07-08 S5 Physics Revision Notes

07–08 S5 Physics Revision Notes – p.1

S5 PHYSICS REVISION NOTES

1.0 HEAT

1.1 Temperature

Temperature is a measure of the degree of hotness of a body.

Celsius temperature scale is determined by two fixed points - the ice point and the steam point

at normal atmospheric pressure.

The lower fixed point is taken as 0 C (ice point - temperature of pure melting ice at normal

atmospheric pressure) and the upper fixed point as 100 C (steam point -

temperature of the steam over pure boiling water at normal atmospheric

pressure). The range is then divided into 100 equal divisions and each

division is 1 C.

The other most common type scale is the Kelvin scale (also called the

absolute scale) and

Kelvin temperature (in K) = Celsius temperature + 273.

Thermometer is a device for measuring temperature. It makes use of a

property which varies with the temperature.

The clinical thermometers have a constriction. It prevents the

mercury column from falling back into the bulb after each

measurement.

Figure 1.1 Temperature scale.

1.2 Heat, Internal Energy & Heat Capacity

Internal energy of a body = kinetic energy + potential energy of all its particles.

Heating is the process in which energy is transferred from one body to another as a result of a

temperature difference and the energy transferred is called heat.

Both heating and doing work (work = force distance moved) are processes in which energy

is transferred from one body to another.

Specific heat capacity of a substance - energy transferred by heating needed to raise the

temperature of 1 kg of the substance through 1 C.

E = mcT, where E is energy to produce a temperature change of T in m kg of a substance. c

is specific heat capacity measured in J kg-1 C-1 or J kg-1 K-1.

Heat capacity C is energy required to raise the

temperature of a body through 1 C, i.e. C =

mc.

Figure 1.2 Measuring the specific heat capacity

of water.


A polystyrene cup is used in the experiment because it takes very little energy from the heater

and as it is a bad conductor, it reduces the energy lost to the surroundings.

The liquid is stirred to ensure that the temperature of the liquid is uniform.

In the experiment, if a glass beaker were used, the measured specific heat capacity would be

larger as the heat loss to the surroundings would be larger.

In the experiment, if half a cup of water were used, the measured specific heat capacity would

be larger as the proportion of heat absorbed by the cup would be larger.

During heating, some energy is absorbed by the container and some energy is lost to the

surroundings.

Energy needed to heat up the water is directly proportional to the mass of water and the

temperature change. This relationship is also true for other substances.

Energy is measured as E = Pt, where P is the power rating of the immersion heater used and t

is the time.

To measure the specific heat capacity of a metal

block, the apparatus are set up as shown. The metal

block is placed on a polystyrene tile and its sides

are wrapped with some cotton wool to reduce the

energy loss.

Figure 1.3 Measuring the specific heat capacity of metal.

When two bodies having different temperatures are put in contact, energy is transferred from

the hot body to the cold body. The energy lost by the hot body = the energy gained by the cold

body. [Exam Technique] Assumption used in calculation.

When ice is mixed with a liquid, its temperature drops. When all the ice cubes melt, the

temperature of the liquid is lower than that of the surroundings, there is a heat flow from

the surroundings to the liquid. The temperature increases.

Water has a very high specific heat capacity. This explains why coastal areas have a cooler

summer and a milder winter than inland areas.

Water can also be used as a coolant in motor cars.

[Exam Technique] Water has a specific heat capacity 4200 J kg-1 C-1 means that 4200 J is

required to increase the temperature of 1 kg of water by 1 C.

[Exam Technique] If a question is using the word “change” (e.g. how does it affect/what

change…), use the following wordings: decreases, increases or remains unchanged.

[Exam Technique] If a question is asking for an explanation of a change, follow this rule:

Theory, Conditions, Conclusion.

1.3 Transfer of Heat

The three transfer processes are conduction, convection and radiation.


Conduction occurs when two objects at different temperature are in contact. Heat is

transferred from a hot object to a cool object through the contact surface. When one part

of an object is hot, molecules in that part vibrate vigorously. By collisions among molecules,

kinetic energy is transferred to molecules in other parts of the object.

Metals are good conductors of heat because they make use of free electrons to transfer energy.

Example: As tile conducts heat better than carpet, heat conducts away from our feet more

readily through tile than carpet. Hence a tile floor feels colder.

Demonstration: water and air are bad conductor of heat:

Figure 1.4 Figure 1.5

Example: Clothes for extreme cold environments are usually filled with goose-down. Air is a

very good insulator. They trap air effectively and prevent heat loss.

Convection occurs in liquid or gas. When air (or water) around the heating elements is

heated, it expands and becomes less dense. Therefore the air rises. Cool air in the oven is

denser. It sinks and takes the place of the rising air. As a result, a convection current is

formed. The air in the oven is heated up and in turn heats up the food.

Example: Some ovens have a fan inside because it is used to mix the hot air and the cool air

so that the air is heated up evenly.

Example: The coiled tube in dehumidifier is designed in a coiled shape because the coiled

tube increases the contact surface area with air and helps to condense water from the air.

In order to prevent the dehumidifier from overheating, the coil is painted black to radiate

heat, the air fan creates a flow of air current, the metal fins carry heat away by

conduction and the holes allow a flow of air current.

The heating elements in electric kettles and electric water heaters are located near the bottom

because the whole tank of water can be heated evenly by convection and it is to prevent

overheating in case the level of water is too low.

Air-conditioners are usually installed near the ceiling.

Radiation is an energy transfer process through the emission of infra-red (IR) radiation.

IR radiation is an electromagnetic wave and it can travel through a vacuum. IR radiation is an

invisible light with a wavelength longer than that of red light.

The wavelength of IR radiation emitted depends on the temperature of the object. If the object

gets hotter, the wavelength will be shorter.

An object with a dull surface is a good emitter as well as a good absorber of IR radiation.

An object with a shiny surface is a poor emitter as well as a poor absorber of IR

radiation.

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Example: A black surface is a good absorber of radiation. Therefore, painting the pipes in the

solar hot water systems black can make them more effective in absorbing radiation from the

Sun.

Thermal flask: The foam reduces heat transfer by conduction and convection. The foam are

poor conductors of heat. The air inside the foam is broken into many tiny bubbles, which

reduce convection of air inside the foam. Moreover, there is no medium in vacuum for the

transfer of heat by either conduction and convection. Therefore, the transfer of heat is

greatly reduced. So the heat insulation of vacuum between the double glass walls is better

than that of foam. To reduce heat loss by radiation, the inner surface of walls of the glass

container is painted silvery to reduce heat transfer. A thermal flask can also store cold

liquids and keep them cold for a period of time. The glass walls of the thermal flask can

reduce heat transfer, and so it can keep the temperature of the liquid at constant for a

period of time.

Part of the solar energy emitted from the sun is absorbed by the Earth, the lands and oceans are

therefore warmed up. Gases like carbon dioxide, chlorofluorocarbons, methane, nitrous oxide

and water vapour in the atmosphere absorb infra-red radiation emitted from the warmed earth,

and this warms up the atmosphere. The atmosphere radiates infra-red to the space and to the

lands and oceans. As a result, the Earth is kept warm. This process is called the greenhouse

effect. The gases mentioned above are known as greenhouse gases. The concentrations of

greenhouse gases in the atmosphere are increased by human activities, e.g. using air

conditioners, burning fossil fuels, etc. If the greenhouse effect is too strong, the Earth will

overheat.

1.4 Change of State

The three states of a substance are solid, liquid and gas. It may change from one state to

another if it is heated or cooled.

When a substance is changing its state, energy is

absorbed or given out without a change of its

temperature. This energy is called latent heat.

Figure 1.6 Cooling curve.

In the example, when a solid is heated, A =

solid, B = solid + liquid, C = liquid and

melting point = 60 CFigure 1.7 Heating curve.

The specific latent heat of a substance is the

energy transferred by heating to change the


state of 1 kg of the substance without a change of temperature, .

The specific latent heat of fusion of water is the energy

needed to change 1 kg of ice to water without a change of temperature. Its value is .

Figure 1.8 Measuring the specific latent heat of fusion of water.

Since ice melts at room temperature, a control is needed.

