PHYSICS FORM TWO

TOPIC 1: STATIC ELECTRICITY

Concept of Static Electricity

The Concept of Static Electricity

Explain the concept of static electricity

Static electricity refers to the electric charges stored on a conductor.

The Orign of Charges

Explain the origin of charges

When a plastic pen is rubbed with a cloth, it acquires the property of attracting small bits of paper or light objects. In this case, the plastic pen is said to be electrified.

Electrification by rubbing was observed a long time ago by ancient Greeks. After the discovery of electricity, things were grouped into two groups, electrics and non-electrics. Electrics refer to things which are readily electrified while non-electrics are reverse of the former.

The two Types of Charges

Identify the two types of charges

There are two types of charge:

1. positive charge
2. negative charge

Identification of charge

Suspend a polythene rod A rubbed with fur. Bring another polythene rod B rubbed with fur up to the rod A. Take a plastic rod and rub it with fur. Bring the plastic rod to up to the suspended rod A. Repeat the exercise with acetate and glass rod rubbed with silk cloth.

Observation

An electrified polythene rod repels another electrified polythene rod. An acetate rod rubbed with silk repels another acetate rod rubbed with silk cloth but it attracts a plastic rod rubbed with fur.

Explanation

Polythene and plastic when rubbed with fur becomes electrified with the same kind of electricity known as negative electricity (charge).

Acetate and glass when rubbed with silk cloth becomes electrified with the same kind of electricity called positive electricity(charge).

Charging is the process of electrifying a body.

A positively charged body carries positive charges and a negatively charged body carries negative charges.The symbols used for positive and negative charges are + and – respectively.

The Fundamental Law of Static Electricity

State the fundamental law of static electricity

The Fundamental law of electrostatic charges states that:“Like charges repel each other while unlike charges attract each other”

Charging Bodies Using Different Methods

Charge bodies using different methods

In order to understand the process of charging we have to understand the structure of bodies or things. All bodies are made up of extremely small, indestructible bits of matter called atoms.

An atom consists of a nucleus surrounded by electrons. The nucleus consists of proton and neutron.The protons are positively charged while electrons are negatively charged and the neutrons are neutral.

The whole atom is electrically neutral because it contain equal number of protons and electrons.

The following are the methods of charging;

1. Rubbing
2. Induction
3. Contact

Charging by rubbing

A polythene rod rubbed with fur becomes negatively charged.Rubbing results in the transfer of electrons from fur to the polythene rod.

Fur becomes positively charged because some of its electrons are transferred to the polythene rod.The polythene gains excess electrons and hence it becomes negatively charged.

Note:It is only the electrons in matter which can be transferred by rubbing.

Charging by induction

A charged polythene rod is held near uncharged copper rod suspended from a cotton thread.

The electrons of the copper rod are repelled by the negatively charged polythene rod.Hence the electrons move to the far side of the copper leaving behind a net positive charge on the side facing the polythene rod.

Touch the copper rod with your finger when the charged rod is still in position. The electrons from copper rod flow through your body to the earth. Leaving it with a net positive charge. Remove the finger from the copper rod and finally remove the charged polythene rod.

The rod has therefore been positively charged by electrostatic induction.The charges that appear on the copper rod are called induced charges.

Charging by contact

A charged body (eg; positively charged metal can) is brought in contact with uncharged body B.

Detection of Charges

The Structure of a Gold-leaf Electroscope

Describe the structure of a gold-leaf electroscope

The instrument used to detect the presence of electric charges is called gold leaf electroscope. It consists of an insulated brass rod with two pieces of thin gold foil at one end and a brass cap at the other end.

When the brass cap is touched with a charged object the leaves of the electroscope spread out. This is because the charge on the object is conducted through the brass cap and the brass rod to the leaves.

As they received the same kind of charge, the leaves repel each other and thus spread apart, this is charging by contact.

If you touch the brass cap with your finger, the charge is transferred through your body to the earth and the leaves of the electroscope then collapse together.

Function of an electroscope

1. Testing for the sign of the charge on the body.
2. Identifying the insulating properties of materials.
3. Detecting the presence of charge on a body.

The Sign of Charges

Determine the sign of charges

The true sign on a body has to be determined before use; the instrument that can be used to determine the presence of charge is called an electrophorus.

An electrophorus consists of a circular slab of insulating material (polythene) together with a brass disc (conductor) on an insulating handle.

An electrophorus works by electrostatic insulation and hence can be used to generate positive charges from single negative charges. The charge produced on the insulating slab is negative. The top disc is then placed on it. Since the surface is only in contact at relatively few points, a positive charge is induced on the lower surface and corresponding negative charge is produced on its top surface.

The top of the upper disc is then touched briefly using a finger, hereby carrying away the negative charge to the earth; this is called EARTHING.

Steps of Charging and Discharging of a Gold-leaf Electroscope

Identify steps of charging and discharging of a gold-leaf electroscope

The polythene slab is charged negative by rubbing it with fur. The brass disc is then placed on top of the slab so that the two charges become induced onto respective materials.

Note:Contact does not negatively charge the disc because it is not flat and makes contact with the slab at a few points only. When the brass disc is touched with a finger, electrons on the upper surface are repelled to the earth.

There is a force of attraction between the metal disc and the base. A spark (electric energy) is normally produced upon their separation. This spark can be used for lighting gas burners in laboratory.

The electrophorus can now be used to charge a gold leaf electroscope.

It can be used to charge a gold leaf electroscope by:

1. Contact
2. Induction

By contact

Here a positively charged electrophorus is made to touch the brass cap of the gold-leaf electroscope. The leaf of the gold-leaf electroscope diverges.

When a charged electrophorus is brought into contact with the electroscope, the latter gets charged and the leaves diverge. It acquires a negative charge. This is determined using the charged rods. When a positively charged glass rod is brought near the cap. It causes the leaf to collapse.

By induction

Induction- is the transfer of opposite effects from one body to another without contact.

In order to obtain a charge of a given sign, the inducing charge must be of an opposite charge. If charge is placed on an insulator at a given location the excess charge will remain at the initial location. The particles of the insulator do not permit the free flow of electrons. Charge present in an insulator or conductor.

Discharging a gold leaf electroscope

Having charged a gold leaf electroscope by contact and induction, the same can be discharged effectively through induction.

If while the electroscope is being charged by induction you touch the brass cap, electrons will leave the electroscope through your hand and onto the ground. If the charged metal rod is removed, the electroscope will remain charged. The charge remaining on the electroscope will be the opposite of the charge on the rod.

If a negatively charged object is now brought near the brass cap electrons in the brass cap are repelled and moved down to the leaves. This cancels the positive charge. With no net charge, the leave collapse back together.

If the object is removed, the electrons return to the metal cap leaving the leaves of the electroscope with a net positive charge again and they separate.

Conductors and Insulators

Difference between a Conductor and Insulator

Distinguish between a conductor and insulator

Conductors

Are bodies, which readily allow electric charge in motion to flow through them

OR

Are materials that permit some electrons to flow freely from atom to atom within the materials examples are copper, steel, iron, silver and gold.

When there is excess of positive or negative charge on an object made of a conducting material, the conduction electrons will move to minimise the repulsive force.

Insulators

These are bodies, which do not allow electric charges to flow through it. Insulators on the other hand do not allow their electrons to flow freely from at atom to atom; this is because the electrons in their atoms move around their nuclei in various equal magnitudes to the charge on the protons. The electrons are also firmly attracted to the nucleus hence bound to these atoms.

Capacitors

Capacitor is a device which is used for the storage of charges consisting of two conductors, parallel-nearly separated by air or any other dielectric.Dielectric is an insulating medium used between plates of a capacitor.

Mode of Action of a Capacitance

Explain mode of action of a capacitance

Consider two unequal metal cans which were made to stand on the caps of two identical electroscopes.These cans are given equal charges of Q units from an electrophorus disc. The charged disc is lowered inside a can until it touches the bottom. In this way the whole of the charge is given up to the can and goes to the outside.

It will be noticed that the leaf divergence is greater for the small can, showing that it has acquired higher potential than the larger can.In this case, the larger can is said to have a larger capacitance while the smaller can has a lower capacitance.When the two cans are joined by a wire electricity flows from the smaller can to the larger can until potentials are equalized.

The Action of a Capacitor

Explain the action of a capacitor

The positive charge on A induces an equal and opposite charges on opposite sides of B. These induced charges will respectively raise and lower the potential of all points in their neighborhood and in particular they will affect the potential of plate A.

As far as A is connected , however the negative induced charge will have the greater effect. The net result is is that the potential of A is slightly reduced.

B is next earthed either by touching it with a finger or by connecting it to the nearest cold-water pipe. Immediately the leaf shows a great decrease in divergence. This implies a big decrease in potential, and hence a big increase in capacitance of A.The presence of the earthed plate B results in a very large increase in the capacitance of A.

Construction of an Air-filled Capacitor

Describe the construction of an air-filled capacitor

This constitute two parallel metal plates with air band between them.A flat metal A is set up vertically on insulating legs and is connected to a gold leaf electroscope by means of a wire.

The plate is then given a positive charge by induction with a negatively charged ebonite rod. The divergence of the leaf indicates the potential of the plate.A second insulated plate B is now brought up slowly into a position parallel to A.

When B is very close to A but not touching it, it will be noticed that the leaf divergence decreases very slightly.We conclude from this that the potential of A has been decreased by the presence of B, and hence its capacitance has increased slightly.

Equivalence Capacitance of a Combination of Capacitors

Determine equivalence capacitance of a combination of capacitors

Factors affecting the capacitance of a parallel-plate capacitor.

There are three factors which affect the capacitance of a parallel-plate capacitor, namely;

1. Area of plates
2. Distance apart of the plates.
3. Dielectric between the plates.

Relative permeability (dielectric constant) of a medium

Relative permeability is the ratio of the capacitance of a given capacitor with the medium as dielectric to the capacitance of the capacitor with a vacuum as the dielectric.

It has no units since it is a ration of similar quantities.Paraffin wax has a relative permeability of about 2 while that of mica is about 8.

Charge Distribution Along the Surface of a Conductor

Charge on a Conductor Reside on its Outer Surface

Recognise that charge on a conductor reside on its outer surface

Usually, charges are distributed on the outer surface of conductors of different shapes.

Investigating surface distribution of a charge on conductors

• A proof plane is pressed into contact with the surface at various places of the conductor.
• The charges on the proof plane are then transferred to the electroscope.
• The divergence of the leaf will give a rough measure of the amount of charge transferred and hence surface density of the charge.

