carrying conductor in a magnetic field.

When a conductor carries a current in a magnetic field a force acts on it.

The direction of the force depends on the directions of the field and current.

The factors affecting the magnitude of the force are;

a) The current flowing in the conductor

b) The strength of the magnet

c) The length of the conductor in the magnetic field.

The relationship between the directions of the current, field and force are mutually perpendicular.

They are summarized in a law called Fleming’s right-hand rule or the motor rule.

This rule states that “if you hold the first finger, the second finger and the thumb of your left hand mutually perpendicular to each other, so that the first finger points in the direction of the magnetic field and the second finger points in the direction of the current in the conductor, then the thumb points in the direction of the force acting on the conductor”.

Applications of the force on a conductor.

Simple D.C motor.

Consists of a rectangular coil of wire mounted on an axle which can rotate between the poles of a magnet.

For the rotation to be continuous the ends of the coil is connected to half -rings called the split-ring commutators.

The battery terminals are attached to brushes which slide on these half-rings. D.C motors are useful as car starter motors, hand drills, machine motors, fans etc.

Chapter Seven

Hooke’s Law.

Hooke’s law states that “the extension of a spring is proportional to the applied force, provided that the force is not large enough to deform the spring permanently”.

Mathematically expressed as Force α extension.

Spring constant

Since Force α extension then Force / Extension = constant (k). The constant of proportionality (k) is called the spring constant. F / e = k or Force (N) = k e. The spring constant is a measure of the stiffness of a spring.

The greater the constant the stiffer the spring.

The spring constant varies with the following;-

a) Material – identical springs mad of different materials will have different constants i.e.steel and copper.

b) Diameter – the stiffness decreases with the increase in diameter.

c) Thickness of the wire – a spring made of a thicker wire is stiffer than the one made of thin wire of the same material.

d) Length of spring – a short spring is stiffer than a longer one.

e) Number of turns per unit length – a spring with higher number of turns per unit length is less stiff than the one with fewer turns per unit length.

Example

1. If the springs shown below are similar and the constant of proportionality (k) is 100 Nm-1, determine total extension in each arrangement.

The spring balance

It is made up of a spring mounted in a metal or plastic casing.

The spring is fitted with a pointer which moves along a calibrated scale divided into ten equal parts.

Examples

1. A load of 4 N causes a certain copper wire to extend by 1.0 mm. Find the load that will cause a 3.2 mm extension on the same wire. (Assume Hooke’s law is obeyed).

Solution

F α e also F1 / F2 = e1 / e2 = F2 = (4 × 3.2) / 1.0 = 12.8 N. 2. A body of 200 g was hung from the lower end of a spring which obeys Hooke’s law. Given that the spring extended by 100 mm, what is the spring constant for this spring? Solution F = α e, F = k e. F = 200 × 10-3 kg × 10 N /kg = 2 N. Extension = 100 × 103 m = 0.1 m.

Spring constant (k) = 2 / 0.1 = 20 N/m.

3. Two identical springs, whose spring constant is 6.0 N/cm, are used to support a load of 60 N as shown below. Determine the extension of each spring.

Solution

Since the springs are parallel their spring constant equals 2k. Therefore extension = Force / k = 2 F / k = 60 / 2 × 6 = 5 cm. Each spring will extend by 5 cm.

Chapter Eight

Waves I

A wave is simply a disturbance that moves through a medium . Other waves do not require a medium to travel i.e. they can travel in a vacuum, are known as electromagnetic waves e.g. radio, X-rays, gamma rays UV rays etc. Other waves require a material medium to be transferred and are called mechanical waves i.e. water, sound waves etc.

Transverse and longitudinal pulses and waves.

1. Transverse waves – they consist of a crest and a trough. In this case the displacement of the medium caused by these pulses are perpendicular to the direction in which the wave (disturbance) travels.

A pulse is a single non-repeated disturbance.

If the pulses are repeated periodically (regularly) they produce a series of waves called periodic transverse wave train.

They can be produced as shown below. Examples are water waves, light and radio waves.

