Final Qualitative List

7/27/2019 Final Qualitative List

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www.studyguide.pk Physics Solved Past Paper Questions

Measurements

When using a digital voltmeter and digital ammeter to determine the resistance of a wire, state one

possible random error which could occur in the use of the digital meters. How could this error be kept to a minimum? Explain why the voltmeter must have a resistance much greater than that of the wire,

which resistance it is trying to measure, in order to avoid a systematic error in the use of the

voltmeter. [5] N95/III/I

Quantization error (rounding-off error), where the reading is rounded up or down.

Hence a reading of 2.3 could actually be anything between 2.25 to 2.35.

Quantization errors, like all random errors, can be minimized by taking several readings of V and I and

finding the average, or by plotting a graph of V versus I and drawing a best fit line to even out under

and over estimations.

Additionally, using higher voltages and currents, and digital meters with greater precision and moredecimal places will also reduce the random error.

The voltmeter has to have a much greater resistance than that of the wire so that it will draw minimal

current away from the wire when connected across it.

This is to minimize the systematic error arising from the reduction in potential difference across the

wire when the voltmeter is connected.

Kinematics

A ball is thrown vertically upwards. Explain how air resistance would affect the time taken for the ball

to reach its maximum height, and the maximum height to which it rises. J81/I/13

The time will be shorter. Air resistance increases the downward resultant force and hence the

deceleration experienced by the ball, thus bringing to rest sooner. (Newton’s 2nd

Law of Motion)

Without air resistance, v=u-gt hence t=(u-v)/g = u/g since v=0. But with air resistance, t=u/(g+a),

where a is the additional non-constant deceleration due to air resistance.

The maximum height will be lower. Air resistance increases the downward resultant force and hence

the deceleration experienced by the ball, thus bringing it to rest within a shorter distance. (Newton’s

2nd Law of Motion). Without air resistance, v²=u²-2gs hence s=(u²-v²)/2g = u²/2g. But with airresistance, s=u²/2(g+a) where a is the additional non-constant deceleration due to air resistance.

When a train leaves a station, it accelerates from rest along a straight track. Explain why, in practice,

trains do not have a constant acceleration even though their engine power remains constant. [3]

N90/III/I

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In practice, air resistance increase with speed. (F=kv²) The resultant force acting on the train, which is

equal to the forward engine force subtract the air resistance, thus decreases with increasing speed.

Since acceleration is proportional to the resultant force according to Newton’s 2nd

Law of Motion, the

acceleration decreases with increasing speed.






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When a driver sees the traffic light turn red, he steps on the brake so that the car will come to a stop.

The total stopping distance = thinking distance + braking distance. Explain why thinking distance is

proportional to speed whereas braking distance is not. Describe in words the relationship between

braking distance and speed. [7] J89/II/9

During the thinking phase, the brake has not been depressed hence there is no deceleration. Hence

the speed is constant during this phase. Since distance traveled is equal to the product of the car’s

speed and the reaction time ie. s=ut, the thinking distance is proportional to speed. The constant of

proportionality is the reaction time t.

During the braking phase, the brake exerts a retarding force on the car hence there is deceleration.

The speed decreases non-linearly with distance hence braking distance cannot be proportional to

speed. Using the equation v²=u²-2as s=u²/2a. The braking distance is thus proportional to the

square of the initial speed.

An archer tries to hit a target pointing his arrow at an angle to the horizontal. Neglecting air

resistance, the angle calculated is 32 degrees. Suggest with a reason whether the angle would in

practice be larger or smaller than that calculated for the arrow to hit the target. [3] N2000/II/2

Larger. In practice, there is air resistance hence the arrow will fall short of the target. In order to reach

the target, it thus has to aim to hit further than the target. The range of the arrow is R=u²sin2θ/g. The

maximum range occurs when 2θ=1 ie. 2θ=90˚ or θ=45˚. The closer the angle is to 45˚, the larger the

range. Hence if an angle is larger than 45˚, it should be decreased in order to increase the range. On

the other hand, if an angle is smaller than 45˚, it should be increased. In this case 32˚ is less than the

optimal angle of 45˚, hence the angle should be increased.