Charge on a Conductor is Concentrated on Sharply Curved Surfaces

Show that charge on a conductor is concentrated on sharply curved surfaces

So far we have considered excess charges on a smooth, symmetrical conductor surface. What happens if a conductor has sharp corners or is pointed? Excess charges on a nonuniform conductor become concentrated at the sharpest points. Additionally, excess charge may move on or off the conductor at the sharpest points.

To see how and why this happens, consider the charged conductor. The electrostatic repulsion of like charges is most effective in moving them apart on the flattest surface, and so they become least concentrated there. This is because the forces between identical pairs of charges at either end of the conductor are identical, but the components of the forces parallel to the surfaces are different. The component parallel to the surface is greatest on the flattest surface and, hence, more effective in moving the charge.

The same effect is produced on a conductor by an externally applied electric field, as seen inFigure(c). Since the field lines must be perpendicular to the surface, more of them are concentrated on the most curved parts.

Excess charge on a nonuniform conductor becomes most concentrated at the location of greatest curvature. (a) The forces between identical pairs of charges at either end of the conductor are identical, but the components of the forces parallel to the surface are different. It isF∥that moves the charges apart once they have reached the surface. (b)F∥is smallest at the more pointed end, the charges are left closer together, producing the electric field shown. (c) An uncharged conductor in an originally uniform electric field is polarized, with the most concentrated charge at its most pointed end.

Lightning Conductor

The Phenomenon of Lightning Conductor

Explain the phenomenon of lightning conductor

Lightning is a gigantic electric spark discharge occurring between two charged clouds or between a cloud and the earth.

Ligthning conductor is a long pointed iron rod with its lower end buried in the earth and the other above the highest part of the building which is used to protect the building from lightning damage.

The Structure and Mode of Action of Lightning Conductor

Describe the structure and mode of action of lightning conductor

Structure of a lightning conductor

It consists of a long thick pointed copper rod with its lower end buried in the earth(earth plate) and the other end reaching above the highest part of the building and ending in several sharp spikes. -It is fixed to the side of the building.

Mode of action of lightning conductor

When a negatively charged thunder-cloudpasses overhead it acts inductively on the conductor,charging the points positively and the earth plate negatively.

The negative charge on the plate is, of course, immediately dissipated into the surrounding earth. At the same time point action occurs at the spikes. Negative ions are attracted to the spikes and becomes discharged by giving up their electrons. These electrons then pass down the conductor and escape to earth.

At the same time positive ions are repelled upwards from the spikes and spread out to form what is called a space charge. This positive space charge, however, has a negligible effect in neutralizing the negative charge on the cloud.

Note:Without the protection of a lightning conductor the lightning usually strikes the highest point, generally a chimney, and the current passes to earth through the path of least resistance. Considerable heat is generated by the passage of the current and sometimes it may set into fire.

A Simple Lighting Conductor

Construct a simple lightning conductor

A simple lightning conductor

TOPIC 2: CURRENT ELECTRICITY

Electric current is the rate of charge flow past a given point in an electric circuit, measured in Coulombs/second which is named Amperes. In most DC electric circuits, it can be assumed that the resistance to current flow is a constant so that the current in the circuit is related to voltage and resistance by Ohm's law. The standard abbreviations for the units are 1 A = 1C/s.

Concept Of Current Electricity

Current Electricity

Define current electricity

Current electricity is a fundamental quantity and is the amount of charge passing a given point in a circuit divided by the time required for the passage of charges.

Electrical current (I) =quantity of charge (Q)/Time (t)

I =Q/t

Q = I.t

Electric current = rate of flow of charge

= (the number of charge carried per second x charge of a single electron)

From this definition the SI unit of an electric current is I =Columbus(C)/Second (s)

I = c/s = A

This unit is commonly known as an Ampere (A). Other units are milliamperes (mA), kilo amperes (KA) and Microampere (mA).

Their equivalents to the ampere are as follows:

1A = 10-3mA

1A= 10-6mA

1KA = 1000A

So when a steady electric current of 1A is flowing in a circuit a coulomb of charge passes a given point of the circuit per second.

An instrument used to measure electric current is called an Ammeter.

In this chapter we shall study the sustained movement of electric charge called electric current. To maintain a steady flow of electricity charge capable of moving and ways of causing them to move. Secondly, there must be a closed path around which the charge moves. This path is known as electric circuit.

A coulomb

This is the quantity of electricity, which passes a given point in circuit in 1 second when a steady current of 1 ampere flows.

In electric current there are flows of electrons through the conductor. Electrons are negatively charged while protons are positively charged. The motion of the charge through the circuit transfers energy from one point to another. This means that the actual directors of an electric current are opposite to the conventional direction.

Uses of current electricity

Current electricity is mainly used for:

1. Cooking
2. Lighting
3. Communication; and
4. Heating among many other uses

Different Sources of Current Electricity in Everyday Life

Identify different sources of current electricity in everyday life

All sources of electric currents work by converting some kind of energy into electrical energy. The two basic sources are:

1. Batteries e.g. Mobile phone battery, car dry cell batteries and also car alternator.
2. Generator

Batteries convert chemical energy into electrical energy. While generators convert mechanical energy into electrical energy.

Other sources of electric energy include water (hydroelectric power), water currents i.e. ocean waves, solar energy and wind energy.

Hydroelectric power is very reliable except in time of severe drought. This is because electricity is generated from water in dams and waterfalls, which depends on rainwater. Turbines are used to generate electricity form falling water.

Solar cells trap and convert solar energy into electric energy. Space ships and satellite use solar cell to convert sun light into electricity.

Simple Electric Circuits

Simple Circuit Components

Identify simple circuit components

An electric circuit contains a source of moving charge (battery or generator), connecting wires made of conducting materials (usually copper metal) and various electrical devices such as bulbs, switches, resistors, ammeters and voltmeters.

Voltmeters measure potential difference in volts. While resisters opposes the flow of current. The circuit may also contain devices for controlling the amount of current. These include:

1. Rheostat
2. Fuse
3. Circuit breakers, as well as devices for measuring current such as ammeters and galvanometers.

The table below shows list of some common circuit component and their purpose.

Circuit device	Purpose
Connecting wire	Carry current from point to point in a circuit.
Wire joined
Wire crossing (can be connected)
Cell	Supplies electrical energy
Battery (4 cells)	Supplies electrical energy
Battery (multiple cells)
Alternating current (AC) supply
Lamp/bulb	Supplies electrical energy
Resistor	Impedes the flow of current
Switch	Open and closes a circuit
Rheostats (variable resistors	Control amount of current. For example the brightness of a lamp)
Galvanometer	Detecting the presence of current
Ammeter	Measures current
Milliammeter
Voltmeter	Measures potential Difference (voltage)
Capacitor	Store charges

Simple Electric Symbols

Identify simple electric symbols

Connecting wire

Wire joined

Wires crossing

Cell

Battery

Battery (multiple cells)

Alternating current (AC) supply

Lamp/bulb

Resistor

Switch

Rheostats (variable resistors)

Galvanometer

Ammeter

Milliammeter

Voltmeter

Capacitor

Potential Difference (P.D)

Potential difference or voltage is a measure of electrical energy.

Potential difference (p.d) between the +ve and –ve terminals of a battery causes a current to flow along any conducting path that links them.

The Concept of Current, Voltage and Resistance

Explain the concept of Current, Voltage and Resistance

CURRENT

An electric current in a material is the passage of charge through the material. In metals free electrons carry charge. In solutions such as sodium chloride it is carried by charged particles known as ions.

Insulators like wood and plastic do not contain charge carriers at all as every electron is firmly fixed onto their atoms. The electrons are not free to move.

The rate of flow of electrons in a material is called electric current. It is measured in amperes (A) using an Ammeter. Connection can damage them. Therefore when connecting the ammeter, the red wire should be connected to the +ve terminal of a battery.

A current of 1A is equivalent to a flow of6.25 x 1018electrons per second and 1 electron has a charge of 1.6x 10-19c.

Current in simple circuit is the same at all points.

Once the circuit is complete, electric charges inside cells and other sources of electric charge are forced out into the circuit.

The electric energy is normally given out as light and heat, as energy goes through the bulb. A car headlamp has about 4A of current passing through it while a small torch uses about 0.2A.

VOLTAGE

When several cells have been joined together, they form a battery. Every cell has a voltage, commonly referred to as potential difference (p.d). This potential difference (p.d) causes the flow of electrons (charges) in a circuit.E.g. A dry cell has a voltage of 1.5v. This voltage is normally marked on the cell.

Voltage is measured by using a voltmeter. The SI unit for voltage is the volt (V). If each coulomb if charge is given 1 joule of potential energy, then the p.d across the terminals of a battery is 1 volt.

The p.d between the ends of a connecting wire is zero since there is almost no loss of potential energy over this section.

P.d across the battery = sum of p.d around a conducting path, whereas voltage provides the driving force to an electric current, this force is always opposed.

RESISTANCE

Is the opposition flow to an electric current. As current flows through the circuit it encounters some opposing force. This force determines the amount of current flowing in an electric device.

The property of conductors that oppose the flow of electric charges depends on the relationship between current and voltage across their ends as discovered by George Ohm. He observed that voltage across a conductor was directly proportional to electric current flowing through it provided that temperature and other physical conditions of the conductor were kept constant.

Hence, V x I

V= IR

R is the constant of proportionality. This constant is called resistance and the above relationship is known as Ohms law.

Resistant (R) = p.d across the conductor/Current through the conductor

Therefore a resistance of 1ohm is obtained when a p.d of 11V cause a current of 1A to flow in a circuit.

name	symbol	conversion	example
milli-ohm	mΩ	1mΩ = 10-3Ω	R0 = 10mΩ
ohm	Ω	-	R1 = 10Ω
kilo-ohm	kΩ	1kΩ = 103Ω	R2 = 2kΩ
mega-ohm	MΩ	1MΩ = 106Ω	R3 = 5MΩ

A resistor

Is a device especially designed to offer resistance to the flow of an electric current, Resistors include rheostats (variable resistor) and fixed resistors.

Ohm's Law

Ohms law states, “At constant temperature and other physical factors, the potential difference across the end is directly proportional to the current passing through a conductor (wire).”

A graphical representation of Ohm's law. The graph of voltage against current

The gradient of the particular graph represents resistance. This is constant for a particular wire or conductors. Doubling the voltage would double the current; a graph of this kind passes through the origin.

FACTORS THAT AFFECT THE RESISTANCE OF A CONDUCTOR

The resistance of a conductor is affected by the following factors:

Length of the conductor

The longer the wire, the higher the resistance, short lengths of wire produce resistors of low resistance while long lengths of the same wire are good for high – value resistance.