2. Longitudinal waves – these are waves whereby the particles of the medium vibrate parallel to the direction of movement of the disturbance .

When several turns of a spring are pulled together (compression) and then released they tend to spread out to their original position.

When pulled apart (rarefaction) they also turn to their original position.

In this case the displacement of the spring is parallel to the motion of the wave and this is known as longitudinal. Examples are the sound waves.

Characteristics of waves

1. All waves have speed which depends on the nature of disturbance.

2. All waves have wavelength (distance between two successive points in a wave ).

Represented by the symbol λ and is measured in metres. 3. All waves have frequency ‘f’ which is the number of waves passing a point in one second. It is measured in cycles per second or hertz (Hz). The period of a wave is the time required for a complete wave to pass a given point.

Therefore T = 1 / f or f = 1 / T (period is measured in seconds).

The speed ‘v’ is given as; v = λ / T, since f = 1 / T then v = (1 / T) × λ = f λ or v = f λ. This is the wave equation.

4. All waves have amplitude which is the maximum displacement of the particles of the medium as the wave passes.

Examples

1. A rope is displaced at a frequency of 3 Hz. If the distance between two successive crests of the wave train is 0.8 m, calculate the speed of the waves along the rope.

Solution

v = f λ = 3 × 0.8 = 2.4 m Hz = 2.4 m/s.

2. The figure below illustrates part of the displacement-time graph of a wave travelling across water at a particular place with a velocity of 2 ms-1. Calculate the wave’s;

a) Amplitude

b) Frequency (f)

c) Wavelength (λ)

Solution

a) From the graph, maximum displacement (a) = 0.4 cm

b) From the graph, period T = time for one cycle = 0.20 seconds

So f = 1 / T = 1 / 0.20 = 5 Hz.

c) Velocity = f λ hence λ = 2 / 5 = 0.4 m.

Chapter Nine

Sound.

Sound is an important example of a longitudinal wave which is composed of both compressions and rarefactions. The frequency range in which compressional disturbances occur is called the sonic spectrum and is very large.

Sound is a range of compressional wave frequencies sensitive to human ear and is known as audio range which ranges from 20 Hz to 20,000 Hz.

Compressional waves with frequencies above and below the audio range are called ultrasonic and infrasonic frequencies respectively.

Nature and transmission of sound waves.

Sound waves require a material medium for transmission from one point to another. Sound waves therefore cannot be transmitted in a vacuum.

The rate of transmission diminishes as you move from solids, to liquids then to gases.

Characteristics of sound waves

1. Intensity and loudness – intensity of sound refers to the rate of flow of energy through an area.

The loudness of a sound generally varies with the intensity of sound.

The frequency of sound waves determines their intensity while the amplitude determines their loudness.

2. Frequency and pitch – pitch refers to the sharpness of a sound and is determined by its frequency.

3. Fundamental tones and harmonics – fundamental frequency is the vibration in a wire which has the lowest possible frequency.

The fundamental frequency and the tones with the frequencies that are whole multiples of the fundamental are called harmonics.

The fundamental frequency is also the first harmonic.

The number of segments vibrating in a string depends on the point at which the string is plucked.

4. Quality of sound or timbre – quality of sound can be improved by adding the second harmonic to the fundamental frequency hence the quality depends on the number of harmonics produced simultaneously and their relative intensities.

Echo

Echoes are produced by reflection of sound waves from hard surfaces such as a wall or a cliff.

To hear an echo, the sound waves travels double the distance between the source and the reflector. So to determine the velocity of sound ‘v’ between two successive claps is given as v = distance from the reflecting surface / half the time taken between two successive claps Hence; speed ‘v’= distance / time = m/s.

Example

A boy strikes a railway line (steel) with a hammer.

If the speed of sound in steel is 5,200 m/s, determine the time taken for the sound to reach another boy 2.3 km down the railway line with his ear on the rail.

Solution

Time taken = distance / speed = 2300 / 5200 = 0.44 seconds.