Describe qualitatively the motion of bodies falling in a uniform gravitational field with air resistance.

A falling object has 2 forces acting on it. Its weight acts vertically downwards. Drag force due to air

resistance acts vertically upwards. Drag force increases with velocity of the object. When the drag

force is equal to the weight of the object, the object is said to achieve terminal velocity.

In the study of kinematics, we normally adopt a coordinate system as a frame of reference. Explain

why this is necessary. [1] IJC Prelims 08/II/1

It helps us define the starting point for measuring any quantity.

Explain why it is technically incorrect to define speed as distance traveled per second. Include in your

answer the correct statement defining speed. [2] N04/III/1






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The second is not the only unit of time measurement, nor is it the smallest division of time interval.

“Distance traveled per second” is the average speed within a time interval of one second. Speed

should be defined as the rate of change of distance traveled.

State the conditions necessary for the kinematics equations to be applicable. [2] N98/III/1

Constant acceleration and linear motion.

How do you reduce air resistance?

By bending the body forward into a more streamlined shape, the initial horizontal velocity at whichthe body is projected at is increased, increasing the horizontal distance moved.

Dynamics

A ship is moving towards the dock is decelerated by its engine. Explain qualitatively how the law of

conservation of momentum applies to this example. [4] N88/II/8

Considering the ship and water to be one system, the decelerating force is an internal force. Since

there is no net external force acting on the system, the total momentum of the system is conserved.The momentum lost by the ship is transferred to the water.

Describe the circumstances under which a body is said to be weightless. J79/I/1

A body is weightless when its acceleration is equal in magnitude and direction to the gravitational

field strength at its location. Under such circumstances, the reaction force between the body and the

floor will be zero.

Case 1: Body in a lift under free fall near the Earths’ surface. The body’s acceleration is g, the

gravitational field strength is g. Since a=g, the body is weightless.

Case 2: Body in space station orbiting the Earth. The body’s acceleration is equal to the gravitational

field strength at its location. Since a=g, the body is weightless.

Case 3: Body which is stationary or moving at constant speed deep in outer space. The body’s

acceleration is zero, the gravitational field strength at its location is also zero. Since a=g=0, the body is

weightless.






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Some makes of cars have, as a safety feature, regions at the front and rear which are designed to

collapse on impact. Give a brief physical explanation of how this design may help to protect

passengers from serious injury in the event of a collision. N85/II/2

In the event of a collision, the initial momentum and final momentum of the car is predetermined by

the speed at which it was traveling. However, by collapsing upon impact, the safety regions increase

the time for this momentum to change. This reduces the rate of change of momentum of the car and

its passengers. Since the resultant force acting on the passengers is proportional to their rate of

change of momentum (Newton’s 2nd

Law of Motion), the resultant force acting on them is less and

they are protected from serious injury.






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A prototype space gun used to launch satellites accelerates the satellite at 2.67x104m/s². Suggest why

it would be impossible to use this space gun for manned space flights and why it would be

advantageous to site the gun on the equator pointing eastwards. [4] N90/III/1

The human body is not able to withstand such a high acceleration. Human pilots can withstand an

acceleration up to a maximum of 9g without blacking out. An acceleration of 2.67x104m/s² will

represent a force 2800 times a person’s weight, which will not only cause a black out but also crush

the astronaut in the satellite, if it were manned.

The Earth rotates about its own axis from west to east. The space gun can make use of this initial

eastward momentum of the satellite on Earth to fling the satellite into space, thus reducing the

amount of fuel or explosives needed to launch it into orbit. As locations at the equator have the

largest radius of orbit, objects located at the equator move with the greatest speed and kinetic energy

compared to those located at other latitudes. Hence the total change in kinetic energy of the satellitebetween the Earth’s surface and in orbit will also be the lowest.