Temperature

An increase in temperature of a conductor means an increase in its resistance and vice versa. This is important in resistance thermometers. The resistance of metal conductor increases with increase in temperature.

Types of material

The conducting ability of the material has to be considered. A chrome wire has more resistance than a copper wire of the same dimension. That is why copper is mostly used for connecting wire.

Cross – sectional area

A thin wire has more resistance than a thick conductor. The filament of a bulb is made of very thin tang stem wire. It therefore has a high melting point.

With all other factors being equal, a long wire has more resistance than a short wire and thin wire has more resistance than a thick one. Therefore resistance of a conductor varies depending on the current flow.

The SI Units of Current, Voltage and Resistance

State the SI units of Current, Voltage and Resistance

Current

The rate of flow of electrons in a material is called electric current. It is measured in amperes (A) using an Ammeter. The SI unit for current is ampere.

Voltage

Voltage is measured by using a voltmeter. The SI unit for voltage is the volt (V)

Resistance

Resistant (R) = p.d across the conductor/Current through the conductor. The SI unit for resistance is Ohm.

Connecting Simple Electric Circuits

Connect simple electric circuits

CONSTRUCTION OF SIMPLE ELECTRIC CIRCUITS

Consider a circuit consisting of a battery, a switch and 2 bulbs.

When the switch is closed, current flows through the wires and the bulbs light up. The circuit is said to be complete. When the switch is opened, no current flows through the wire, as the path carrying current is broken. The circuit is said to be incomplete.

If we want to be able to control the brightness of the lamp, we include a rheostat into the circuit.

In a circuit an ammeter is always connected in series with the battery. Current has to pass through the ammeter if it is to be measured correctly.

Unlike an ammeter, a voltmeter must be connected in parallel with component so as to measure the voltage drop across it. The figures show a simple electric circuit in which the ammeter and voltmeter are connected in series and parallel respectively.

As already learnt, resistance is the ratio of the potential difference across the ends of the conductor,a very good conductor will have 0 resistance.

Resistance of resistor R could be calculated using the formula:- R = V/I

R = V/I

Not that the rheostat (variable resistor) moves, it varies with the length of the conductor being used.

Example 1

A battery of 5V has a resistance wire of 20Ω connected to it. Calculate the current in the circuit.

Solution;

I = V/R = 5V/20Ω

I = 0.25A

Therefore,

Current in the circuit = 0.25A

Example 2

Calculate the reading of the Voltmeter P and the ammeter Q in the electric circuit below.

Solution:

Being a single loop circuit, current is the same at all points.

Q = 3A

Sum of p.d in external circuit = p.d across battery

3V + P = 13V

P = 10V

Therefore:

Q = 3A and Voltmeter P = 10V

Note: for a single loop or simple circuit.

1. Current is the same at all points around the circuit
2. The sum of the potential differences around a conducting path from one battery terminal to the other terminal within the circuit is the same as the p.d across the battery.

Electric Current and Voltage

Measure electric current and voltage

MEASUREMENT OF ELECTRIC CURRENT

Since we cannot see electric current to measure it, we must observe some of its visible effects, like deflection of pointers.

Beside an ammeter, an electric current is measured using Milliammeter and microammeters. These devices are normally connected in series with the source of current e.g. circuit with a galvanometer connected in series.

Galvanometer in series

Galvanometer can only measure very small current of a few hundred microamperes. To measure large currents a resistor is added to make current flow through it and a very small amount of current flows to the galvanometer. This combination is called an ammeter.

On the other hand voltage is measured depending on the amount of current passing through the circuit. In Ohmic device it is given as V^I.

Simple Electric Circuits

Analyse simple electric circuits

Combination of resistors

There are two main methods of connecting circuit components, in series or in parallel. Resistors can be connected either in series or in parallel depending on the desired output.

Series combination

In series arrangement the resistors are connected end to end.

In a simple circuit

V = V1 + V2 or V- (V1 + v2)= 0

This means that the sum of the p.d across the resistors is the same as the p.d across the battery.

Current is the same at all points around the circuit.

Resistors connected in series

Parallel combination

Resistors are connected across two common points in a parallel arrangement.

Note; Potential difference is from a single source and so is the same for all the branches. However the current is different in each branch.

From Ohm's law;

Note:

When bulbs have to be powered by a single source of electric current, the bulbs are connected in parallel. This is practiced in car and home lighting system.

The advantage of parallel arrangement over series arrangement is that:

1. The full p.d of source is applied across each bulb irrespective of the number of bulbs.
2. Switching one bulb on and off does not affect the others.

Example 3

consider the figure below:

Given that the p.d a cross the cell is 24V, calculate the p.d across the 4Ω and 6Ω.

Solution;

Total resistance in the circuit = 4Ω + 6Ω= 10Ω

Using Ohm’s law. I = V/R,

Current in the circuit = 24V/10Ω= 2.4A

This implies the 2.4A passed through the 4Ω resistor.

The pd across it can be obtained through V=IR

p.d = 2.4A x 4N = 9.6V

Note that the p.d across two resistors adds up to the battery p.d.

p.d across the 6Ω = (24-9.6) V

= 14.4V

Therefore,

P.d across the 6Ω =14.4V

TOPIC 3: MAGNETISM 

Concept of Magnetism

The Orign of Magnetism

Explain the origin of magnetism

Chinese were the first to use the metal magnetite called lodestone. A Lodestone was capable of attracting small iron pieces and it was used as a crude navigation compass by Greeks. Lodestones were the earliest magnets.

Iron, nickel and cobalt are the only naturally occurring magnetic materials. Magnet has two ends known as magnetic poles in which the greatest attraction power is concentrated.

Magnetic and Non-magnetic Materials/Substances

Identify magnetic and non-Magnetic material/substances

Magnetic substances

These are substances which have a property of being attracted by a magnet.E g; iron,steel,cobalt and nickel.

• Pole strength refers to the ability of a magnet to attract objects.
• Ferromagnetic substanceshave very high magnetic susceptibility (easily magnetized).Eg; iron, nickel and cobalt.
• Electromagnet is the substance which requires electric current to attain magnetism.
• Permanent magnet is a substance which is already a magnet and it doesn’t require electric current to attain magnetism.

Non-magnetic substances

These are substances which are not attracted by a magnet.Eg; copper, brass, aluminium,glass,plastic and wood.These substances have very weak magnetic properties.

The Properties of Magnets

State the properties of magnets

Magnets have a tendency of attracting magnetic substances and have no action on non-magnetic materials.

Types of magnetic materials

There are three types of magnetic materials:

1. Diagmatic materials: Are substances which have a tendency to repel from a stronger to weaker magnetic field. Eg; bismuth, water, gold,air,hydrogen,common salt,diamond,silver and copper.
2. Paramagnetic materials: Are substances which become weakly magnetized when placed in magnetic field. Eg; aluminium,platinum,chromium,oxygen and manganese.
3. Ferromagnetic materials: Are substances which becomes magnetized when placed in magnetic field. Their magnetic domain become aligned in one direction when they are placed in magnetic field. Eg; iron, cobalt and nickel.

Magnetic domain refers to the molecular magnets lined up with each other which constitute ferromagnetic materials.

The direction of magnetic poles varies from one domain to another if the magnet is unmagnified

Types of Magnets

Identify types of Magnets

Magnets may also be classified according to their shapes. This includes:

1. Horse shoe magnet
2. Rod magnet
3. Field magnet
4. Bar magnet

Application of Magnets

Identify application of magnets

Magnets are used in:

1. women handbags closing
2. picking up heavy loads
3. electrical appliances like meter and receivers
4. sound and video recording equipment
5. computer memory and disks
6. electrical trains

Magnetisation and Demagnetisation

The Concept of Magnetisation and Demagnetisation

Explain the concept of magnetisation and demagnetisation

Magnetisation:Is a process of making a magnet from a magnetic substance.

Demagnetisation:Is the process by which a magnet is made to lose its magnetism.

Demonstrating Magnetisation and Demagnetisation

Demonstrate magnetisation and demagnetisation

Methods of magnetisation

There are various ways, including;

1. Induction
2. Stroking
3. Electrical method

Induction method.

This is done by placing a piece of unmagnetised steel bar near or in contact with a pole of a magnet and then removing it.

In this case an iron nail placed near a bar magnet will be induced with magnetism.

Stroking method

This is done by stroking a bar magnet into an unmagnetised steel bar.There are two stroking methods, namely;

1. Single touch: A magnetised bar magnet is formed by a single stroke.-A steel bar is stroked repeatedly by a very strong bar magnetism the same direction with the north pole i.e from A to B. The bar magnet is lifted at B and then returned at A. After several strokes the steel bar will be magnetised with north pole at A and south pole at B.
2. Double touch: Two bar magnets are used to magnetise a single steel bar. The steel bar is magnetised by two bar magnets from its center to its ends using left and right hands simultaneously for several times. Between each stroke the two bar magnets are lifted up high and returned to the center for another stroking.

In this case the steel bar will be magnetized with south pole at A and north pole at B.

Note:

1. In both single and double touch methods, the magnetising magnet none of their strengths.
2. Between successive strokes, the pole is lifted high above bar, otherwise the magnetism already induced in it will tend to be weakened.3.Consequent poles will be formed at the center of the steel bar when the two bar magnets placed at the center are of like poles. Same poles will be obtained on both ends.

Electrical method

A cylindrical coil wound with many of insulated copper wire is connected in series with a battery. A steel bar is placed inside the solenoid and the current switched on and off.When the steel bar is removed and tested, it is found to be magnetised.

Note:If the current is switched off for so long, the bar will not be magnetized.The poles of the bar magnet depends on the direction of flow of current. The end at which the direction of the current is in clockwise direction will be south pole and if anticlockwise it will be north pole.

Methods of demagnetization

Electrical method

The magnet is placed inside a solenoid through which an a. c is flowing.The magnet is withdrawn from the solenoid while the current is flowing pointing in the W-E direction. When the magnet is held in W-E direction, it doesn’t remain with residue magnetism due to induction from earths magnetic field.

Other methods of demagnetisation include;

1. Heating a magnet.
2. Hammering while pointing E-W direction.

Methods of Storing Magnets

Design methods of storing magnets

Magnets are stored in magnetic keepers.They are stored in pairs,with unlike poles together and with pieces of iron(magnetic keepers) across both ends.The keepers are magnetised by induction.

Magnetic Fields of a Magnet

The Concept of Magnetic Fields of a Magnet

Explain the concept of magnetic fields of a magnet

Magnetic field:Is a space surrounding a magnet in which a magnetic force is exerted or experienced. It consists of magnetic field lines which are imaginary lines of force around a magnet from North Pole to South Pole.