The set-up for the control experiment is identical to

the original set-up except that the heater is not connected to the power supply. The control

experiment can measure the amount of ice melted in room temperature.

The experiment can be improved by:

To ensure a good (thermal) contact between the ice and heater

To increase the surface area of contact between the ice and heater

To enable the temperature of ice to be more close to 0 C The specific latent heat of vaporization of

water is the energy needed to change 1 kg of

water to steam without a change of temperature. Its value is .

Figure 1.9 Measuring the specific latent heat of

vaporisation of water.

To improve the result of the experiment, one

can immerse the heating coil completely in

water, surround the beaker with insulating

material or use a polystyrene cup.

1.5 Melting, Boiling and Evaporation

Increasing the pressure lowers the melting point and raises the boiling point of water.

Decreasing the pressure lowers the boiling point of water.

Adding impurities, e.g. salt, to water lowers its melting point and raises its boiling point.

Evaporation is the changing of a liquid to a vapour which occurs at temperatures lower than

the boiling point. Evaporation takes place at the surface of the liquid.

A layer of oil can reduce the amount of energy lost from the water to the surroundings,

by reducing the rate of evaporation.

The dryer can speed up the rate of evaporation of water from wet hair as follows: the average

kinetic energy of the water molecules in the hair will increase. More water molecules at

the water surface gain enough energy to escape from the water. In addition, the water

molecules escaped from the water surface will be blown away by the breeze from the


dryer.

Although heat is still supplied to boil the water, the temperature does not change because it is

absorbing latent heat of vaporization in changing its state.

Steam will release a large amount of energy when it condenses (releases latent heat of

vaporization). This explain why steam at 100 °C causes more severe burns to human skin than

boiling water.

To save energy in cooking, the heater is turned to ‘low’ setting after water boils. The cooking

time would not be lengthened as the temperature of the water remains at 100 C. The

energy absorption rate of the food remains unchanged.

Temperature is a measure of the average kinetic energy of the molecules. As the temperature

rises, the molecules gain energy and move faster.

When the molecules of the water with greater kinetic energy leave, the average kinetic

energy of molecules in the liquid decreases. The temperature drops. It explains why the

temperature of a cup of water drops because of evaporation.

The molecules in a body have both kinetic and potential energy. Kinetic energy is due to the

motion of the molecules; potential energy arises from attractive forces between the molecules.

A temperature rise indicates an increase in the average kinetic energy of the molecules. A

change of state indicates an increase in potential energy of the molecules. In both cases, the

internal energy of the body increases.


2.0 MECHANICS

2.1 Position and Movement

There are two types of quantities – scalar and vector. Scalar quantities have magnitude only,

e.g. time, speed, mass etc. Vector quantities have both magnitude and direction, e.g.

displacement, velocity, acceleration, force, momentum etc.

Addition of vectors can be done by using ‘tip-to-tail’ method or ‘parallelogram’ method.

Resolution of vectors can end up with a series of components.

Quantities

1. Time [s]

2. Displacement [m] (c.f. distance)3. Velocity [ ] (c.f. speed, average vs spontaneous)

4. Acceleration [ ] (retardation, deceleration)

A motion can be studied by the use of a ticker-tape timer. It

usually produces 50 dots per second (50 Hz) on a length of tape

pulled through it. The time interval between 2 adjacent dots is

called a ‘tick’. If a tape is cut into 5-tick strips and the successive

strips are pasted up side by side, a tape chart is formed. We can

then convert it to a v-t graph.

Figure 2.1 Speed-time graph of a uniformly accelerated motion

To find the speed of a block moving down from an inclined plane, a ticker-tape timer can be

used. Attach a paper tape to the block. Switch on the timer and release the block. The speed of

the block can be calculated from the dots on the tape. (or the tape can be used to construct a

tape chart and its speed (acceleration) can be calculated.)

The slope of a s-t graph gives the speed of the body.

For a v-t graph, the slope gives the acceleration of the body whereas the area under the

graph gives the total distance travelled.

For a uniformly accelerated motion along a straight line, we have v = u + at, ,

When a car is to brake, reaction time is the time lag for a driver between seeing the danger and

stepping on the brake; thinking distance is the distance the car travels after the driver has seen

the danger and before the brakes are on; braking

distance is the distance the car travels after the brakes

have been put on; and stopping distance is the

thinking distance plus braking distance.

Figure 2.2 Typical v-t graph for a car when it brakes.

The braking distance depends on the road condition

and the performance of the car such as the wetness of the road , the tyre’s quality, etc.


Large arrows (chevrons) are painted on the highway and road signs are set up to remind drivers

of this safety distance. When the car is on a slope, a component of its weight acts downhill

along the slope. As a part of the braking force is used to overcome this component, the

decelerating force is reduced and the deceleration is smaller. As a result, the stopping

distance would become larger. So the distance between two arrows should be longer.

In the absence of air resistance, all objects fall with the same acceleration.

In calculation, we use g = 10 m s-2, acceleration due to gravity. The acceleration is

independent of its mass when it is falling.

[Exam Technique] In describing a motion, break it down into different time interval and use the

terms such as remains at rest, moves with constant velocity, moves with uniform

acceleration, etc.

[Exam Technique] Prepare v-t and a-t graphs for free fall (with and without kinetic loss when

the object hits the ground.

[Exam Technique] For every graph, the physical quantity of the

slope = quantity of y-axis quantity of x-axis

area = quantity of y-axis quantity of x-axis

[Exam Technique] In plotting a graph,

Axes should be labeled with appropriate scales

Points should be correctly plotted

Graph (either a straight line or a smooth curve) should be drawn appropriately

[Exam Technique] In sketching a graph,

Axes should be labeled with appropriate scales

Some values should be shown on the graph

2.2 Force and Motion

Newton’s First Law of Motion

Inertia is the tendency of a body to maintain its state of rest or of constant speed along a

straight line (Galileo’s law of inertia).

Every object remains in a state of rest or uniform speed along a straight line unless acted

on by an unbalanced force.

Newton’s Second Law of Motion

The acceleration of an object is directly proportional to, and in the same direction as, the

unbalanced force acting on it, and inversely proportional to the mass of the object, F ma.

F = ma

Newton’s Third Law of Motion

To every action there is an equal and opposite reaction.

Note that action and reaction act on different objects.


Force is measured in newtons (N). 1 N is the force that gives an object of mass 1 kg an

acceleration of 1 m s-2.

Note that unbalanced force, resultant force, accelerating force and net force means the same

thing.

The mass of an object is a measure of its inertia. The weight of an object is the gravitational

force acting on it by the Earth, W = mg. It is measured in newtons (N).

Force is a vector. It can be added (resultant) using the tip-to-tail or the parallelogram methods.

It can also be resolved (component) into two perpendicular components.

Component of weight down the runway = mg sin .

To test whether an inclined plane is friction-compensated or not, attach the trolley to a tape

which is passing through a ticker-tape timer. Slightly move the trolley until it begins to

move. If the dots on the tape are equally spaced, the plane is friction-compensated. (If it is

not, adjust the slope of the runway until the dots in the tape have equal space.)

When a person wants to jump up, he exerts a force against the ground when he jumps up

vertically. By Newton’s 3rd Law, there is an equal but opposite normal reaction acting on

the player by the ground. As the reaction is greater than his weight, by Newton’s 2nd Law,

he accelerates upwards as there is a net upward force acting on him.

Friction arises whenever an object slides or tends to slide over another object. It always acts in

a direction that opposes or prevents motion.

If a lorry is loaded, the inertia increases. By Newton’s second law of motion, its

deceleration would become smaller when the brake is applied. As a result, its stopping

distance and stopping time increase, and the chance of having an accident is larger. This

explains why a loaded lorry cannot travel too fast in a motorway.

[Exam Technique] In free body diagram, use weight, normal reaction, friction, tension and/or

electric (electrostatic)/magnetic force.

[Exam Technique] In testing a pair of action and reaction, identify the “actor” and “reactor”, i.e.

A and B. (use the rule: A acts on B (action), B acts on A (reaction). For example, a man is

standing on the floor. The weight of the man (Earth acts on the man) and the normal reaction

(Ground acts on the man) do not form an action-reaction pair as they act on the same object.