Factors affecting the speed of sound

a) Temperature – speed increases with increase in temperature especially gases since the change in liquids and solids is small it can be neglected.

b) Nature of transmitting medium – different substances transmit sound waves at various speeds as shown below

(i) Air – 346 m/s

(ii) Hydrogen – 1339 m/s

(iii) Water – 1498 m/s

(iv) Aluminium – 5,000 m/s

(v) Iron – 5,200 m/s

(vi) Glass – 4,540 m/s

Example

A girl claps her hands once at a distance 250 m from a vertical cliff.

If the temperature in the surrounding is 50oC, how long does it take for her to hear the echo?

Solution

Distance travelled = 250 × 2 = 500 m

Speed of sound = (331.5 m/s at 00) the speed in air increases at about 0.6 m/s per 0C.

Therefore speed at 50oC = 331.5 + (0.6 × 5) = 334.5 m/s

Time taken = distance / speed = 500 / 334.5 = 1.5 seconds.

Chapter Ten

Fluid Flow

Fluid in physics refers to liquids and gases.

  • To study fluid flow we have to make the following assumptions:

    1. We consider fluids to be incompressible

    2. We assume that they have little or no internal friction or viscosity.

    Streamline and turbulent flow.

    The path followed by a small element of a moving fluid is called a line of flow . A streamline is a curve whose tangent at any point is in the direction of the fluid velocity at that point.

    A streamline flow occurs when all elements of a fluid passing a particular point follow the same path or line of flow as the elements that passed through that point previously.

    A streamline flow is achieved only when the speed is low.

    If the speed increases it is characterized by whirls and eddies then it becomes a turbulent flow. Turbulent flow generally occurs when the speed is high and where there are sharp bends along the path of the fluid.

    Equation of continuity

    Consider a fluid flowing (streamline flow) through a horizontal pipe with different cross - sectional areas as shown.

    Let the cross -sectional area in both sections be A1 and A2 and the corresponding speeds of the fluid be V1 and V1 respectively.

    The volume of fluid flowing per second in each section is given by; V = A L = A v t = A v. Where L, v t and v is the distance moved in one second.

    Since the volumes in each section is the same, then A1 V1 = A2 V2 , hence A v = constant.

    The above equation is known as the equation of continuity. Since A1 A2 , then V2 V1 . i.e. the speed increases when a tube narrows.

    The quantity (A v) is called volume efflux i.e. volume flowing per second.

    Example.

    A horizontal pipe of cross-sectional area 50 cm2 carries water at the rate of 0.20 litres per second. Determine the speed;

    a) Of the speed of water in the pipe.

    b) When the tube narrows to 20 cm2 at another point.

    Solution

    a) Volume efflux = o.20 l per second = A v From V (volume) = A v, then v = V / A = 0.20 × 10-3 / 50 × 10-4 = 0.04 m/s b) Since A1 v1 = A2 v2 then v1 = (0.05 × 0.04) / 0.02 = 0.1 m/s

    Bernoulli’s principle

    Daniel Bernoulli (1700 – 1782) explained the variation of pressure exerted by a moving fluid when its speed is changed. The pressure is lower where the speed is higher.

    Bernoulli’s principle states that “For a fluid flowing through a tube, the sum of the pressure, the kinetic energy per unit volume and the potential energy per unit volume of the fluid is a constant”. Mathematically expressed as;

    P + ½ ρ v2 + ρ g h = constant. Where P – pressure, ρ – density, v= velocity, g – acceleration due to gravity and h – height.

    Bernoulli’s effect

    When air is blown through the tunnel formed, the area marked ‘T’ collapses inwards showing that pressure outside is more than the one inside the tunnel.

    The pressure inside the tunnel decreases as the air through it increases in speed.

    Applications of Bernoulli’s principle.

    1. Car carburetor– inside the carburetor the air passage is partially constricted at the point where petrol mixes with air hence air intake increases the speed of air while decreasing the pressure inside for petrol to vaporize quickly before it gets to the cylinder where combustion occurs.

    2. Horizontal pipe – for a streamline flow through a pipe the term ρ g h is eliminated from the Bernoulli’s equation leaving P + ½ ρ v2 = constant, indicating that pressure in liquid is greatest when speed is least.