The Magnetic Lines of Force around a Magnet using Iron Fillings or Compass Needle

Illustrate the magnetic lines of force around a magnet using iron fillings or compass needle

Experiment.

Aim:To study the properties of magnetic field lines around a bar magnet.

Materials: Iron fillings, bar magnets and a piece of paper.

Procedures

• Place a sheet of plane paper over a bar magnet.
• Sprinkle iron fillings on the sheet of paper.
• Gently tap the sheet of paper.

Observation

• Iron fillings will form a pattern which depends on the magnetic lines of force of the magnet.
• The lines of equal magnetic strength are seen flowing between magnetic poles .The lines are referred to as lines of magnetic flux or field lines. The pattern magnetic force is called a magnetic field.
• When investigating a magnetic field with iron fillings the field is strongest where the fillings are crowded.
• By investigating a magnetic field lines and a bar magnet using a small compass needle, the magnetic flux(lines) runs from north pole to south pole.

Neutral point is a point at which the resultant magnetic flux density is zero.

this area, X, the two magnetic field s cancel or neutralize each other.It happens when two like magnetic poles are brought together.

Therefore neutral point is;

1. an area in a magnetic field where the resultant magnetic field strength is zero.
2. a point which exists where two magnetic field neutralize each other.

The Methods of Magnetic Shielding

Explain the methods of magnetic shielding

Magnetic shielding:Is a screen made from high permeability material used to isolate any material from unwanted magnetic fields

Example; The electron beam in the cathode ray tubes of TV sets, and very delicate measuring instruments are shielded(protected)from magnetic influence by placing them in soft iron cases with thick wells.

Here the object is shielded from the strong magnetic fields by a soft iron ring around it

Earth's Magnetic Field

The Phenomenon of Earth's Magnetism

Explain the phenomenon of earth's magnetism

Earth is imagined as a single big magnet, with its south seeking pole near the geographic north called a north magnetic pole and the north seeking pole is near geographic south pole called south magnetic pole.

The earth behaves as if at its center there is a short piece of a bar magnet inclined at a small angle to its rotation (spinning) axis. When a bar magnet is hanged horizontally with a string, it will oscillates for a short time and then comes to rest with its poles pointing in the N-S direction due to the earth’s magnetic field.

This gives a notion that the earths north pole is in the southern hemisphere where any magnets north pole will always point.The two earth’s magnetic poles are joined by a line called magnetic meridian.The geographic meridian joins the true north and true south.

Direction of Earth's Magnetic Field

Determine direction of earth's magnetic field

Compass needle:Is a thin magnet balanced on a point, usually at the center of gravity used to identify N-S direction.Spinning a compass needle, it will eventually come to rest with its poles pointing to the N-S direction.This gives direction at any point on the earth’s surface.

The Earth's Magnetic Lines of Force about a Bar Magnet

Locate the earth' magnetic lines of force about a bar magnet

The magnetic field lines around a bar magnet can be mapped with the help of a magnetic compass. The magnetic field lines due to a bar magnet are closed loops. They leave at the north pole and enter at the south pole. When you plot the magnetic field lines around a bar magnet, the horizontal component of the earth’s magnetic field, B0, influences the magnetic field induction, B, due to the bar magnet. At points close to the bar magnet, magnetic induction B due to the bar magnet is very high as compared to the horizontal component of the earth’s magnetic field, B0. Thus, B0is negligible.

According to the inverse square law of magnetism, magnetic field induction B due to the bar magnet decreases as we move away from it. At certain points around the bar magnet, B and B0are equal in magnitude and opposite in direction. Therefore, they cancel each other out, and the resultant magnetic field is zero.

Thus, the point where magnetic field induction B due to a bar magnet is equal in magnitude and opposite in direction to the horizontal component of the earth’s magnetic field induction, B0, is called a neutral point.

The neutral points around a bar magnet can be located in two different cases

1. When the north pole of the bar magnet points towards the earth’s north pole
2. when the south pole of the bar magnet points towards the earth’s north pole.

When the north pole of a bar magnet points towards the north pole of the earth.

• Fix a sheet of white paper on a drawing board with brass pins.
• Take a compass needle, place it at the centre of the paper, and mark the north and south directions.
• Draw a straight line along the paper connecting the two points. This represents the magnetic meridian of the earth.
• Represent the geographical directions at the corner of the paper.
• Draw an arrow from the geographical south to the geographical north on the right side of the paper to indicate the direction of the horizontal component of the earth’s magnetic field, B0.
• Take a bar magnet and place it at the centre of the paper such that the north pole of the bar magnet points towards the north pole of the earth.
• Now place the compass needle at the north pole of the bar magnet and mark a point where the north pole of the compass needle is.
• Shift the compass such that the south pole of the compass needle is at the point you just marked.
• Mark another point at the north of the compass needle, and then shift the compass, as done earlier.Repeat the procedure till the compass needle reaches the other end of the bar magnet.
• Join all the points to get a continuous smooth curve, which represents a magnetic field line.
• Repeat the procedure from the north pole of the magnet, but from different points, and draw the magnetic field lines.

The two points on either side of the bar magnet at equal distances from its centre, where the compass needle does not show any specific direction. At these points, the magnetic field induction B due to the bar magnet and the horizontal component of the earth’s magnetic field induction, B0are equal in magnitude and opposite in direction. The resultant magnetic field is zero. These points represent the neutral points denoted by N1and N2. These two points fall on the equatorial line of the bar magnet.

Thus, when the north pole of a bar magnet points towards the geographical north pole of the earth, the two neutral points lie on the equatorial line of the bar magnet such that they are equidistant from the centre of the bar magnet.

The Angle of Inclination (dip) and Angles of Declination

Measure the angle of inclination (dip) and angles of declination

Angle of dip is the angle between the direction of the earth’s magnetic flux and the horizontal.

Measurement of angle of dip

The angle of dip is not constant over the earth’s surface; it varies from place to place.

This difference is brought about by the earth’s magnetic field direction at a point on the earth’s surface. The easiest way to measure the angle of dip is using a thin iron rod.The rod is suspended by length of a thread such that it balances horizontally.

Without disturbing the position of attachment, the rod is magnetised by bringing close a bar magnet and touching. On re-suspending the rod will dip with its north pole pointing downwards as shown in the diagram above. Using a protractor, the angle between the axis of the rod and the horizontal can be measured.

Angle of declination

Is the angle between the magnetic meridian and geographic meridian. The angle of declination varies from place to place all over the world. Maps shows declination at different points of the world.

Application of Earth's Magnetic Field

State the application of earth's magnetic field

The earth’s magnetic field is used to:

• indicate poles of unknown magnets.
• enables the use of magnetic needle.

TOPIC 4: FORCES IN EQUILIBRIUM 

Moment of a Force

The Effects of Turning Forces

Explain the effects of turning forces

A force is a push or pull which when applied to a body it will change its state either by stopping it if it was in motion or making it move if it was at rest.

If a body under the action of a net externalforceis allowed to rotate about a pivot, the body will tend to turn in the direction of the applied force.

Examples of turning effect of force:

• A person pushing a swing will make the swing rotate about its pivot.
• A worker applies force to a spanner to rotate a nut.
• A person removes a bottle’s cork by pushing down the bottle opener’s lever.
• Force is applied to a door knob and the door swings open about its hinge.
• A driver can turn a steering wheel by applying force on its rim.

The Moment of Force

Determine the moment of force

Moment of forceabout a point is the turning effect of the force about that point. The change of state of a body can appear in several forms and the most common form is the turning effect which is referred to as moment of a force.

The unit for a force isNewton, Nwhile that for moment of a force isNewton-meter, Nm.

Moment = Force, F x Perpendicular distance, x.

Moment = Fx

Consider the diagram below;

Moment of W₁ about the fulcrum. = W₁d₁

Moment of W₂ about fulcrum = W₂d₂

The Principle of Moments

State the principle of moments

The Principle of moments states that:”If a body is in equilibrium under a force which lie in one plane, the sum of the clockwise moments is equal to the sun of the anticlockwise moments about any point in that plane.”

Activity 1

Experiment.

Aim: To determine the moment of a force.

Materials and apparatus:Meter rule, several different weights, inelastic cotton thread, knife edge and a marker pen.

Procedures

• Balance the meter rule horizontally on a knife edge.
• Mark a balance point as C. Use the marker pen to do that.
• Suspend a meter rule from a fixed axis through C. Suspend unequal weights W₁ and W₂ from the meter rule by using thin cotton threads.
• Adjust the distance d₁ and d₂ of the weights W₁ and W₂ from C until the meter rule balance.
• Repeat the experiment five times using different values of W₁ and W₂.Record the results on the table as shown below.

W₁(g)	W₂(g)	d₁(cm)	d₂(cm)	W₁ d₁ (gcm)	W₂ d₂ (gcm)

Observation:In each case it will be found that W₁ d₁ is equal to W₂ d₂.

The Principle of Moment in Daily Life

Apply the principle of moment in daily life

Moment of a force is used in the following:

• Is applied by a hand to unscrew a stopper on the bottle.
• Is applied by a spanner to unscrew a nut on a bottle.
• Turning a steering wheel of a car.

Centre of Gravity

Centre of Gravity

Explain centre of gravity

Center of gravity of a body is the point at which the weight of a body appears to be concentrated. OR center of gravity of a body is the point of application of the resultant force due to the earth attraction on the body.The center of gravity of a regular body is found to be at its geometrical center.

Example 1

1. Centre of gravity of a uniform meter rule is at the 50cm mark.
2. Centre of gravity of a circular object is at its center.

The center of gravity of irregular bodies can be found experimentally.

Centre of Gravity of Regular Shaped Body

Determine centre of gravity of regular shaped body

Activity 2

Experiment.

Aim; To determine the center of gravity of a regular body (meter rule)

Materials and apparatus: Meter rule, a known weight and a spring balance.

Procedures

• Balance the meter rule on a fulcrum and mark the position where the meter rule balances horizontally by the letter G.
• Hang a known weight from one end of the meter rule and determine the position where the meter rule balances and mark it X.
• Measure the distance XC and XG(C is the point at the end of the meter rule where an object of known weight, w is attached).

The weight, w of the meter rule always acts at G downwards. Thus it will create a moment to balance the moment due to w.

Results

The mass of the meter rule, w is determined by using the principle of moments.Taking moments about X;

Clockwise moments = Anticlockwise moments

w₁ .XC =w. XG

Centre of Gravity of Irregular Shaped Body

Determine centre of gravity of irregular shaped body

Activity 3

Experiment

Aim: To determine the center of gravity of irregular plate.