2.3 Work, Energy and Power

Work is defined as the product of force and the distance moved in the direction of the force, i.e.

W = Fs. Its unit is joule (J).

If the force is at an angle of to the direction of motion, W = Fs cos.

Work is done whenever energy changes from one form to another.

The three types of mechanical energy are:

1. Kinetic energy - energy possessed by a moving object.


2. Gravitational potential energy - energy possessed by an object because of its position

above the ground.

3. Strain energy - energy possessed by an elastic object when it is stretched, compressed or

twisted. Kinetic Energy, K.E. = ½

Potential Energy, P.E. = mgh

Principle of Conservation of Energy states that energy can be changed from one form to

another, but it cannot be created or destroyed.

Note that in an elastic collision, both momentum and kinetic energy are conserved. In an

inelastic collision, momentum is conserved but kinetic energy is reduced.

In a pendulum, there is a continuous change between kinetic energy and potential energy.

However, there is no workdone by the tension of the string as the path of movement is

normal to the direction of tension. There is no displacement along the direction of tension.

There is a continuous change in P.E. and K.E. in a simple pendulum and its velocity at different

height is calculated by K.E. = P.E. In many cases, the maximum

kinetic energy gained is less than the loss in the potential energy

because there is energy loss due to air resistance.

Figure 2.3 Energy change of a free fall.

When an object is stopped, its mechanical energy is changed into

internal energy. So in many collisions, kinetic energy may not

conserve as some energy may change to heat and sound energy.

Power is the rate at which energy is transferred or work is done, i.e. P = W/t. Its unit is watt

(W).

For a moving object, power = force speed.

The world’s energy sources will run out in the not-so-distant future. We must save energy and

look for alternative sources such as wind energy, tidal energy, solar energy, geothermal energy,

hydroelectric energy, nuclear energy and biomass energy.

Efficiency is calculated by the output energy divided by the input energy; it is usually

represented by use of percentage and increases with the load. The useful energy output can be

calculated by interpreting the use of a particular machine/situation. Energy is wasted in (i)

overcoming friction and (ii) moving the movable parts of the machine, i.e. workdone against

friction and workdone used in rasing the movable part of the machine.

[Exam Technique] Prepare discussion of energy conversion, e.g. P.E. is converted to K.E. and

heat, etc.

2.4 Momentum

Elastic collision is the collision in which the mechanical energy is conserved; inelastic collision

is one in which the mechanical energy is not conserved.


We only need to check that whether there is a change of the kinetic energy to see if the collision

is elastic or not.

Momentum = mass velocity [ ]

Conservation of Momentum

In a collision, total momentum of the colliding objects before collision is equal to the total

momentum after collision, provided there is no external forces acting on the objects.

For ALL collision, we can use the formula .

For some collision, e.g. a trolley collides with plasticine fixed to the ground, the total

momentum is not conserved. As the plasticine is fixed to the ground, there is external force

on the plasticine by the ground. So the total momentum of the trolley and the plasticine

are not conserved.

Impulse is the change of momentum, i.e. Ft = mv. Its unit is N s or kg m s-1.

For car safety, a car is designed to have collapsable front and rear sections and a strong

passenger section; and of course, seat-belt is another safety device.

On motorway, the crash cushion systems should not be replaced by concrete blocks because the

collision time will be shorter. A larger force will be exerted on the car during collision.

Principle of a water rocket: When the trigger is pulled, the compressed air exerts a force on

the water and forces the water out. By Newton’s third law of motion, the water in turn

exerts a reaction on the rocket and lifts the rocket up.

[Exam Technique] Comment of law of conservation of momentum, e.g. Momentum is not

conserved in the impact because there is an external force exerted by the ground on the

target during the impact.

[Exam Technique] If data of experiment were given in a collision, check both conservation of

momentum and kinetic energy.


3.0 WAVES

3.1 Reflection of Light

We can see an object because it emits light (luminous) or reflects light (non-luminous) to our

eyes.

Light rays from a very distant object are almost parallel.

According to the laws of reflection, the incident ray, the reflected ray and the normal all lie on

the same plane and the angle of incidence

equals the angle of reflection.

A plane mirror can produce a clear image as

there is regular reflection.

Figure 3.1 Regular reflection.

From the study of plane mirrors, the image can

be located by producing the reflected rays

backwards to a position which is behind the mirror. Since light does not actually pass through

the image, the image cannot be picked up by a screen (i.e. it is not real).

Note that light rays cannot pass through the mirrors (c.f. when they are lenses).

The properties of the image formed by a plane mirror include: the image is virtual, same size

as the object and upright but laterally inverted; and the image distance equals the object

distance.

Plane mirrors can be used in dressing rooms and in periscopes.

[Exam Technique] To draw the ray diagram of a plane mirror, use the fact that the image

distance is equal to the object distance, i.e. first mark the image before drawing light rays.

[Exam Technique] The reflected ray (or its projection) of an object will pass through the

corresponding point of its image.

[Exam Technique] If there are light rays coming from the object through the image, the image

is real; otherwise, no reflected ray can be picked up by a screen and the image is virtual.

[Exam Technique] To determine whether an image is upside down, two light rays from the

object is enough as in the case of a periscope.

Figure 3.2 The image is upright as determined by the two reflected light rays.


3.2 Refraction of Light

When light travels from one medium to the other, its wavelength and speed change, and the

light ray is refracted at the interface.

When light passes from a less dense to a denser medium, e.g. from air to water, it is bent

towards normal; i.e. the angle of refraction is smaller than the angle of incidence.

When light passes from a denser to a less dense

medium, e.g. from glass to air, it is bent away

from the normal.

Figure 3.3 Light ray travels from one medium to another.

According to laws of refraction, the incident ray,

the refracted ray and the normal all lie in the same

plane and sin i

sin rn , where i is the angle of incidence; r the angle of refraction and n is a

constant.

In general, for light passing from medium 1 into medium 2, n n1 1 2 2sin sin , n1 and n2 are

refractive indices of the media.

Figure 3.4 Figure 3.5 Figure 3.6

The larger the refractive index the more the light is bent in the material.

If a light ray hits the surface at a greater angle than C, the critical angle, it is totally reflected

inside (total internal reflection).


Figure 3.7 Light ray hitting a semi-circular block.

The critical angle and the refractive index is related by n1

sin C .

Total internal reflection occurs when

Light rays travel from an optically denser medium to an optically less dense medium, and

The angle of incidence is larger than the critical angle.

Applications of total internal reflection include to use prisms as mirrors in periscopes (to avoid

multiple images formed in the case of a plane mirror) and glass fibres are used by doctors to see

into the human body, e.g. to take pictures from stomach; and are used in optical fibre

communications.

Figure 3.8 Right-angled prisms used in a periscope. Figure 3.9 Glass fibre

A prism is used in periscope instead of plane mirror because using prisms can prevent

formation of multiple images.

Advantage of using optical fibres over copper wires in communication:

Optical fibres are lighter than copper wires.

Optical fibres carry more information than copper.

Optical fibres transmit signals with little loss than

copper wires.

Example: As the refractive index of diamond is larger than

that of glass, the critical angle of diamond is smaller than

that of glass. More light would be total internally reflected

inside the diamond than in glass. So more light would emerge

from its upper surface which makes the diamond more

sparkling than the glass.

Figure 3.10 Diamond.

[Exam Technique] The frequency of a light ray depends on its source. Since the speed of light

is reduced when it travels from air to glass, by the wave equation, the wavelength is also

reduced.

[Exam Technique] The refractive index of air is approximately equal to 1. When applying the

general formula n n1 1 2 2sin sin , to calculate the angle of refraction when light travels from

air to a medium (or vice versa), take n = 1 for air.


[Exam Technique] Always use i = angle measured in air in applying sin i

sin rn .

[Exam Technique] When a light ray travels from a dense medium to a less dense medium, light

rays splits into two rays at the interface (if the incident angle is smaller than the critical angle).

[Exam Technique] Total internal reflection can only occur when light travels from a dense

medium to a less dense medium, so for light travelling from air to glass, for example, total

internal reflection will not occur.