    When this is combined with the equation of continuity, the pressure is then greatest when the pipe is widest hence the following observation.

    3. Dynamic lift - when air is blown at the top a flat sheet of paper the ends of the paper moves upward and this because the speed of air on top of the paper is greater than below and according to Bernoulli’s principle the pressure on top lowers and the pressure below becomes sufficient enough to produce a force which moves the paper upwards.

    This is what is referred to as the dynamic lift since it is caused by motion.

    The upward force is equal to the product of the pressure difference and the area of the surface lifted.

    It is applied in the taking off of air-planes, the trajectory of a spinning ball, paint sprayer and Bunsen burner among others.

  • KCSE Revision Notes Form 1 to Form 4 - All Subjects - Free Download - KCSE - Download Free KCSE Form 1 2 3 4 Notes - KCSE Revision
  • Physics Notes Form 1
  • Physics Notes Form 2
  • Physics Notes Form 3
  • Physics Notes Form 4
    KCPE Results » List of National Schools in Kenya (Classified According to Clusters) » National Secondary Schools in Kenya » List of All Secondary Schools in Kenya Per County » Form 1 Intake - Selection Criteria, Selection List » KCSE Results » Secondary Schools in Kenya » KNEC - Kenya National Examinations Council KCPE Results Performance » KNEC - Kenya National Examinations Council » KCSE Results

    Secondary School Scholarships in Kenya » Kenya Postgraduate Scholarships » Undergraduate Scholarships for Kenyan Students » Kenya Scholarships for Kenyan Students Studying in Kenya » Kenya Undergraduate Scholarships » The Kenya Youth Education Scholarship Fund - Scholarships Kenya - Scholarships KCSE Results » KCSE Results Top 100 Schools - Kenya Certificate of Secondary Education – KCSE » KCSE Top 100 Candidates » Kenya Certificate of Secondary Education – KCSE » KNEC - Kenya National Examinations Council » Secondary Schools in Kenya » KNEC - Kenya National Examinations Council » Free KNEC KCSE Past Papers

    Kenya Scholarships for Undergraduate Students » Kenya Scholarships for Postgraduate Students » Undergraduate Scholarships for Kenyan Students » Kenya Undergraduate Scholarships » Full Undergraduate Scholarships for Kenyans » Kenya Postgraduate Scholarships » Scholarships & Grants » Undergraduate Scholarships » Universities in Kenya » Kenya Universities and Colleges Central Placement Service (KUCCPS) » Colleges in Kenya » KASNEB Registration & Results » Secondary Schools Scholarships in Kenya » Undergraduate & Graduate Scholarships for Kenyans

    Powerful Motivational Quotes for Students » Success Quotes for Students » KCSE Motivational Quotes for KCSE Candidates » KCSE Success Quotes for KCSE Candidates