Materials and apparatus:Card board, plumb line, inelastic cotton thread, clamp, clamp rod and a marker pen.

Procedures

• Make an irregular shaped piece of card board.
• Make three small holes well-spaced round the edge of the cardboard.
• Sus

Types of Equilibrium

The Condition for Equilibrium

Explain the condition for equilibrium

Equilibrium:A body is said to be balanced if its center of gravity is directly above the point of support.

Stable, Unstable and Neutral Equilibrium

Explain Stable, Unstable and Neutral equilibrium

There are three types of equilibrium, namely:

1. Stable equilibrium
2. Unstable equilibrium
3. Neutral equilibrium

Stable equilibrium:A body is said to be in stable equilibrium if is given with small displacement the center of gravity will be raised and the body returns to its original position after displacement.

Unstable equilibrium:A body is said to be in unstable equilibrium if when given a small displacement the center of gravity will be lowered and the body doesn’t returns to its original position after displacement.

Neutral equilibrium:A body is said to be in neutral equilibrium when a small displacement doesn’t alter the position of the center of gravity; the body is at rest in whichever position it is placed, eg, rolling a sphere or a barrel.

Conditions of Stable, Unstable and Neutral Equilibrium in Daily Life

Apply conditions of stable, unstable and neutral equilibrium in daily life

Application of turning effect in daily life

• Is applied by a hand to unscrew a stopper on the bottle.
• Is applied by a spanner to unscrew a nut on a bottle.
• Turning a steering wheel of a car.

Exercise 1

.The moment of a force about a point is 1120 Nm.If the magnitude of the force is 5600N,find the perpendicular distance between the point and the line of action of the force

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TOPIC 5: SIMPLE MACHINES

Simple Machines

A simple machine is a non-powered mechanical device that changes the direction or magnitude of a force. In general, they can be defined as the simplest mechanisms that use mechanical advantage (also called leverage) to multiply force. A simple machine uses a single applied force to do work against a single load force. Ignoring friction losses, the work done on the load is equal to the work done by the applied force.

Concept of Simple Machines

Nowadays man can do many things without necessarily using much of his own energy. Many can fly by using aeroplane, raise a heavy load, and drive a nail into wood by using a hammer. All of these are achieved using machines.

The Concept of a Simple Machine

Explain the concept of a simple machine

Machine:

Machine is any device, which is used for simplifying work. Examples of machines are: a crowbar, a seesaw, a claw hammer, a pulley and an inclined plane.

Types of machine:

There are two types of machines

1. Simple machine
2. Complex machine

What is simple machine?

Simple machine is any device, which requires single force in operation to simplify work e.g. Claw hammer, a pulley, and an inclined plane. In a simple machine, a force is applied at one convenient point to overcome another force acting at another point.

Simple Machine

The diagram above shows a stone being shifted. Force is applied at one end of the bar in order to exert an upward force on the stone. The down ward force is called effort and the weight of the stone is called load.

Effort is the force used to operate a machine. And Load is the resistance, which machines overcome.

The terms Applied in Simple Machine

Explain the terms applied in simple machine

Terms used in simple machine

Mechanical Advantage

Mechanical advantage (M.A) is the ratio of load and effort

Mathematically:

-

Mechanical advantage has no SI unit.

Example 1

Example 1

A simple machine raises a load of 100N by using a force 50N. Calculate the mechanical advantage.

Solution;

-

Example 2

Example 2.

A force of 20N raises a load of 100kg. Calculate mechanical advantage of the machine.

Solution

-

img4

Velocity ratio

Velocity ratio is the ratio of distance travelled by effort and distance travelled by load. Or Velocity ratio is the distance moved by effort per distance moved by load.

-

Example 3

Example

In a certain machine a force of 10N moves down a distance of 5cm in order to raise a load of 100N through a height of 0.5cm calculated the velocity ratio (V.R) of the machine.

Solution:

Distance by Effort = 5cm

Distance moved by load = 0.5cm.

From

-

Efficiency of Machine

Efficiency of machine is the ratio of work output and work input.

Work output = Load x Distance moved by Load

Work input = Effort x Distance moved by Effort

-

A perfect machine has 100% Efficiency. Therefore M.A is equal to V.R.

Note: most machines are imperfect machines since efficiency is less than 100% this is due to the friction and heat and loss of energy.

Example 4

Example1:

A certain machine with force of 10N moves down a distance of 5cm in order to raise a load of 100N through a height of 0.5cm.

Calculate:

1. M.A
2. V.R
3. Efficiency of machine

Solution:

Date given:

Effort = 10N

Load = 100N

Distance moved by effort = 5cm

Distance of load= 0.5cm

Efficiency machine?

Efficiency of machine () = M.A x 100%

-

Different Kinds of Simple Machine

Identify the different kinds of simple machines

Different Kinds of Simple Machines

Types of Simple Machines

• LEVERS
• PULLEYS
• INCLINED PLANE
• THE SCREW AND SCREW JACK
• WHEEL AND AXLE
• HYDRAULIC PRESS

Levers

A lever is a rigid body, which when used turns about a fixed point called a fulcrum or pivot. It is used to shift heavy loads.

The Three Classes of Levers

Identify the three classes of levers

Classes of Levers

There are three classes of levers:

1. First class lever
2. Second class lever
3. Third class lever

First Class Lever

Is the class lever whereby the pivot is between load and effort. Examples of first class levers are: see-saw, crowbar, pair of scissors and claw hammer.

First Class Lever

Second Class Lever

Is the class lever where by load is between pivot and load. eg, wheel barrow, tongs, nutcracker, bottle opener.

Second Class Lever

Third Class Lever

Is the class lever whereby Effort is between load and pivot. Eg, fishing load.

Third Class Lever

The Mechanical Advantage, Velocity Ratio and Efficiency of Lever

Determine the mechanical advantage, velocity ratio and efficiency of lever

Mechanical Advantage of Lever

M.A =X/Y

M.A =Load arm/Effort arm

Levers in Daily Life

Use of levers in daily life

The reason for a lever is that you can use it for amechanical advantagein lifting heavy loads, moving things a greater distance or increasing the speed of an object.

• Increase force:You can increase the applied force in order to lift heavier loads.
• Increase distance moved
• Increase speed: You can increase the speed that the load moves with Class 1 or Class 3 levers.
• Pulleys

  A pulley is a grooved wheel, which is free to turn about an axle that is fixed in a frame.

  Different Pulley System

  Identify different pulley systems

  Types of Pulleys

  1. Single fixed pulley
  2. Single movable pulley
  3. The block and tackle system of pulley

  Single fixed pulley

  This is the type of pulley whereby effort is applied at one end of the tape in order to raise the load. Single fixed pulleys are used to raise small objects e.g. Flags. Consider the diagram below:-

  Single fixed Pulley

  

  M.A and V.R of single fixed pulley

  

  Single Movable Pulley

  Single movable pulley is the one which load is multiple of Effort.

  Load = 2E

  Consider the following diagram

  Single movable pulley

  

  M.A and V.R of single movable pulley

  

  The block and tackle system of pulley

  When two or more pulleys are fixed in a frame, a block is formed. The pulleys in each block are fixed independently on separate axles. Consider the diagram below:-

  Block and tackle system of pulley

  

  Note; mechanical advantage = Load/Effort

  Velocity ratio of Block and tackle system is equal to the number of pulleys.

  Example 5

  Example 1

  A block and tackle pulley system has a velocity ratio of 4. If a load of 200N is raised by using a force of 75N. Calculate the mechanical (i) Advantage of the system (ii) efficiency of the system.

  Solution;

  Data given

  Velocity ratio (V.R) = 4

  Load = 200N

  Effort = 75N

  M.A =?

  M.A and Efficiency of block and tackle pulley system

  

  Mechanical Advantage, Velocity Ratio and Efficiency of Pulley System

  Determine mechanical advantage, velocity ratio and efficiency of pulley system

  VR of block and tackle

  When the lower two pulleys move up a vertical distance y, corresponding to movement y of the load L, each pulley releases a length y of the rope on each side giving a total length 2y.

  With all this movement of pulleys, the effort E is moved down a distance of 2 x 2y or 4y.Thus, VR = (distance moved by effort)/(distance moved by load at the same time) = 4y/y = 4

  VR = Number of pulleys of the system.

  Efficiency of block and tackle

  From, ε = MA/VR X 100%

  ε = (number of pulleys )/(number of pulleys) x 100%

  Note:Then, for a perfect block and tackle pulley system, ε = 100%.

  But in practical case the MA is less than the number of pulleys, hence the efficiency of pulleys system is less than 100% due to friction losses.

  MA of block and tackle.

  From MA = load/effort

  MA = (Effort x Number of pulleys of the system)/Effort

  MA = Number of pulleys of the system.

  Pulley in Daily Life

  Use of pulley in daily life

  Uses of Pulleys

  Pulleys have been used for lifting for thousands of years. The most prevalent and oldest example are their uses on ships and boats. The block and tackle have been a key tool for raising sails and cargo. Another major use for pulleys is withcranes.

  Pulleys have been used also in modern times with various machines and systems. Even in the space age, pulleys have been an important aspect for the construction and operations of spacecraft and aircraft. It is with a pulley system that rudders for an aircraft are controlled.

  Pulleys are used in everyday life, from vehicles to moving equipment such as cranes.
  
  

  Inclined Plane

  The Concept of Inclined Plane

  State the concept of inclined plane

  An inclined plane is a sloping plane surface, usually a wooden plank used to raise heavy load by pulling or pushing them along the surface of the plane.

  An inclined plane

  

  Mechanical Advantage, Velocity Ratio and Efficiency of Inclined Plane

  Determine mechanical advantage, velocity ratio and efficiency of inclined plane

  Mechanical advantage of the inclined plane

  M.A = Load/Effort

  V.R of inclined plane = Length of the plane/Height of the plane

  Example 6

  Example:

  A loaded wheelbarrow of weight 800N is pushed up an inclined plane by a force of 150N parallel to the plane. If the plane rises by 50cm for every 400cm distance measured along the plane, find the velocity ratio, mechanical advantage and efficiency of the plane.

  Solution:

  Data given

  Load = 800N

  Effort = 150N

  Length of plane = 400cm

  Height of the plane = 50cm

  V.R =?

  M.A=?

  =?

  M.A, V.R and Efficiency of Inclined Plane

  

  Inclined Plane in Daily Life

  Apply inclined plane in daily life

  Application of Inclined Plane

  Inclined planes are widely used in the form ofloading rampsto load and unload goods on trucks, ships, and planes.Wheelchair rampsare used to allow people inwheelchairsto get over vertical obstacles without exceeding their strength.Escalatorsand slantedconveyor beltsare also forms of inclined plane.