3.3 Lenses

A convex lens is thicker at centre than at the edges while a concave lens is thinner at centre.

A convex lens can converge parallel light rays to a point, the principal focus. Since light rays

can come from either side of the lens, a convex lens has two principal foci and it is also called a

converging lens.

A concave lens refract parallel light rays outwards and the refracted rays appear to come from

a point, the principal focus.

Since a concave lens turns parallel rays into divergent rays, it is also called a diverging lens.

The centre of the lens is called the optical centre and the distance of the focus to the centre is

the focal length.

The shorter the focal length of a lens, the more powerful it is (i.e. it has a shorter focal length).

Certain construction rules can be followed to study the nature of the images formed.

Figure 3.11 Construction rules for convex lens and concave lens.

There are two types of images formed by a convex lens. If the object is close, the image is

virtual, erect and magnified. In this case, it is used as a magnifying glass. If the object is far

away, the image is inverted and real.

A concave lens can only give one type of image. It is always virtual, erect and diminished and

on the same side of the lens as the object.

magnificationheight of image

height of object or magnification

image dis ce

object dis ce

tan

tan


Figure 3.12 Ray diagrams of convex and concave

lenses.

To find the focal length of a convex lens, you can use the convex lens to capture a sharp

image from a distant object on a screen; measure the distance from the screen to the lens

and this distance is equal to the focal length of the lens.

Figure 3.13 Capturing image of a distant object on a screen

A convex lens can be used as a magnifying

glass. When an object is placed inside the

principal focus of the lens, it gives an erect

and magnified image.

Figure 3.14 A magnifying glass


Concave lens is used as a rear view safety lens can increase the field of view of the driver

when looking backward, enable the driver to see things behind that cannot be seen

through side mirrors or inside rear mirrors and enable the driver to see things hidden in

the blind spot at the back of the car.

[Exam Technique] The image of the lens is formed at the intersection of the refracted rays. It is

because light travels in straight lines and we are used to this fact. When we see an object

through a lens, we think that the refracted rays all come from their intersection and an image is

formed there.

[Exam Technique] Since light rays from a very distant object are almost parallel, we can use

this fact to find the focal length of a convex lens.

[Exam Technique] When you are asked for the explanation of the lens used, use the following:

The lens is a convex lens because only convex lens can form a real image/a magnified

image.

The lens is a concave lens because the image formed is erect and diminished.

3.4 Wave Motion

All waves carry energy

Transverse Wave - vibrations of the particles on the wave are at right angles to the

direction of travel of the wave (e.g. water wave, light). A continuous transverse wave consists

of a series of crests and troughs.

Longitudinal Wave - vibrations of the particles on the wave are along the direction of

travel of the wave (e.g. sound). A continuous longitudinal wave consists of a series of

compressions and rarefactions.

Amplitude (A) - size of maximum disturbance measured from resting position (unit: m)

Wavelength () - minimum distance in which a wave repeats itself (unit: m)

Wavelength of a transverse wave is the distance between two successive crests (or

troughs)

wavelength of a longitudinal wave is the distance between two successive compressions

(or rarefactions)

Frequency (f) - number of waves produced in one second (unit: Hz)

Period (T) - time taken for one wave to be produced (unit: s)

Frequency and period are related as: f1

T

Period of vibration is the time taken for a particle on the wave to make one complete

vibration

Wave speed (v) - distance travelled by a wave in one second (unit: ms 1 )

Particles on a wave within one wavelength vibrate with same frequency and amplitude but


there is a phase lead from one particle to the next.

Particles which are one wavelength apart vibrate exactly in phase

Particles which are half a wavelength apart vibrate exactly out of phase (i.e. when one particle

is moving down the other is moving up and vice versa)

Wavelength can be defined as the distance between two successive particles which are

vibrating in phase (As particle makes one complete vibration, wave moves forward a distance

equal to one wavelength)

wave speed = frequency wavelength [ v = f ]

[Exam Technique] Make sure you know the terms to describe waves and how they can be

found from a given diagram, e.g. A = 1 cm, = 4 cm, etc. in the following diagram.

Figure 3.15 Displacement-distance graph of a transverse wave.

[Exam Technique] Make sure you know how to determine the particle movement (Copy the

waveform next to the original one, terms used are moving upwards, moving downwards,

momentarily at rest), e.g. A, C, E are momentarily at rest; B is moving upwards while D is

moving downwards.

Figure 3.16 Particle motion in a transverse wave.

[Exam Technique] Method of demonstrating a transverse wave: Place the cork into the ripple

tank. The cork moves in a direction perpendicular to the direction of propagation of the

wave.

[Exam Technique] Method of demonstrating a longitudinal wave: Light up a candle. The

candle is placed in front of the speaker cone. The flame moves along the direction of

propagation of the sound.


3.5 Properties of Waves

When water waves pass through a cork on the water, the cork will move upwards and

downwards. It does not move away with the wave.

Properties of water waves can best be studied using a ripple tank. Bright lines correspond to

wave crests and dark lines to wave troughs.

Wavelength is represented by the distance between two adjacent bright (or dark) lines.

Continuous waves can be frozen using a stroboscope (strobe). Waves are frozen if strobe

frequency is equal to the wave frequency, or half, one-third, etc., of its value.

If strobe frequency is twice the wave frequency, the wavelength appears to be halved (double

viewing).

The wave frequency is equal to the maximum strobe frequency which freezes the wave

pattern without any change in wavelength.

If the strobe frequency is slightly too high, waves appear to move backwards. If the strobe

frequency is slightly too low, waves appear to move forward.

The properties of waves, reflection, refraction, diffraction and interference, can be studied

by using ripple tank. A cloth is used to cover the edge to absorb the water wave so that no

reflected water wave will interrupt the wave pattern.

Reflection of water pulses by straight barriers and curved barriers is very similar to the

reflection of light rays by plane mirrors.

Figure 3.17 Reflection of water waves.

To study refraction of water waves, a sheet of perspex

is put in the ripple tank. When plane waves enter the

shallow region, wavelength is reduced (wave speed is

also reduced since frequency stays the same).

Figure 3.18 Refraction of water waves.

When plane waves enter the shallow region at an

angle to the boundary, waves also change direction, i.e.

they are refracted

Refraction takes place whenever there is a change in

wave speed when waves cross a boundary between two media.

Diffraction is the bending of waves around obstacles. Bending is more marked if the obstacle


is comparable in size to the wavelength. Wave speed and wavelength stay the same.

Figure 3.19 Diffraction of water waves.

At some places in the ripple tank, two waves arrive in step or in phase. Crest of one wave

meets the crest of other wave there to give a bigger crest (constructive interference). At other

places, two waves arrive exactly out of phase. Crest of one wave meets the trough of other

wave there and they cancel each other (destructive interference).

Constructive interference: path difference, , is equal to whole number wavelengths, i.e. 0, ,

2, 3 and so on.

Destructive interference: path difference is equal to 12 , 1 1

2 , 2 12 and so on.

Figure 3.20 Interference of water waves.

In Figure 3.20,

At B, = S2B – S1B = 4½ – 2½ = 2,

constructive interference occurs.

At C, = S1C – S2C = 4 – 2½ = 1½,

destructive interference occurs.

Nodal lines: lines joining places of destructive

interference.

Antinodal lines: lines join places of constructive interference.

On increasing separation of the sources, nodal (and antinodal) lines increases in number

and also become closely spaced; if the separation is further increased, nodal lines become so

close together that they are hardly observable.

[Exam Technique] Draw wave pattern for the four properties of waves.

[Exam Technique] To increase the wavelength of water waves:

Increase the depth of water in the ripple tank

Lower the frequency of vibration of the vibrator

[Exam Technique] Frequency is determined by the source while the wavelength (and speed)

determined by the medium. So in refraction, the frequency of light will not be changed but

the wavelength will be decreased when it enters into the glass.


3.6 Wave Nature of Light and Sound

Interference is a unique property of waves and light, showing interference, must be a wave.

All waves in the electromagnetic spectrum show reflection, refraction, diffraction and

interference. They travel through empty space at same speed (the speed of light 3 108 m s-1).