    a a a physics notes! chapter 1 introduction to physics college physics notes download klb physics book 4 download physics notes form 3 electronics form four notes form 1 past papers form 1 past papers with answers form 1 physics notes form 1 physics questions and answers form 1 physics revision notes form 1 physics syllabus form 1 physics test paper pdf form 2 physics exam paper form 2 physics exam paper 2016 form 2 physics exam paper free download form 2 physics exam paper with answer form 2 physics final year exam paper 2 form 2 physics past papers form 2 physics revision notes form 2 physics short notes form 2 physics syllabus form 3 past papers form 3 physics exam paper form 3 physics notes form 3 physics past papers form 3 physics questions form 3 physics questions and answers pdf form 3 physics revision notes form 3 physics syllabus form 4 exam papers form 4 physics notes form 4 physics revision notes form 4 physics syllabus form 4 physics topics form 5 physics topics form five physics notes form four physics notes form four physics questions and answers form four physics questions and answers pdf form four physics topics form four revision papers form one exams form one past papers form one physics examination form one physics past papers pdf form one physics questions and answers form one physics questions and answers pdf form one physics topics form one term one physics exam form three physics notes form three physics notes pdf form three physics questions and answers form three physics questions and answers pdf form three physics topics form two notes form two physics notes form two physics notes pdf form two physics questions and answers form two physics questions and answers pdf form two physics syllabus form two physics topics high school physics notes high school physics study guide introduction of physics form one introduction to physics notes k.l.b physics notes kcse physics notes kcse physics syllabus kenya secondary school physics syllabus pdf klb physics book 1 pdf klb physics book 2 pdf klb physics book 3 pdf klb physics book 3 pdf download klb physics book 4 notes klb physics book 4 pdf klb physics book 4 pdf download klb physics book 4 topics klb physics form 1 klb physics form 1 pdf klb physics form 2 klb physics form 2 notes klb physics form 2 pdf klb physics form 2 pdf download klb physics form 3 klb physics form 3 pdf klb physics form 3 pdf download klb physics form 4 klb physics form 4 pdf klb physics form four notes klb physics form one notes klb physics form three notes klb physics form two notes klb physics notes klb physics notes form 4 klb physics pdf maktaba tetea notes necta form four past papers necta past papers form 4 2016 necta past papers form six necta past papers form two necta physics past papers necta physics practicals necta questions and answers necta review questions notes za physics form one notes za physics form three past papers 2014 physic form 4 chapter 1 mind map physic notes physics book 4 pdf physics exam form three physics form 1 exams physics form 1 mid year exam physics form 1 past papers physics form 1 pressure physics form 1 questions and answers physics form 1 questions and answers pdf physics form 2 exam paper 2014 physics form 2 exams physics form 2 notes physics form 2 past papers physics form 2 pdf physics form 2 questions and answers physics form 2 questions and answers pdf physics form 3 exams physics form 3 notes pdf physics form 3 past papers physics form 3 questions and answers physics form 3 syllabus physics form 4 chapter 1 conversion of units physics form 4 chapter 1 exercise physics form 4 chapter 1 exercise and answers physics form 4 chapter 1 exercise pdf physics form 4 chapter 1 mind map physics form 4 chapter 2 physics form 4 chapter 2 exercise and answers physics form 4 chapter 2 exercise pdf physics form 4 chapter 2 experiment physics form 4 chapter 2 formula physics form 4 chapter 2 mind map physics form 4 chapter 2 momentum physics form 4 chapter 2 notes pdf physics form 4 chapter 2 objective questions and answers physics form 4 chapter 2 paper 2 physics form 4 chapter 2 slideshare physics form 4 chapter 3 physics form 4 chapter 3 questions and answers physics form 4 chapter 4 notes pdf physics form 4 chapter 5 light questions and answers physics form 4 chapter 5 notes pdf physics form 4 exam paper 1 physics form 4 exams physics form 4 exercise physics form 4 exercise pdf physics form 4 module with answer physics form 4 notes chapter 1 physics form 4 notes free download physics form 4 notes pdf physics form 4 paper 2 questions and answers physics form 4 past papers physics form 4 questions and answers physics form 4 revision notes physics form 5 chapter 1 exercise and answers physics form 5 chapter 1 notes pdf physics form 5 chapter 2 notes pdf physics form 5 chapter 2 slideshare physics form 5 chapter 3 notes pdf physics form 5 notes pdf physics form four book physics form four notes pdf physics form four questions physics form four study notes physics form four topics physics form one physics form one book physics form one notes physics form one notes pdf physics form one study notes physics form three book physics form three notes physics form three study notes physics form two book physics form two notes physics form two notes pdf physics form two questions physics form two study notes physics form two topics physics module form 5 physics notes physics notes for class 11 pdf physics notes for class 12 pdf physics notes form 1 free download physics notes igcse physics notes pdf physics simple notes physics spm notes download physics spm notes pdf physics spm questions physics study guide answers physics study guide pdf physics study guides radioactivity form four secondary physics notes pdf spm notes success physics spm pdf tahossa past papers