  In a funicular or cable railway a railroad car is pulled up a steep inclined plane using cables. Inclined planes also allow heavy fragile objects, including humans, to be safely lowered down a vertical distance by using the normal force of the plane to reduce the gravitational force. Aircraft evacuation slides allow people to rapidly and safely reach the ground from the height of a passenger airliner.
  
  

  Screw Jack

  The Structure of a Screw Jack

  Describe the structure of a Screw Jack

  Structure of Screw Jack

  A screw Jack consist of a cylinder with a spiral ridge runs round it. The spiral is called the thread (T) and the distance between two adjacent threads is called the pitch (p) of the screw.

  Consider the following diagram.

  The bolt and screw

  

  The Screw Jack

  

  The Mechanichal Advantage, Velocity Ratio and Efficiency of a Screw Jack

  Determine the mechanical advantage, velocity ratio and efficiency of a Screw Jack

  Mechanical advantage of the screw jack

  M.A = Load/Effort

  Velocity ratio (V.R)

  V.R = Circumference of circle of radius (R)/Pitch of screw

  V.R = 2pR/P

  Example 7

  Example 1

  A screw jack with a pitch of 0.2cm and a handle of length 50cm is used to lift a car of weight 1.2 x 104N. If the efficiency of the screw is 30%, find:

  1. The velocity ratio and mechanical Advantage of the machine
  2. The effort required to raise the car

  Solution;

  Date given

  Pitch = 0.2cm

  Radius= 50cm

  Load = 1.2 x104N

  Efficiency of jack =30%

  V.R=?

  M.A=?

  Effort+?

  -

  

  The Screw Jack in Daily Life

  Use the Screw Jack in daily life

  Screw jacks are used to lift heavy loads despite the large friction they produce. The heavier the load the higher the friction force. They are self-locking, meaning that when the applied force is removed, they do not rotate backwards. They are used in adjusting workplace chairs and tables. They also help in pulling and pushing machine equipment as well as tightening mechanical parts.
• Wheel and Axle

  The Structure of a Wheel and Axle

  Describe the structure of a wheel and axle

  Structure of Wheel and Axle

  A wheel and axle is a simple machine that consists of a wheel and axle mounted with the same axis of rotation. The radius of the wheel is always greater than that of the axle.

  Consider the diagram below:

  Wheel and Axle

  

  The Mechanical Advantage, Velocity Ratio and Efficiency of a Wheel and Axle

  Determine the mechanical advantage, velocity ratio and efficiency of a wheel and axle

  Mechanical advantage of Wheel and Axle

  M.A = Load/Effort

  Velocity ratio ( V.R)= radius of wheel (R)/radius of axle (r)

  Example 8

  Example 1

  A wheel and axle of efficiency 80% is used to raise a load of 2000N. If the radius of the wheel is 50cm, and that of the axle is 2cm, calculate

  1. The velocity ratio and mechanical Advantage of machine
  2. The effort required to overcome the load

  Solution

  Data given

  Efficiency = 80%

  Load = 2000N

  Radius of wheel (R)= 50cm

  Radius of axle (r) = 2cm

  V.R=?

  M.A=?

  Effort?

  -

  

  The Wheel and Axle in Daily Life

  Use the wheel and axle in daily life

  Application of Wheel and Axle

  Wheels help people do work in two ways. First, likeleversorinclined planes, wheels allow you to do something easy for a longer time, instead of doing something hard for a shorter time. If you turn a large wheel fixed to an axle, the axle will also turn. You can turn the large wheel easily (but it takes a lot of turning to go all the way around).

  The axle will go around a much shorter distance, but with more force. So you can use a wheel to create a mechanical advantage - you can turn something heavy, by spinning a large wheel attached to an axle that is attached to the heavy thing.

  That's how a pencil sharpener works. Or, you can do it the other way around - use a lot of force to turn the axle, and that will spin the wheels really fast. That's what cars do.Wheels are the most important part of pottery wheels, wagons and cars, but also ofwheelbarrows,spinning wheels, water wheels, windmills, andpulleys.

  Also, wheels on a wagon only touch the ground at one spot at a time, keeping the rest of the wagon off the ground. This makes lessfriction, so that the wagon is easier to move than if you were pulling it along like a sled.

  
  

  Hydraulic press

  The Structure of Hydraulic Press

  Describe the structure of Hydraulic Press

  Structure of Hydraulic Press

  A hydraulic press is a machine that has a bed or a plate in which the metallic material is placed so that it can be crushed, straightened or moulded.

  Mechanical Advantage, Velocity Ratio and Efficiency of a Hydraulic Press

  Determine mechanical advantage, velocity ratio and efficiency of a Hydraulic Press

  In hydraulic press small force (Effort) applied on the small piston is used to overcome a much greater force (load) on the large piston.

  When a small effort (E) is applied downwards on the effort piston of radius (r) the load piston of radius (R) lifts the load (L).

  Consider the diagram below:

  Hydraulic Press

  

  By the principle of transmission of pressure in liquid, the pressure on effort piston is equal to the load piston.

  -

  

  VELOCITY RATIO OF HYDRAULIC PRESS

  If friction is neglected the work done by the effort E is equal to the work done on the load (L). So if the effort piston is moved by distance x and the load piston raised up by a corresponding distance Y, it follows:

  -

  

  Note: Due to friction, efficiency of the hydraulic press is not 100%

  The Hydraulic Press in Daily Life

  Use the Hydraulic Press in daily life

  Uses of a Hydraulic Press

  A hydraulic press is used for almost all industrial purposes. But basically it is used for transforming metallic objects into sheets of metal. In other industries, it is used for the thinning of glass, making powders in case of the cosmetic industry and for forming the tablets for medical use. The other common uses of the hydraulic presses are as follows:

  For crushing cars

  A hydraulic press is the heart of any car crushing system. In this process, a hydraulic motor applies a large pressure on the fluids into the cylinders. The fluid pressure makes the plates rise and with a large force, the plate is driven on the car thereby crushing it.

  Fat-free cocoa powder

  While processing the cocoa beans, a liquid known as chocolate liquor is derived. For making fat-free cocoa powder, this liquid is squeezed out in a hydraulic press. After this stage, this liquid is processed further to make a powder. The powder thus derived is cocoa powder, which is fat-free.

  For sword making

  In the process of making swords, a hydraulic press is used to give a flat shape to the raw steel.

TOPIC 6: MOTION IN STRAIGHT LINE.

Motion In Straight Line

Motion is the change of position of an object from one place to another. There are two types of motions; i.Circular motion-Is the motion of an object in a circle. Examples; a/. motion of the electron around the nucleus of an atom b/.revolutionary movement of the earth around the sun. ii.Linear motion-Is the motion of an object in a straight line.

Distance and Displacement

Difference between Distance and Displacement

Distinguish between Distance and Displacement

Distance Is the length between two points or two objects.It is a scalar quantity i.e. it has a magnitude only but no direction. Its symbol is X or S and the SI unit is meter (m). Other units used are Kilometer (km) and Centimeter (cm)

Displacement Is the distance in a specific direction. It is a vector quantity i.e. it has both magnitude and direction.

Differences between distance and displacement

Distance	Displacement
Is the length moved by an object between two points	Is the distance in a specific direction
It is a scalar quantity	It is a vector quantity

The SI Units of Distance and Displacement

State the SI units of Distance and Displacement

The symbol for distance is X or S and the SI unit is meter (m). Other units used are Kilometer (km) and Centimeter (cm)

The standard unit of displacement in the International System of Units ( SI ) is the meter (m).

Speed and Velocity

Difference between Speed and Velocity

Distinguish between Speed and Velocity

Speed

Speed is the distance moved by an object in a unit time or is the rate of change of distance . It is a scalar quantity.

Velocity

Velocity is the displacement moved by an object per unit time or is the rate of change of displacement. It is a vector quantity and its symbol is U or V.

Formula for speed and velocity

Speed(velocity) = Distance/displacement x time taken

X = Vt

Note:36km/h = 10m/s

Differences between speed and velocity

Speed	Velocity
Is the rate of change of distance	Is the rate of change of displacement
It is a scalar quantity	Is a vector quantity

The SI Unit of Speed and Velocity

State the SI unit of Speed and Velocity

The SI unit of speed and velocity is meter per second (m/s). Other units are Km/h or cm/s

The Average Velocity of a Body

Determine average velocity of a body

Types of velocity

1. Initial velocity, U – Is the velocity of a body at the start of observation
2. Final velocity, V – is the velocity of a body at the end of observation
3. Average velocity –is the average or mean between initial and final velocity or is the ratio of the total displacement to the total time.
4. Uniform or constant velocity Is the one whereby the rate of change of displacement with time is constant.
5. Absolute velocity is the actual velocity of a moving object recorded by a stationary observer
6. Relative velocity is the velocity of a moving object recorded by a moving observer .
7. Instantaneous velocity is the velocity of a moving object recorded at any time.

Acceleration

Acceleration is the rate of change of velocity or is the change in velocity per unit time Mathematically. Acceleration, a = (final velocity, v – initial velocity, u)/time, t

Velocity Time-graph

Interpret velocity time-graph

This is velocity against time graph. Consider a body accelerating uniformly from rest to a certain velocity v within time t. This can be represented graphically as shown below;

Distance

• The distance x moved by the body is given by the area under the curve.
• In this case is the area of triangle OBC.

Acceleration.

•  The acceleration is given by the slope of the triangle OBC.

The Acceleration of a Body

Determine the acceleration of a body

Example 1

A car starts from rest and accelerates to a velocity of 120m/s in one minute. It then moves with this speed for 40seconds finally decelerates to rest after another 2 minutes. Calculate;

1. the distance travelled
2. the total time taken for the whole motion
3. the deceleration
4. the average velocity

Soln

1st stage; acceleration u =0, v = 120m/s,t1 =1min=60s

2nd stage; uniform vel u=v=120m/s,t2=40s

3rd stage; Deceleration u=120m/s,v=0,t3=2min=120s

• 1st stage; s =average vel x time = ( (120+0)/2)60 = 3600m
• 2nd stage; s = vt = 120 x 40 = 4800m
• 3rd stage; s = average vel x time = ((v=u)/2)t = ((120+0)/2)120 = 7200m

Total distance, s T =3600+4800+7200 =15600m

Total time taken = 60 + 40 + 120 = 220s

from v = u + at

120 = 0 + 60a

60a = 120

a = 2m/s.