Electromagnetic waves are a form of travelling electrical and magnetic transverse waves; given

off by electrons as they vibrate or lose energy

Visible spectrum - white light passes through a prism is separated into its constituent colours:

red, orange, yellow, green, blue, indigo and violet. Violet light has the shortest wavelength and

red light the longest. Eye is sensitive to this range of wavelengths which are from 4 10-7 m to

7 10-7 m.

Infra-red radiation - invisible radiation lies beyond the red end of the spectrum. It is emitted

by all objects; the amount and wavelength of radiation depend on temperature. It has many

useful applications such as infra-red photographs, infra-red scanners, infra-red remote

controls, infra-red telescopes.

Ultra-violet radiation -invisible radiation lies beyond the violet end of the spectrum. It has

many useful applications such as:

ultra-violet lamps used by the bank to check signature on a savings account passbook

and for identifying fake banknotes

sterilizes water from drinking fountains in school

washing powder contains fluorescent chemicals which glow in sunlight, making the shirt

look ‘whiter than white’ in daylight

Radio Waves - have the longest wavelength in the electromagnetic spectrum. It is produced by

making electrons vibrate in an antenna. It is used to transmit sound and picture information

over long distances.

Long waves are used for long distance broadcasting because diffraction is more significant

for longer wavelength.

Microwaves - radio waves with wavelengths of a few centimetres or less. It is used in satellite

communications, radar and TV transmission.

Radar (Radio Detection And Ranging) - microwaves with short wavelengths are reflected by

small objects. A radar system consists of an antenna, a transmitter and a receiver. The antenna

whirls around continuously to scan surrounding area and the transmitter sends out a narrow

beam of microwaves in short pulses. The direction and the range (distance) of an object can

then be found.

X-rays and gamma rays have the shortest wavelengths in the electromagnetic spectrum. X-

rays are emitted when fast moving electrons hit a metal target (x-ray tube). Long wavelength x-

rays can penetrate through flesh but not bone (used in x-ray photography). Short wavelength x-

rays can even penetrate through metal (used in industry to inspect welded joints for faults).

Gamma rays are emitted by radioactive substances. It is more dangerous than x-rays since they

carry more energy and are more penetrating. It is used in hospitals to kill cancer cells.


Sound is produced by vibrations; sound sources such as a tuning fork, a guitar, a flute and a

loudspeaker all have some parts which vibrate.

Sound cannot travel through a vacuum but it can travel through solids, liquids, and gases. It is

a wave because it demonstrate interference.

It is a longitudinal wave because the vibrations of air are along the direction of travel of sound.

Speed of sound in air is about 330 m s-1 at 0 C; but it increases as the temperature increases.

In a thunderstorm, lightning is seen before thunder is heard because the speed of light in air is

much higher than that of sound.

Note is sound produced by regular vibrations (e.g. a tuning fork or a musical instrument).

Noise is caused by irregular vibrations.

Pitch of a note depends on the frequency of sound. High frequencies give rise to high-pitch

notes.

Loudness of a note depends on the amplitude of sound wave. The intensity varies inversely

as the square of the distance.

Quality of a note depends on the number and amplitude of the overtones which accompany the

fundamental frequency, i.e. the waveform.

Men can only hear sound from about 20 Hz to 20 kHz (audio frequency range) and varies

from person to person and decreases with age. Sound waves with frequency above 20 kHz are

called ultrasonic waves.

Ultrasonic has many applications such as:

ultrasonic spectacles help a blind person to find his way around

ships use ultrasonic waves (sonar) to measure the depth of sea and to detect shoals of fish

ultrasonic waves are used to form

images of unborn babies

to clean small and delicate objects,

e.g. jewellery and watch

movements

Figure 3.21 Working principle of radar.

[Exam Technique] To find the distance

s between the radar station and the

aircraft, use the formula where v = 3 108 m s-1 and t = time interval between sending

signal and receiving signal.

[Exam Technique] Other examples involving reflection include:

To prevent the stealth bomber to be detected, the engine of the plane should be very

quiet. The plane is painted in black.

The reception of TV signal is affected when an aeroplane flies overhead because the

aeroplane reflects the TV waves. The waves traveling directly to the aerial interfere

with the signals reflected by the aeroplane. As a result, the reception is affected.


[Exam Technique] Other examples involving diffraction include:

Sound waves can bend around a corner but light cannot because the wavelength of sound

is comparable to the size of a corner but the wavelength of light is much smaller. So

the degree of diffraction of light around a corner is much smaller.

The radio reception is better than the TV reception in hills because the wavelength of the

radio waves is longer than that of the TV waves. The radio waves are diffracted

more by the hills, so the radio reception is better.

The smaller speaker cone is more suitable for emitting high-frequency sounds. If the

smaller cone is used, the sound wave of shorter wavelengths will bend around the

rim and diffract to the surroundings more significantly.

[Exam Technique] Other examples involving interference include:

To demonstrate interference, connect the two loudspeakers to the signal generator by

wires. The two loudspeakers should be placed about 1 m apart. Adjust the signal

generator to a suitable frequency, so that notes are emitted by the loudspeakers. (If

one walks slowly across in front of the loudspeakers, he/she should be able to hear

loud and soft sounds alternatively.) Move the microphone slowly across in front of

the loudspeakers. Alternative maxima and minima would be displayed in the CRO.

This demonstrates the interference of sound.

At point of destructive interference, the sound level is not equal to zero as there is

background noise.

Along the bisector PQ of the two loudspeaker,

there is always constructive interference.

Figure 3.22 shows the variation of the meter

reading along PQ.

Figure 3.22 Meter reading along

PQ.

[Exam Technique] There are many questions in

comparing radar and sonar.

Radar (microwave) is transverse while sonar (sound) is longitudinal.

Radar is traveling faster than sonar so the latter cannot be used to detect airplane.

Radar is absorbed by water so that it cannot be used to detect the depth of the sea bed, etc.


4.0 ELECTRICITY AND MAGNETISM

4.1 Electrostatics

Electric charges are of two types: positive (+) and negative (). Experiments show that like charges repel; unlike charges attract.

Methods of charging include:

by friction (for plastic materials)

by an EHT supply

by a Van de Graaff generator

by induction (charging process by induction does not involve any loss of charge from the

charged rod)

by charge sharing

Earthing - process of charge sharing with the earth.

An electric field is represented by a series of lines called field lines going from a positive

charge to a

negative

charge.

Figure 4.1 Electric field patterns

The charge on a conductor stays on the outside surface and tends to accumulate at sharp

points. Air molecules can be ionized by charges on a sharp point of a conductor. This produces

a stream of air called electric wind leaving the sharp point.

The lightning conductor helps to reduce the risk to the building in two ways:

Streams of positive ions flow out from the spikes, reducing the induced charge on the roof

and cancelling out some of the charge on the cloud.

The lightning conductor provides a route for electrons to pass into the ground if lightning

occurs.

Electric charges produced by friction can be troublesome or even hazardous. Precautions have


to be taken in transporting petrol in tankers; refuelling an aircraft; working in an operation

theatre, etc. This is done by providing a route for the charge built up to go to the ground.

Two important applications of electrostatics: electrostatic precipitation and photocopying.


4.2 Electric Circuits

Current is measured in ampere, written as A. (milliampere (1 mA = 10-3 A), microampere (1 A

= 10-6 A))

Current is the rate of charge flowing in a circuit. It is measured by an ammeter. In a simple

circuit, the current through every part is the same.

Free electrons in the conducting loop are driven by the battery to go round the circuit from the

terminal to the + terminal. They gain electrical energy from the battery and the energy is

changed into heat and light energy when they pass through the lamps.

Note that there is no energy change in the copper connecting wires.

Electromotive force (e.m.f.) of a battery gives the energy supplied to each coulomb of charge

within the battery (e.m.f. of a battery is 1 volt if each coulomb of charge is given 1 joule of

electrical energy).

Potential difference (p.d.) or voltage across each lamp in the circuit gives the electrical

energy which changes into other forms of energy when 1 coulomb of charge passes through the

lamp (p.d. across two points in a circuit is 1 volt if 1 joule of electrical energy is changed into

other forms of energy when 1 coulomb of charge passes between the points).

e.m.f. and p.d. are both measured in volts, written as V. E.m.f. of a battery is measured by a

voltmeter connected across its terminals; p.d. across the lamps is measured by connecting a

voltmeter across each lamp.