    1 a a kcse past papers 2014 kcse marking schemes 2016 kcse papers 2016 kcse prediction questions 2018 kcse exam 2018 kcse questions a a kcse past papers advance-africa.com kcse rev quiz agriculture mock papers agriculture paper 2 questions and answers pdf alliance mocks 2017 ap biology essay questions and answers arabic exam 2016 arabic oral exam questions betrayal in the city essay questions and answers pdf betrayal in the city essay questions with answers betrayal in the city, ,,revision questions biology book 3 klb biology essay questions and answers form 4 biology essay questions and answers form 4 pdf biology essays pdf biology exam questions and answers pdf biology form 2 questions and answers pdf biology form 3 notes pdf biology form 3 questions and answers pdf biology form 3 syllabus biology form three reproduction biology form three-questions and answers biology kcse - kcse biology questions and answers - kcse biology essay questions and answers - kcse biology paper 1 2015 - kcse biology notes - kcse 2015 biology paper 2 - kcse biology practical 2015 - kcse biology practicals - kcse biology 2011

    biology kcse 2017 biology kcse questions biology paper 1 questions and answers biology paper 2 questions and answers biology paper 3 questions and answers biology questions and answers for high schools biology questions and answers for high schools pdf biology questions and answers form 2 biology questions and answers multiple choice biology questions and answers on cells biology questions and answers online biology questions and answers pdf biology revision notes form 3 business past kcse past papers c.r.e form one notes pdf cambridge igcse computer science cambridge igcse computer science answers cambridge igcse computer science coursebook pdf download cambridge igcse computer science revision guide pdf cambridge igcse computer science study and revision guide pdf cambridge igcse computer science workbook - free download cambridge igcse computer science workbook pdf caucasian chalk circle essay questions chemistry paper 1 questions and answers chemistry paper 2 questions and answers chemistry paper 3 question and answer chemistry past papers form 1 chemistry past papers form 2 cie past papers computer science 0478 computer science igcse past papers xtremepapers computer science paper 2 2017 computer science past papers a level computer science past papers o level computer studies form 1 questions computer studies form 3 past papers computer studies past papers computer studies questions and answers pdf county mocks 2017 cre form 2 notes pdf cre form 3 notes cre form 3 notes pdf cre form 4 notes cre form 4 notes pdf cre form one notes cre kcse 2016 cre notes cre notes form 2 cre notes pdf cre paper 1 with answers cre paper 2 cre paper 2 topics cre preparation notes cre questions form one cre revision notes cre revision questions and answers download kcse past papers with answers dvance kcse past papers edexcel igcse computer science past papers english paper 3 question paper - 2014 kcse english paper 3 question paper - 2015 kcse english paper 3 question paper - 2016 kcse english paper 3 question paper - 2017 kcse english paper 3 question paper - 2018 kcse essay questions and answers on betrayal in the city essay questions based on betrayal in the city find download kcse past papers with answers - kcse past papers pdf download - kcse 2013 marking scheme - kcse mathematics past papers pdf - free kcse past papers and marking schemes - kcse mock papers pdf - kcse past papers 2014 pdf - kcse past papers 2015 - kcse past papers 2010 find kcse biology essay questions and answers - kcse biology practicals - kcse biology paper 1 2015 - biology essay questions and answers form 4 - kcse biology questions and answers - ap biology essay questions and answers - kcse biology notes - kcse biology paper 2 2012 - kcse biology paper 2 2015