Average velocity = total distance/time

va = 15600/220

va = 71m/s

The Concept of Retardation

Explain the concept of retardation

Deceleration (retardation) is the rate of decrease of velocity or is the decrease in velocity per unit time. Uniform acceleration or retardation Is the one whereby the rate of increase or decrease of velocity is constant or it doesn’t change.

Note;

• when a body starts from rest or is brought to rest, its velocity is zero
• when the velocity of a body is constant or uniform, its acceleration is zero
• when the velocity of a moving object increases, its acceleration becomes positive
• when the velocity of a moving object decreases, its acceleration becomes negative called retardation.

Equations of Uniformly Accelerated Motion

Equation of Uniformly Accelerated Motion

Derive equation of uniformly accelerated motion

There are three equations of motion;

Newton’s first equation of motion

It is given by; v = u + at

whereby;

• u = initial velocity
• v = final velocity
• a = acceleration
• t = time taken

PROOF;

From the formula of acceleration; a = (v-u)/t

• at = v – u at + u = v
• v = u + at proved!

Newton’s second equation of motion

It is given by

whereas;

• s=distance travelled
• u=initial velocity
• t=time taken
• a=acceleration

PROOF;

Suppose an object starts from rest with intial vel,u to final vel,v after time t The distance ,S moved is given by S = Average vel x time S =( (u+v)/2)t

Substitute Newtons first eqn,gives; S = ((u+u+at)/2)t

S = ((2u+at)/2)t

S = ut + 1/2at. proved!

Newtons third equation of motion

It is given by V2 = U2+ 2as

where v=final velocity; u =initial velocity; a = acceleration; s = distance covered.

PROOF

From Newton’s first eqn; v = u + at

Equations of Accelerated Motion in Daily Life

Apply equations of accelerated motion in daily life

Activity 1

Apply equations of accelerated motion in daily life

Motion under Gravity

The Concept of Gravitational Force

Explain the concept of gravitational force

The acceleration of a free falling body is known as the acceleration due to gravity denoted by g and controlled gy gravitational force of the earth.

When two bodies of different masses are released from a certain height h above the ground, they will reach the ground at different times with the heavier one reaching earlier before the lighter one.

The reason is that the air resistance is more effective on lighter bodies than in heavier bodies, consequently this affect acceleration due to gravity in a reverse manner.

But dropping a light object and a heavy object in a vacuum they will reach the ground at the same time due to the absence of air resistance effect.

Consider the following two cases;

Case I

Consider a body falling freely from a certain height h and uses time t to reach the ground.

In this case: acceleration, a = acceleration due to gravity g

Initial velocity, u = 0

Final velocity, v.

Case II

Consider a body thrown vertically upwards from the ground with an initial velocity u to a certain height h and then comes back to the ground after time t.

In this case;

• Acceleration, a = -g
• Initial velocity = u
• Velocity at h = 0
• Final velocity at the ground = v

Acceleration due to Gravity

Determine acceleration due to gravity

A simple pendulum is a small heavy body suspended by a light inextensible string from a fixed support and it is normally used to determine acceleration due to gravity.

It is made by attaching a a long thread to a spherical ball called a pendulum bob. The string is held at a fixed at a fixed support like two pieces of wood held by a clamp and stand.

If the bob is slightly displaced to position B,it swings to and from going to C through O and back to B through O. When the pendulum complete one cycle/revolution the time taken is called the period of oscillation, T.

Definitions

1. Period ,T is the time taken by the pendulum bob to complete one complete cycle.
2. Angular displacement is the angle made between the string and the vertical axis when the bob is displaced to a maximum displacement.
3. Amplitude is the maximum displacement by which the pendulum has been displaced.
4. Length of pendulum is the length of the string from the point of attachment on the wooden pieces to the canterof gravity of the bob.

From the experiments, it has been observed that, changing the weight of the bob and keeping the same length of pendulum, the period is always constant provided that all swings are small though they may be different in size.

The period T of the pendulum is given by;

Where; l = length of pendulum; g = acceleration due to gravity

Also

It follows that if we plot a graph of l against T. it is going to be a straight line with a slope g/4Π2and y –intercept equal to 0.

When the bob is raised to point B it will gain potential energy and the bob will swing due to the conservation of energy from potential to kinetic energy.

• At B and C all energy is P.E.
• At O all energy is K.E.
• P.E at B = K.E at O.

If the pendulum swung in vacuum the oscillations would have been continuous. But practically, air friction causes losses of energy of the pendulum bob. That is why after a certain time the oscillations cease.

The Application of Gravitational Force

Explain the application of gravitational force

Activity 2

Experiment

Aim: Determination of acceleration due to gravity by using the simple pendulum.

Materials and apparatus: A simple pendulum, stand, clamps and stop watch.

Procedures

• Tie a piece of thread to a brass bob(about 100g)
• Suspend a bob with a thread between wooden pieces by clamping them on to a stand.
• Pull the bob slightly to one side and release the bob. Make sure the bob swings 50 complete oscillations.
• To be more accurate, perform three measurements for each length l of the pendulum.
• Repeat the procedures with l = 60cm and 50cm.
• Record the results as in the table below. -Plot the graph of l against T2

Results

Length, l (cm)	Time for 50 oscillations.				T (s)	T² (s²)
	t₁ (s)	t₂ (s)	t₃ (s)	Average(s)

Observation

The graph obtained will be a straight line through the origin.

The slope of the graph is given by;

From this equation, the acceleration due to gravity can be computed easily

TOPIC 7: NEWTON'S LAW OF MOTION.

1st law of Motion 

The Concept of Inertia

Explain the concept of inertia

Inertia is the ability of a resting body to resist motion or a moving body to continue moving in a straight line when abruptly stopped.

The more mass a body has, the greater its inertia and vice versa is true.

Newton's First Law of Motion

State Newton's first law of Motion

Newton’s 1st law of motion states that “Everybody will continue in its state of rest or of uniform motion unless an external force acts upon it”

Verification of Newton's First Law of Motion

Verify Newton's first law of Motion

Activity 1

Experiment

Aim: To verify Newton’s 1st law of motion.

Materials and apparatus: Glass, manila card and small coin.

Procedures.

A small coin is placed on a manila card and the card is positioned on top of the glass such that the coin is directly positioned over the open mouth of the bottle.

Flick the card at C. Make sure that the card is not tilted by moving the finger in the horizontal plane.

Observation: When the card is flicked away quickly by finger, the coin drops neatly into the glass. The coin dropped into the glass because there was no force applied on it when the card was flipped.

Conclusion: The coin continued to be at rest as the card was flicked quickly. This experiment verify Newton’s 1st law of motion.

2nd law of Motion

The Concept of Linear Momentum

Explain concept of linear momentum

Linear momentum of a body is the product of mass and velocity of that body.

Momentum = Mass, m x Velocity, v

Hence P = mv

The SI Unit of Linear Momentum

State the SI unit of linear momentum

The unit of momentum is kilogram meter per second(kgm/s)

Linear Momentum

Determine linear momentum

When two bodies, a heavy one and the light one are acted upon by an external force at the same time(collide) the light body builds up a higher velocity than the heavy one but the momentum they gain remain the same in both cases.

i.e Momentum before collision = Momentum after collision. This is what we call the conservation of momentum and is described by Newton’s 2nd law of motion.

Newton's Second Law of Motion

State Newton's second law of Motion

Newton’s 2nd law of motion states that “The rate of change of momentum is proportional to the applied force and it takes place in the direction of a force”

Consider a body of mass, (m) acted by an external force (f) from an initial velocity (u) to the final velocity (v) within a time interval (t).

Change of momentum = mv – mu

Hence the Newton’s 2nd law of motion can be summarized as;

“The force is directly proportional to acceleration of the object and the acceleration of the same body is inversely proportional to its mass”

F α ma

F = kma but k = 1

Hence F = ma

If a mass of 1kg is accelerated with an acceleration of 1m/sÇ then the force of 1N is said to be acting on it.

Newton is the force which when acting on a body of mass 1kg it produces an acceleration of 1m/s..

Verification of Newton's Second Law of Motion

Verify Newton's second law of Motion

A trolley experiences an acceleration when an external force is applied to it. The aim of this datalogging experiment is explore the relationship between the magnitudes of the external force and the resulting acceleration.

Apparatus and materials

• Light gate, interface and computer
• Dynamics trolley
• Pulley and string
• Slotted masses, 400 g
• Mass, 1 g
• Clamp
• Ruler
• Double segment black card (see diagram)

Take care when masses fall to the floor. Use a box or tray lined with bubble wrap (or similar) under heavy objects being lifted. This will prevent toes or fingers from being in the danger zone.

Procedure

1. Select the falling mass to be 100 g. Pull the trolley back so that the mass is raised to just below the pulley. Position the light gate so that it will detect the motion of the trolley soon after it has started moving.Set the software to record data, then release the trolley. Observe the measurement for the acceleration of the trolley.
2. Repeat this measurement from the same starting position for the trolley several times. Enter from the keyboard '1'( 1 newton) in the force column of thetable.
3. Transfer 100 g from the trolley to the slotted mass, to increase it to 200 g. Release the trolley from the same starting point as before. Repeat this several times. Enter '2' (2 newtons) in the force column of the table.
4. Repeat the above procedure for slotted masses of 300 g and 400 g.

Conservation of linear Momentum

Difference between Elastic and Inelastic Collisions

Distinguish between Elastic and Inelastic Collisions

Elastic collision

This is the type of collision whereby each body moves with a separate velocity after collision. In this type of collision both energy and momentum are conserved.

Inelastic collision

Is the type of collision whereby all bodies move with the same velocity after collision. This velocity is known as common velocity. In this type of collision energy is not conserved, only momentum is conserved.

Impulse is the change of momentum which is given asm the product of force and the time taken to change momentum.

F = mv – mu –Ft is the impulse of a force which is given by mv – mu.

The Principle of Conservation of Linear Momentum

State the principle of conservation of linear Momentum

Principle of conservation of linear momentum states that, “When two or more bodies acts upon one another; that is when they collide their total momentum remains constant, provided that there is no external force acting”

Momentum before collision = Momentum after collision

Consider two bodies of masses m₁ and m₂ moving with initial velocities u₁ and u₂ and then move with final velocities v₁ and v₂ respectively after they collide one another.

From the principle of conservation of momentum: Momentum before collision = Momentum after collision

m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂

The Principle of Conservation of Linear Momentum in Solving Problems

Apply the principle of conservation of linear momentum in solving problems

Activity 2

Apply the principle of conservation of linear momentum in solving problems

3rd law of Motion

Difference between Action and Reaction Forces

Distinguish between Action and Reaction Forces

Consider a book of mass, m which is at rest on a table. This book will exert on a table with a force equal to its weight. The table exert an equal upward force.