The p.d. across the ends of a conductor is directly

proportional to the current flowing through it,

provided that the temperature and other physical

conditions are unchanged (Ohm’s law).

Figure 4.2 Ohm’s law

The opposition of a conductor to current is called resistance. Resistance of a conductor is

defined as:

resistance p d across conductor

current through conductor

. . or R

V

I

Resistance is measured in ohms, written as .

A rheostat is a variable resistor which is used to control the current flowing in the circuit

and the voltage across the, e.g. bulb.


As the p.d. across the lamp increases, the brightness increases and so does the filament

temperature. The ratio V/I shows that the resistance of the filament increases as the temperature

rises. The resistance of most metals increases with temperature, though some increase more

than others.

Figure 4.3 p.d across a lamp

The resistance of a metal wire depends on its length and thickness. For the same wire, the

resistance R is directly proportional to its length l, i.e. R l. this means that doubling the length

doubles the resistance. For wire of the same length and material, the resistance R is inversely

proportional to its cross-sectional area A, i.e. R . This means that doubling the area halves the

resistance.

In a circuit, resistors may be connected in series, in parallel, or some other complicated ways.

Two resistors, R1 and R2 , are connected in series. If R is the equivalent resistance, R R R 1 2 .

The equivalent resistance is always higher than the resistance of any one of the resistors.

Two resistors, R1 and R2 , are connected in parallel. If R is the equivalent resistance,

1 1 1

1 2R R R . The equivalent resistance is always smaller than the resistance of any one of the

resistors.

Power is the rate at which energy is changed from one form to another.

and is measured in watts, written as W.

Power = p.d. current or P = VI.

For a resistor of resistance R, the power dissipated can be calculated as:

P VI I RV

R 2

2

If the power rating of an appliance is given, the electrical energy consumed can be calculated

as Energy = power time or E = Pt

The electrical energy supplied to your home is measured by a kilowatt-hour meter. One

kilowatt-hour is the energy supplied in 1 hour to an appliance whose power is 1 kilowatt. (1


kWh = 3.6 106 J)

[Exam Technique] Use the idea of potential divider to explain the change of brightness of light

bulbs in a circuit, and for calculation as well.

4.3 Electrical Power and Domestic Electricity

In Hong Kong the mains electricity is supplied at 220 V a.c. 50 Hz, in line with the world

standard.

Power stations supply a.c. because the power loss during transmission of electricity is

much smaller for a.c. than for the one-way direct current (d.c.).

The live wire goes alternatively + and . The neutral wire is connected to the earth at the local substation of the electric company.

Although current passes through the wire, its voltage is zero.

The switch is fitted in the live wire. This is to make sure that no part of the appliance and

the cable is ‘live’ when the switch is turned off.

The fuse is a short length of thin wire which overheats and melts when too much current

flows through it. If a fault develops, the fuse ‘blows’ and breaks the circuit before the

cable overheats and causes a fire.

The earth wire is a safety wire. It connects the metal body of the appliance to the earth and can

prevent electric shock in case of a fault.

Figure 4.4 A household wiring plan.

Please note the following:

Thick wires are used to connect the water heater to the mains supply because they have a

small resistance and hence the power loss is reduced.


The electric appliances are connected in parallel with the mains because this

arrangement would enable the appliances to operate at its rated value.

The water heater is not connected to the sockets in the ring circuit but directly connected

to the mains via a separate circuit because the water heater draws a large current from

the mains supply. If it is connected to sockets in the ring circuit together with other

appliances, overloading may happen.

Advantage of the ring circuit arrangement:

The current flows from the consumer unit to the sockets via two paths. Each path

carries half of the current. The chance of overloading is reduced.

If the ring circuit is broken at one point, the ring circuit can still function.

The holes in each socket correspond to the three wires (earth, live and neutral wires; live wire

– the bottom right-hand hole; neutral wire – the bottom left-hand hole; earth wire – the hole

at the top) of the circuit.

Figure 4.5 A three-pin plug and a socket.

For safety reasons, the earth pin is longer and thicker than the live and neutral pins. The

sockets are mechanically protected. The earth pin must enter the top hole before the other two

pins can enter the bottom holes.

Brown to live (L), blue to neutral (N),

yellow and green to earth (E)

Figure 4.6 Colour of different wires

The correct fuse for an appliance can be worked out from the mains voltage and the power

rating marked on the appliance. This should be slightly larger than the normal current.

[Exam Technique] Cost of electricity = cost power time. Change the power in kW in

calculation.


4.4 Electromagnetism

The two poles of a magnet - the north pole (N-pole) and the south pole (S-pole).

Like poles repel each other; unlike poles attract each other.

A magnetic field is the space around which magnetic forces act. It can be studied by using iron

filings. Sprinkle iron filings on a cardboard on a magnet and then tap the cardboard

gently. The pattern of the iron fillings represents the magnetic field pattern.

Field lines run from the N-pole round to the S-pole. Where they are closely spaced, the field

is strong. Where they are widely spaced, the field is weak.

Figure 4.7 Magnetic field patterns

A current can set up a weak magnetic field around it:

The field lines are circles around the wire.

The magnetic field is strongest close to the wire.

Increasing the current makes the magnetic field stronger.

Reversing the current changes the direction of field lines but the field pattern remains

unchanged.

Figure 4.8 Magnetic field due to a current

The direction of the field lines can be worked out from the direction of current using the right-

hand grip rule.

If the right hand grips the wire so that the thumb points the same way as the current, the fingers

curls the same way as the field lines.

Figure 4.9 Magnetic field of a solenoid

A current flows through a long coil called

a solenoid and this produces a magnetic

field similar to that of a bar magnet.


The poles can be worked out from the current through the solenoid using the right-hand grip

rule for solenoid.

If the right hand grips the solenoid so the fingers curls the same way as the current, the thumbs

points to the north pole of the solenoid.

The strength of an electromagnet can be increased by

Inserting a soft iron bar

Increasing the current

Increasing the number of turns per unit length

Relationship between the strength of an electromagnet and the number of turns of its coil can

be investigated as follows: Use the electromagnet to lift up one end of the chain of iron

clips. Count the number of clips that the electromagnet can hold just before the chain

falls. Repeat the above steps by varying the number of turns in the coil and recording the

corresponding changes in the number of clips that the electromagnet can hold just before

the chain falls. In every trial, keep the current constant.

Working principle of the earpiece of a telephone: When a varying current flows through the

coils of the electromagnet, a varying magnetic field is produced. The iron diaphragm

vibrates under the action of the varying magnetic field. The vibrating diaphragm causes

air molecules to vibrate and produces sound wave.

When the switch of the electric bell is pressed,

current flows through the coil. The soft-iron core

is magnetised and becomes a magnet. The iron

spring is then attracted towards the left with its

hammer striking the left metal plate and

produces a note. When the hammer strikes the

bell, the circuit is broken and no current flows

through the coil. The soft-iron core is

demagnetised. The iron spring swings to the back

and the circuit is completed. The above process is

repeated and a continuous sound is produced.

Figure 4.10 An electric bell

A force is produced whenever a current flows in a magnetic

field across it. The directions can be worked out using the

Fleming’s left-hand rule. Hold the thumb and the first two

fingers of the left hand at right angles. The thumb gives the

direction of the force (F) if the first finger points in the same

direction as the magnetic field (B) and the second finger in the

same direction as the current (I).

Figure 4.11 Fleming’s left-hand rule

The force is increased if


the current is increased

a stronger magnet is used

there is a greater length of wire in the magnetic field

Figure 4.12 A d.c. motor

When a current flows round a rectangular coil lies between the poles of a magnet, there is a

turning effect on the coil. An electric motor uses this magnetic turning effect on a coil.

The turning effect on the coil can be increased by

increasing the current

increasing the number of turns in the coil

increasing the strength of the magnetic field

Current flows through the coil via a pair of carbon brushes, which are pushed against a

commutator, or split-ring, by two small springs. The split-ring is fixed to the coil and rotates

with it.