    form 2 biology questions and answers free kcse mocks 2015 free kcse past papers - kcse past papers - knec kcse online past papers - knec kcse results past papers free kcse past papers 2014 free kcse past papers kenya, free marking schemes, download ... free kcse past papers with answers free kcse questions and answers on chemistry free revision papers general biology test questions and answers general science questions and answers pdf history and government paper one topics history form one questions and answers pdf history paper 1 questions and answers history paper 2 questions and answers home science past papers igcse computer science book igcse computer science book pdf download igcse computer science notes igcse computer science paper 2 notes igcse computer science past papers igcse computer science past papers 2014 igcse computer science past papers 2017 igcse computer science pdf igcse computer science pre release material 2018 igcse computer science resources igcse computer science revision notes pdf igcse computer science workbook pdf igcse computer studies past papers interesting biology questions ire kcse past papers k.c.s.e cre paper 1 2017 k.c.s.e geography 2017 k.c.s.e mathematics paper 1 2017 k.c.s.e mocks 2018 k.c.s.e past papers 2014 kcpe 2018 predictions kcpe prediction questions kcse 2010 marking scheme kcse 2010 past papers kcse 2011 cre paper 1 kcse 2011 marking scheme kcse 2012 history paper 2 marking scheme kcse 2012 marking schemes kcse 2013 cre paper 1 kcse 2013 marking scheme kcse 2013 marking scheme pdf kcse 2014 kcse 2015 biology paper 2 kcse 2015 biology paper 3 kcse 2015 marking scheme kcse 2015 past papers kcse 2016 agriculture paper 2 kcse 2016 biology paper 1 kcse 2016 biology paper 2 kcse 2016 computer paper 1 kcse 2017 marking scheme kcse 2017 maths paper 1 kcse 2017 papers kcse 2017 papers and marking scheme kcse 2017 past papers kcse 2017 prediction pdf kcse 2018 cre prediction kcse 2018 leakage kcse 2018 marking scheme kcse 2018 papers kcse 2018 predictions kcse 2019 marking scheme kcse agriculture past papers kcse answers kcse arabic paper 1 kcse arabic paper 2 kcse arabic paper 3 kcse arabic paper 3 2016 kcse arabic past papers kcse biology 2011 kcse biology essay questions and answers kcse biology essay questions and answers - kcse revision questions and answers - kcse chemistry questions and answers - kcse revision papers with answers - kcse past papers with answers - download kcse past papers with answers - kcse questions on the river and the source - kcse revision notes

    kcse biology essay questions and answers - kcse revision questions and answers - kcse chemistry questions and answers - kcse revision papers with answers - kcse past papers with answers - download kcse past papers with answers - kcse questions on the river and the source - kcse revision notes

    kcse biology essay questions and answers pdf kcse biology essays kcse biology essays pdf kcse biology notes kcse biology paper 1 kcse biology paper 1 2017 kcse biology paper 1 2017 pdf kcse biology paper 2 2012 kcse biology paper 2 2015 kcse biology paper 2 2017 kcse biology paper 3 2016 kcse biology paper 3 past papers kcse biology past papers kcse biology past papers and answers kcse biology practical 2016 kcse biology practical past papers kcse biology practicals kcse biology questions and answers kcse biology questions and answers - kcse past papers biology - kcse biology essay questions and answers - kcse chemistry past papers - download kcse past papers with answers - k.c.s.e papers 2015 - k.c.s.e papers 2016 - kcse biology paper 1 2015 - kcse past papers 2015 - kcse past papers 2011 - kcse past papers 2016 - kcse past papers 2017 - 2017 kcse prediction questions - 2018 kcse prediction questions