The downward force exerted by the book(weight) on the table is known as action force while the upward force exerted by the table on the book is known as reaction force.

These two forces acts in opposite direction but they are equal in magnitude.

Where; R = reaction, mg=weight of a book

Newton's Third Law of Motion

State Newton's third Law of Motion

Newton’s 3rdlaw of motionstates that “To every action there is an equal and opposite reaction”

Application of Newton's Third Law of Motion

Apply Newton's third Law of Motion

The person firing a gun will feel the recoil when the bullet leaves the gun.

Consider a gun of mass mg ejects a bullet of mass mb with a velocity vb and the gun recoils with velocity vg.

From the principle of conservation of momentum:

Recoil momentum of gun = Momentum of bullet

mgvg =mьvь

TOPIC 8: TEMPERATURE

Concept of temperature

The Term Temperature

Define the term temperature

Temperature is property of a body, which decides which way heat will flow when it is placed in contact with another body.

The SI Unit of Temperature

State the SI unit of temperature

Temperature refers to the degree of coldness or hotness of a body. The SI unit of temperature is Kelvin (K) known as absolute zero or thermodynamic scale.

Commonly in thermometers we encounter the unit Celsius degree (0C) another scale is called Fahrenheit scale.

Measurement of Temperature

Measurable Physical Properties that Change with Temperature

Identify measurable physical properties that change with temperature

A reliable measurement of temperature is done by a thermometer. Thermometers use measurable physical properties that change linearly with temperature to give temperature reading.

Physical properties that change with temperature are called thermometric properties of a thermometer which include the following:

1. Expansion of liquid when heated. E.g. Alcohol and mercury
2. Expansion of strip of two metals.
3. Generation of an electric current when heated
4. Change in resistance of a wire

The Fundamental Interval of a Thermometer

Define the fundamental interval of a thermometer

When you want to construct a thermometer you must establish two constant temperatures called fixed points. The fundamental interval of thermometer is the difference between the upper fixed point and lower fixed points.

The lower fixed point is the temperature of pure melting ice. Note that impurities lower the melting point of ice.

The Mode of Action of Liquid-in-glass Thermometer

Describe the 'mode' of action of liquid-in-glass thermometer

The working of this type of thermometer is based on the fact that liquid expands when heated and contracts when cooled. Examples of Liquid in glass thermometers are mercury and alcohol thermometers.

These two thermometers are called

1. Mercury in glass thermometer
2. Alcohol in glass thermometer

These thermometers have bulbs, which are reservoirs of liquid, and stems with fine bodies through which liquid rises and falls during the variation of temperatures.

The liquid used in these thermometer types is called thermometric liquids.

Comparison between the thermometric liquids:

Mercury	Alcohol
i. It is good conductor of heat	i.It is fairly a good conductor of heat.
ii. It expands linearly	ii. It expands rapidly
iii. It is clearly seen	iii. It is colourless
iv. It boils at 3600c	iv. It boils at 780c
v. It freezes at 390c	v. It freezes at – 1120c
vi. It does not wet a glass	vi. It wets the glass

Why water is not used as a thermometric liquid

Even though water is very readily available and it is cheap compared to mercury or alcohol, it is not used as thermometric liquid because:

1. Its volume expansion is not linear
2. It wets the glass
3. It has high heat capacity

The Temperature of a Body

Measure accurately the temperature of a body

A clinical thermometer is a typically a mercury in glass thermometer used to measure human body temperature. As the temperature rises the mercury expands and flows up the capillary tube. However, clinical thermometers have some limitations, they are delicate and can break easily, they may spread infection if not properly sterilised and they do not necessarily reflect the core body temperature.

TOPIC 8: SUSTAINABLE ENERGY RESOURCE

Sustainable energy, specifically renewable energy or green energy, is an energy source which can be replenished, that is essentially inexhaustible. Sustainable sources of energy include solar, wind, water, biomass and geothermal. Non renewable energy sources include coal, oil and natural gas.

Water Energy

The Generation of Electricity from Water

Explain the generation of electricity from water

Energy sources are areas of origin of a particular kind of energy. There are two types of sources of energy namely:

1. Renewable sources
2. Non- renewable sources

Renewable sources:These are the energy sources, which can be turned into use again after being used. Example sun, water, wind and fossils.

Non- renewable sources:These are the energy sources, which cannot be turned into use again. Examples: oil, natural gas and charcoal.

Sustainable sources of energy:This refers to natural resources that are used in the production of electricity without destroying the environment. These include:

1. Solar energy
2. Wind energy
3. Sea/wave energy
4. Geo-thermal energy
5. Tidal energy

Water energy refers to the energy obtained from running water by use of turbines and generators. This energy is called hydroelectric power.

Hydroelectric Power (H.E.P):This is electricity produced by running water.Hydroelectric power stations provide about 20% of the world’s electricity. In Tanzania, hydroelectric power stations/plants are found at Mtera, Kidatu and Nyumba ya Mungu.

Production of hydroelectric power

First, a dam is built to trap running water. This is usually in a valley where there is an existing lake. Water is allowed to flow through tunnels in the dam, where they turn turbines, which in turn drive generator.

The generator then produces electricity from water energy. Force of moving water thus turns the generators. Hydroelectric Power plants have no fuel costs and gives off no waste.

NOTE:

1. The dam constructed is made much thicker at the bottom than at the top because the pressure of water increases with depth.
2. Hydro electricity produces no waste products.

The Importance of Water Energy

Explain the importance of water energy

Water energy has the following importance.

1. The energy is virtually available
2. It is environmental friendly
3. It is more reliable than other sources like wind
4. Electricity can be generated constantly
5. The energy increases power very quickly

Application of energy from water

1. In Industries - to drive machine parts
2. Lighting purposes for example in homes
3. Heating and cooking
4. In health facilities i.e. runs incubators and freezers.

A Model of HydroElectric Power Plant

Construct a model of HydroElectric power plant

A model ofHydroElectric power plant

Solar Energy

Solar energyrefers to the energy obtained from the sun by the use of solar cells.

The Sun as a Source of Energy

Explain the sun as a source of energy

We consume energy in dozens of forms.Yet virtually all of the energy we use originates in the power of the atom. Nuclear reactions energize stars, including our Sun. The energy we capture for use on Earth comes largely from the Sun or from nuclear forces local to our own planet.

Sunlight is by far the predominant source, and it contains a surprisingly large amount of energy. On average, even after passing through hundreds of kilometers of air on a clear day, solar radiation reaches Earth with more than enough energy in a single square meter to illuminate five 60-watt lightbulbs if all the sunlight could be captured and converted toelectricity.

The Conversion of Solar Energy to Electric Energy

Explain the conversion of Solar energy to electric Energy

The energy produced by the sun is more than we need. Solar energy can be converted to electricity by using solar cells or photo voltaic cells. The main surface of solar panel is dull black. This enhances the absorption rate of the radiant energy from the sun.

Applications of solar energy

Solar energy has been harnessed by mankind and put to several uses. Below are some of the applications of solar energy:

1. It is used in electric appliances such as television and radios
2. For lighting purposes
3. Spaceship satellites use solar cells
4. Some torches, cars and calculators are powered by solar cells
5. Drying of clothes and farm (food) products.
6. Heating water using a solar hot water system

Though solar cells are expensive, they are very useful in remote and sunny areas.

A Model of Solar Panel

Construct a model of solar panel

A model solar panel

Wind Energy

Wind as a Source of Energy

Explain wind as a source of energy

Wind energy refers to the energy obtained from wind.It can be converted into electricity.Babylonians and Chinese used wind energy as a source of energy to pump water for irrigation 4000 years ago.

Wind energy can be converted into electricity by building a tall tower with a large propeller on top called windmill.

When wind blows, it rotates the propeller, which causes the attached generators to produce electricity.

Note: for more electricity to be produced, more properties are needed.

A Model of a Wind Mill

Construct a model of a Wind Mill

Diagram of a wind mill

A Wind Mill in Daily Life

Apply Wind Mill in daily life

Application of wind energy

For centuries, people have been using the power of the wind to move ships, boats and pump water.

Today, enormous wind energy is used to turn generators that facilitate the production of power. As windmills are efficient, very large turbines are required to providing the much-needed power.

Disadvantages of wind energy

1. Wind energy is not reliable
2. Winds are variables
3. The wind turbines are noisy and can spoil the landscape.
4. Large windy sites are required

Sea Wave Energy

Sea Wave as a Source of Energy

Explain sea wave as a source of energy

The concept of sea water:Sea water around the world is continually moving. The wind causes ocean waves as it blows across the sea. These waves are powerful sources of energy. This can be used to drive generators.

The concept of tides:Tides by definition are the rising and falling of the ocean flow. Tides are produced by the gravitational pull of the moon and to some extent the sun. The change of water levels that the tides produce can be used as an energy source.

The concept of wave energy:There are several methods of getting energy from waves.

The occurrence of waves in a swimming pool:Air is blown in and out of the chamber beside the pool; this makes the water bob up and down, causing waves.

The Conversion of Sea Wave Energy to Electric Energy

Explain the conversion of sea wave energy to electric energy

Electricity can also be generated from tides. As tide rises, water is allowed to enter the upper basin in the dam. Once the high tide has passed, the water on the upper basin is made to flow back to the lower basin through turbines in the barrage. The turbine turns generators, which convert seawater into electricity.

Water energy –is the energy obtained from running water by use of turbine and generators

Sea wave energy –Is the energy obtained from the series of swells of sea water.

Geothermal Energy

Geothermal as a Source of Energy

Explain Geothermal as a source of energy

The word “geothermal” means “Heat”, so geothermal energy is the energy generated by the flow of heat from the earth’s surface. It is the energy associated with areas of frequent earthquakes and high volcanic activity.

Areas like Kilimanjaro and Oldonyo in Tanzaia; and Rift valley in Kenya are geologically well structured to produce efficient geothermal system. The hot spring can cause rocks to be hotter than the earth’s surface. Thermal energy is obtained from radioactive materials that naturally occur in the rocks.

The energy produced can be used in:

• Heating buildings
• Driving generators
• Heating water

The Conversion of Geothermal Energy to Electric Energy

Explain the conversion of Geothermal energy to electric energy

Energy is obtained in the earth’s interior; it is necessary to drill through rocks. This creates vents where pipes are laid to bring the steam from the hot zone to the earth’s surface.

Once the steam has risen to the surface, it is directed into turbines. The steam drives turbines, which again are used to drive electric generators that produce electricity.