The commutator reverses the connection of the coil with the outside circuit every time the

coil passes through the vertical. The current flowing in the coil is thus reversed in its

direction, and so do the forces acting on its sides. This makes the coil keep on rotating in

the same direction.

If there were no commutator, the coil turns, oscillates a few times about the vertical position

and then comes to a rest: When the switch is closed, a current flows through the coil. As the

coil is placed in a magnetic field, there are forces acting on the wires and the coil turns.

When the coil turns to the vertical position, the couple becomes zero. Due to inertia, the

coil shoots through the vertical position to the other side. The direction of the couple

acting on the coil reverses and the coil rotates back in the opposite direction. This process

repeats. The coil will finally stops in a position where the couple acting on it becomes zero.

In a moving-coil meter, the rotation of the coil

is opposed by a pair of hairsprings. The larger

the current, the greater is the deflection of the

pointer.

Figure 4.13 A moving-coil galvanometer.

When a current flows, a pair of forces are

produced and they are acting on the coil.

The coil then rotates. Pointer deflects until


the forces are balanced by the hairspring. The pointer stops steadily and its deflection

shows the value of the current.

The sensitivity of a moving-coil meter can be increased by

increasing the number of turns on the coil

increasing the strength of the magnetic field

increasing the area of the coil

using weaker hairsprings

4.5 Electromagnetic Induction

If a conductor and a magnet move relative to each other, an e.m.f. is induced in the conductor.

This causes an induced current to flow through the conductor.

The induced e.m.f. can be increased by

moving the conductor or the magnet faster

using a stronger magnet

increasing the length of the conductor

The e.m.f. induced in a conductor is directly proportional to the rate at which the conductor

cuts through the magnetic field lines (Faraday’s law of electromagnetic induction).

The direction of the induced current can be found using Fleming’s right-hand rule.

Figure 4.14 Fleming’s right-hand rule.

Lenz’s law: An induced current always flows to oppose the movement which started it.


Figure 4.15 Lenz’s law

When the magnet is pushed towards a solenoid, a current is induced and passes, e.g. from

X to Y, through the galvanometer. When the magnet is inside the solenoid, there will be no

current. When the magnet is moved away from the solenoid, a current is induced and

passes, e.g. from Y to X, through the galvanometer.

Figure 4.16 An a.c. generator

An a.c. generator (alternator) uses a pair of slip rings to pass the induced current in the

rotating coil to the outside circuit. The graph shows how the current varies during one complete

rotation of the coil. The current is greatest when the coil is horizontal - the coil cuts through the

field lines most rapidly.

Figure 4.17 A d.c. generator

An a.c. generator becomes a d.c. generator or dynamo if the slip rings are replaced by a split-

ring or commutator. The commutator reverses the connections of the coil to the outside

circuit every time the coil makes a half turn. A varying d.c. flows in the outside circuit.


The current generated can be increased by

using a stronger magnet

increasing the number of turns in the coil

winding the coil on a soft-iron core

rotating the coil at a higher speed

A moving-coil loudspeaker contains a short coil which is free to

move inside a cylindrical permanent magnet.

When someone speaks in front of the microphone

(loudspeaker), sound wave is produced which sets the

diaphragm as well as the coil into vibration. As the coil is

moving inward and outward, it cuts the magnetic field and

induces a current in the coil. The magnitude of the current

depends on the amplitude of the sound while the frequency of

the current depends on the rate of change of magnetic field

and thus the frequency of the sound. The induced current is

transmitted and amplified. Sound is generated in a moving-

coil loudspeaker.

Figure 4.18 A loudspeaker

A changing current in a coil can produce an induced e.m.f. in a nearby coil. This effect is

called mutual inductance.

When an a.c. passes through the primary coil of a transformer, electrical energy is continuously

changed or transformed from the primary coil to the secondary coil. As a result, an a.c. flows in

the secondary coil.

The a.c. induced in the secondary coil has the same frequency as the a.c. in the primary coil.

The ratio of the primary and secondary voltages in a transformer is equal to the turns ratio of

the transformer: V

V

N

Ns

p

s

p

=

A step-up transformer has more turns in the secondary than in the primary coil. It steps up the

voltage but steps down the current at the same time: I

I

N

Np

s

s

p

=

A step-down transformer steps down the voltage but steps up the current.

Power losses in practical transformers are due to 3 factors

the resistance of the coils

the magnetisation and demagnetisation of the core

eddy currents in the core

Power generated at the power station is stepped up to an extra high voltage for transmission

over great distances. It is stepped down to the supply voltage when it reaches the consumer.

An a.c. voltage is used because it can be stepped up or down easily by transformers


without much loss of power. Thus, the efficiency can be improved.

Stepping up the voltage can reduce the current passing through the cables for a fixed

power output. Since power loss in the wire is equal to , the decrease in I will result in a

reduction of power loss in the wires.

[Exam Technique] The above two points are the advantages of using a.c. and high voltage for

long distance power transmission.

[Exam Technique] There are three equations for power. P = IV is used in calculating input

power. If you are asked to calculated power dissipation, use P = I2R. If you are asked to

calculated the resistance of an electrical appliance with rated voltage and power, use P = V2/R.

[Exam Technique] Sequence of discussing how an induced current is produced: “motion changing magnetic field induced current produced by Lenz’s law direction of current

flow, etc.” The following are two examples:

When S is closed, a magnetic field will be built up in the solenoid. There will be an

induced current flowing in the aluminium ring. By Lenz’s law, the induced current

flows in a direction such that it produces an effect to oppose the change. So the end

of the ring near the solenoid becomes a south pole. The aluminium ring will move

away from the solenoid under the action of the repulsive force acting on it by the

solenoid.

When a person is riding a bicycle, the permanent magnet is made to spin. The coil wound

around soft iron C-core cuts through the magnetic field lines and hence a voltage is

induced in the coil. (Note: the output voltage of the dynamo can be increased by (1)

increasing the number of turns of the coil; (2) using a stronger magnet; (3) riding the

bicycle at a higher speed.)

Figure 4.19 Aluminium ring move away from solenoid Figure 4.20 Dynamo

Electric toothbrush is made use of mutual inductance: In an electric toothbrush, an alternating

current flows through the coil (e.g. coil Y) when the charging unit is connected to the

mains supply. A changing magnetic field is set up in the coil (coil Y) and hence in the

secondary coil (e.g. coil X). An induced e.m.f. is set set in the secondary coil to recharge

the cell.


The function of the soft-iron bar:

To increase the strength of the magnetic field in the coils

To increase the induced e.m.f. (induced current) formed in coil X

To increase the efficiency of recharging the cell


5.0 RADIOACTIVITY

5.1 Radiation and Radioactivity

Radiation comes from the nucleus of the atom. Hence it is often referred to as nuclear

radiation.

Nuclear radiation can be detected by photographic film, cloud chamber, spark counter or

Geiger-Muller tube (or GM counter).

There are 3 types of nuclear radiation:

alpha () particles - nuclei of the helium atom

beta () particles - fast-moving electrons

gamma () rays - electromagnetic waves of very short wavelength, similar to X-rays

Their properties are summarized in the table below:

alpha particles beta particles gamma rays

Nature helium nuclei fast-moving electrons Electromagnetic waves

similar to X-rays

Charge +2 1 no charge

Speed up to 1/10 speed of light up to 9/10 speed of light speed of light

ionizing ability Strong weak very weak

Penetrating power not penetrating: stopped

by a sheet of paper

penetrating: stopped by

5 mm of aluminium

highly penetrating never

fully absorbed: strength

reduced to half by 25

mm of lead

effect of fields very small deflection large deflection no deflection

Detectors photographic film

cloud chamber

spark counter

thin window GM tube

photographic film

cloud chamber

GM tube

Photographic film

cloud chamber

GM tube

Figure 5.1 Deflection of nuclear radiation in an electric

field.

Figure 5.2 Deflection of nuclear radiation in a magnetic

field.


The 3 types of nuclear radiation can be identified from their differences in ionizing ability,

penetrating power and behaviours in magnetic fields.