    kcse business paper 1 2016 kcse business past papers kcse business studies past papers kcse chemistry paper 1 2016 kcse chemistry paper 1 2017 kcse chemistry paper 3 2012 kcse chemistry past papers kcse chemistry past papers and answers kcse chemistry practical kcse computer studies paper 1 kcse computer studies paper 2 kcse computer studies paper 2 pdf kcse cre 2016 kcse cre paper 1 2013 kcse cre paper 1 2015 kcse cre paper 1 2016 kcse cre paper 1 2017 kcse cre paper 2 kcse cre paper 2 2016 kcse cre past papers kcse cre past papers and answers kcse english paper 3 2016 kcse english paper 3 2017 kcse essay questions in betrayal in the city kcse exam papers 2018 kcse exam papers answers kcse french paper 1 kcse french paper 2 kcse french past papers kcse general science syllabus kcse geography paper 2 2016 kcse history paper 1 2012 kcse history paper 2 2016 kcse history paper 2 2017 kcse kiswahili paper 1 2017 kcse marking scheme 2016 kcse marking schemes kcse marking schemes 2017 kcse marking schemes pdf kcse mathematics marking schemes kcse mathematics paper 1 2015 kcse mathematics paper 1 2016 kcse mathematics paper 2 2016 kcse mathematics past papers kcse mathematics past papers pdf kcse mock exams kcse mock papers 2015 kcse mock papers 2017 kcse mock papers 2018 kcse mock papers pdf kcse mock papers pdf 2018 kcse mocks 2017 kcse mocks 2018 kcse music past papers kcse online past papers kcse papers 2015 kcse past papers kcse past papers - kcpe and answers - free mocks online - kcse answers past exams question papers - downloads | kcse papers and marking schemes | exams - kcse mathematics paper 1 questions and answers - kcse cre paper 1 questions and answers - knec past papers free downloads - kcse online registration - kcpe - kcse past papers - knec - knec portal - knec past papers for colleges - kasneb - past papers - kasneb past papers for colleges - cpa past papers - https://www.knec.ac.ke/ - www.knec-portal.ac.ke/ - knec portal: kcse results, online registration, kcse result slip. knec portal confirmation - knec portal kcse results - knec examiners portal - knec website kcse past papers - kcpe and answers - free mocks online - kcse answers past exams question papers - downloads | kcse papers and marking schemes | exams - kcse mathematics paper 1 questions and answers - kcse cre paper 1 questions and answers

    kcse past papers 2007 kcse past papers 2009 kcse past papers 2010 kcse past papers 2011 kcse past papers 2011 pdf kcse past papers 2012 kcse past papers 2013 kcse past papers 2013 -knec kcse past papers 2014 kcse past papers 2014 pdf kcse past papers 2015 kcse past papers 2015 marking schemes kcse past papers 2015 pdf kcse past papers 2016 kcse past papers 2016 pdf kcse past papers 2017 kcse past papers 2017 pdf kcse past papers agriculture and answers kcse past papers arabic and answers kcse past papers art and design and answers kcse past papers biology kcse past papers building and construction and answers kcse past papers business studies and answers kcse past papers chemistry kcse past papers chemistry and answers kcse past papers chemistry pdf kcse past papers computer studies and answers kcse past papers cre and answers kcse past papers electricity and answers kcse past papers english and answers kcse past papers french and answers kcse past papers general science and answers kcse past papers geography and answers kcse past papers german and answers kcse past papers history and government and answers kcse past papers home science and answers kcse past papers hre and answers kcse past papers ire and answers kcse past papers kenya sign language and answers kcse past papers kiswahili and answers kcse past papers marking scheme kcse past papers maths kcse past papers metal work and answers kcse past papers music and answers kcse past papers pdf download kcse past papers physics and answers kcse past papers physics with answers kcse past papers power mechanics and answers kcse past papers with answers kcse past papers woodwork and answers kcse physics past papers kcse prediction 2017 kcse prediction 2018 kcse prediction 2018 pdf kcse prediction papers 2018 kcse prediction questions 2018 kcse prediction questions and answers kcse questions and answers kcse questions and answers. download free kcse past papers from knec. all marking schemes - questions and answers are sourced from knec. kcse revision kcse revision papers 2014 kcse revision | secondary school | text books | text book centre kcse trial 2017 kcse trial exams 2017 kenyaplex kcse past papers kenyaplex past papers for secondary kiswahili paper 3 questions and answers klb biology form 3 pdf klb cre form 1 klb cre form 3 knec ict past papers knec past papers for colleges knec past papers free download knec past papers pdf knec revision papers knec technical exams past papers kusoma.com past papers maths kcse 2017 mock past papers 2017 mock past papers with answers mokasa mock 2017 page navigation papacambridge computer science igcse past kcse papers past papers in kenya pre mocks 2018 pte knec past papers revision sample essays on betrayal in the city school biology notes school geography notes school physics notes school river and the source themes used in betrayal in the city xtremepapers igcse computer science z notes computer science igcse

  • Scholarship 2018/19

    Undergraduate Scholarships,
    Masters Scholarships,
    PhD Scholarships,
    International Scholarships.