In the cloud chamber, the tracks of particles are straight, short and thick. The angle of

the fork track is 90, indicating that the mass of an particle and that of a helium

molecule are the same.

In experiment with a radioactive source, it is also placed in a lead box with a narrow slit

because it can ensure that all radiation will travel in the same direction and thus a fine

beam of radiation will be produced. Moreover, the experiment with particles is also

performed in a vacuum because. particles have short range in air and they will not collide

with air molecules.

The hazard of exposure to ionizing radiations include

It can destroy or damage living cells.

It can lead to cancer.

It can lead to incurable radiation illness.

It can change the DNA structure.

In the room of therapy, the rooms have metallic shielding in the doors and reinforced walls.

They can prevent radiation from leaking out of the rooms.

We are all exposed to a small amount of background radiation. This comes from cosmic rays

and radioactive materials present in rocks, soil, building material and the air, water and food

that we taken into our body.

5.2 Atomic Structure and Nuclear Energy

Rutherford’s scattering experiment showed that most of an atom is empty space and that all the

positive charge and most of the mass of the atom are concentrated in a tiny nucleus.

Rutherford-Bohr model of the atom:

The nucleus is made up of protons and neutrons. These are bound together by a strong

nuclear force.

Electrons and protons carry equal but opposite charges. In a neutral atom, the number of

electrons is the same as the number of protons.

Electrons orbit the nucleus at certain fixed levels called shells.

The number of protons in the nucleus of an atom is called its proton number or atomic

number. The atomic number also gives the number of electrons in the atom.

The total number of protons and neutrons in the nucleus is called its nucleon number or mass

number.

An element with a particular mass number and atomic number is called a nuclide.

Nuclides with the same atomic number but different mass number are called isotopes. Isotopes

which are radioactive are called radioisotopes.


Radioactive decay or disintegration is due to unstable nuclei which break up, emitting alpha or

beta particles or gamma rays in the process.

When a nucleus decays, it changes into a nucleus of another element. The nucleus which decay

is called the parent nucleus and that which results is the daughter nucleus. The daughter

nucleus together with any particles emitted are called decay products.

Alpha decay can be represented by: ZA

ZAX Y He

24

24 , where X is the parent nucleus and Y

the daughter nucleus. The mass number of the daughter nucleus decreases by 4 and the

atomic number decreases by 2.

Beta decay can be represented by: ZA

ZAX Y e 1 1

0 . The mass number of the daughter

nucleus remains unchanged and the atomic number increases by 1.

Gamma emission does not change either the atomic number or the mass number.

Figure 5.3 Graphs of nucleon number against proton number for alpha and beta decays

Radioactive decay is a random process.

The half-life of a radioactive source is the time

taken for the activity of the source to fall to

half of its initial value. It is also the time taken

for half of the nuclei present in any sample to

decay.

A corrected count rate is equal to the recorded

count rate minus the count rate due to

background radiation.

Figure 5.4 A decay curve

If the number of undecayed nuclei is plotted against time, a decay curve is obtained. Note that

the total number of nuclei (parent and daughter) in the sample remains the same all the time.

Artificial radioisotopes can be produced by bombarding stable nuclei with atomic particles.

They have many applications in medicine, industry and agriculture. They are used in

radiotherapy, as tracers, for sterilization of medical equipment, as thickness gauge, flaw

detection, testing of mechanical wear, food preservation, electrostatic precipitation, in lightning

conductor, in smoke detector and carbon dating.

Inside a smoke detector, the particles emitted by the source will ionize the air molecules

to produce ions. The ions are attracted to the electrode with an opposite charge. A current


flows between the electrodes. When smoke particles enter the detector, the smoke particles

block the movement of the charged particles. As a result, fewer ions reach the electrodes,

so the current drops.

radiation should not be used as a medical tracers because

radiation fails to pass through human tissue.

radiation has a low penetrating power.

radiation is more effective in killing cancer cells because the ionizing power of radiation is higher than that of radiation.

When an uranium-235 nucleus is bombarded by neutrons, it splits into two smaller nuclei and

releases a huge amount of energy. The process is called nuclear fission.

When an uranium nucleus splits, two neutrons are emitted. These neutrons can carry on

splitting other uranium nuclei resulting in a chain reaction. If the uranium is above a certain

critical mass, this chain reaction takes place very quickly.

Nuclear fission, if occurring in a controlled way in a nuclear reactor, can be used to generate

electricity. Uncontrolled nuclear fission results in an atom bomb.

When two light nuclei join together to form a large nuclei, a huge amount of energy is also

released. This process is called nuclear fusion.

Nuclear energy has many advantages:

Nuclear energy helps to solve the world’s future energy shortage crisis.

Unlike coal- or oil-fired power stations, there is no fuel transportation problem.

Nuclear energy is in many cases cheaper than coal or oil for generating electricity.

Nuclear energy is clean and causes little environmental pollution. On the other hand,

coal- and oil-fired power stations emit large quantities of fly-ash.

Anti-nuclear groups argue against the development of nuclear energy:

Nuclear energy constitutes an unacceptable hazard to the public. The chance of an

accident happening is very small, but the consequence is extremely serious.

Nuclear energy will not be cheap if large sums of money have to spend on maintaining

and upgrading the safety standards of the reactor.

Nuclear energy is not necessary. Future energy needs can be met by using alternative

energy sources and by conservation.

Any country which operates a nuclear reactor can produce nuclear weapons. The wide

spread use of nuclear energy will lead to the growth of nuclear weapons.

[Exam Technique] In choosing a certain radioactive source for a specific use, two areas have to

be considered – its penetrating power and its half-life. The following are some examples.

To choose a source to detect the leak from underground oil-pipe, a source is suitable

because its penetrating power is highest and is also strong enough to reach the

ground from the leaks underground. The half-life should not be long because it may


cause less or no harm to the environment as its activity will disappear rapidly.

It is the same case applied to the tracer in a human body. The half-live of the source

should be short so that the radioactive material will not remain in the body for a

long time and thus will cause no harm to the patient. On the other hand, however, it

should allow sufficient time for the doctor to check the patient.

In a thickness gauge, α and γ sources are not used because source is not used because

the penetrating power of particles is too low. source is not used because the

penetration power of radiation is too high.

Technetium-99m is more preferable than iodine-131 for use in the test. Firstly,

technetium-99m has a shorter half-life. Secondary, technetium-99m does not emit

beta particles. So it is less harmful to the patient.

[Exam Technique] Other wordings used for a radioactive source of long half life:

The activity of the radioactive source decay very slowly.

Will remain stable for a longer period of time.

The detector can be used for a longer period of time.

The source inside the detector needs not be replaced frequently.

[Exam Technique] If the source is placed far away from the GM counter, the count rate is not

due to particles, no matter what kinds of radiation are emitted by the source because the

range of particles in air is only a few centimeters.

[Exam Technique] A method for determining whether α particles are emitted by the source:

Place the GM tube close in front of the source. Insert a piece of paper in between and

check whether the count rate decreases.

[Exam Technique] In an experiment to investigate the kind of radiation emitted by a

radioactive source, a GM counter is placed close in front of the source and sheets of different

absorbers are placed in turn between the source and the counter. Here is an example to explain

the results which show that the source emits β radiation only and it does not emit α and γ

radiation:

radiation is stopped by a piece of paper. As the count rates remain unchanged

when a sheet of paper is inserted, this shows that source does not emit radiation.

radiation is partially absorbed by 1 mm aluminium. As the count rates drop

significantly when 1 mm aluminium sheet is inserted, this shows that the source

emits radiation.

radiation cannot be absorbed completely by 5 mm lead. As the count rates drop to

background radiation when 5 mm lead is inserted, this shows that the source does

not emit radiation.

Since the source does not emit and radiation, it must emit radiation only.

[Exam Technique] In counting half life, “arrows” can be used. For example, polonium-210 has

a half-life of 140 days. How long will it take for 100 g of polonium-210 to reduce to 12.5 g?


100 g 50 g 25 g 12.5 g. There are 3 half lives. So the time required = 140 3 = 420

days.

07-08 S5 Physics Revision Notes

Documents

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heat capacity c

transfer of heat

heat loss

proportion of heat

heat flow

substance energy

kinetic energy