Describe the concept of weight as the effect of a gravitational field on a mass.

An object which placed in a gravitational field would experience a gravitational force. The magnitude

of the gravitational force experienced is the weight of the object. Weight = mass x acceleration due to

gravity.

In physics we know that every force is an interaction between two objects. Thus, forces always come in

pairs and they all obey Newton’s 3rd

law. Also during the interaction, the principle of conservation of

momentum is observed. In the following examples, describe briefly how the law and the principle are

observed. a) A tennis ball is released from rest, falls vertically to the floor and bounces back again. b)

An alpha-particle travels from a great distance directly towards a gold nucleus, which can be assumed

to be stationary. The alpha-particle returns along the same path without penetrating the nucleus. [8]

AJC Prelims 08/III/4

a) By Newton’s law of gravitation, the tennis ball exerts a gravitational attractive force acting upward

on the floor, so the floor exerts an equal and opposite force acting downward on the ball. At the point

of impact, the ball exerts an electromagnetic repulsive force on the floor downward, and the floor

exerts and equal and opposite force upward on the ball.

When the ball is released from rest, the total momentum of the ball and the earth is zero. When the

ball is falling down, it gains momentum. The floor is gaining momentum upward so that the total

momentum of the system is zero and conserved. The upward momentum of the floor is not observed

due to the large mass of the earth and its small velocity. At the point of impact where both have zero

velocity, the total momentum is zero and conserved. Immediately after the collision, the ball moves

upwards with maximum momentum in the upward direction. The floor will move downwards with

momentum so that the total momentum of the system is zero and conserved. The downward






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momentum of the floor again is not felt due to the large mass of the earth and its velocity is so small

that it is not observed. When the ball is moving up, it loses momentum upward. The floor is also

losing momentum downward so that the total momentum of the system is zero and conserved.

b) There is an electric repulsive force acting on the alpha-particle by the gold nucleus and an equal

and opposite repulsive force acting on the gold nucleus by the alpha-particle. At the point of closest

approach, the alpha-particle exerts the strongest repulsive electric force on the gold nucleus. The gold

nucleus also exerts an equal but opposite strong repulsive electric force on the alpha-particle.

At the great distance, the momentum of the alpha-particle is towards the gold nucleus and the gold

nucleus has zero momentum. When the alpha-particle slows down as it approaches the gold nucleus,

its loss of momentum is transferred to the gold nucleus. The gold nucleus will have velocity, hence itsmomentum is in the same direction so that the total momentum of the system is conserved.

Immediately after the impact, the alpha-particle moves in the opposite direction with small speed. Its

momentum is in the opposite direction. The gold nucleus will continue to move with greater

momentum in the other direction so that the total momentum of the system is conserved. When the

alpha-particle speeds up in the opposite direction, its momentum will increase in the opposite

direction. The gold nucleus will speed up in the other direction and its momentum will increase in the

other direction so that the total momentum of the system will remain conserved.

When a neutron hits a stationary carbon atom elastically head on, it loses 0.284 of its kinetic energy

and retains only 0.716 of its kinetic energy. Discuss qualitatively the effect on the kinetic energy lost if the collision is not restricted to head-on collisions only. Explain why very light particles such as

electrons and massive particles such as uranium nuclei are unsuitable for slowing down neutrons. [10]

N89/II/12

If the collision is glancing and not-head on, the kinetic energy lost by the neutron will be less than

0.284. This is because only the component of the neutron’s momentum acting along the radial

direction of the stationary carbon atom will be involved in the energy transfer. The tangential

momentum, on the other hand, will be totally retained with the neutron. Hence the kinetic energy

transferred from the neutron to the stationary carbon will be less. In order to slow down neutrons,

neutrons have to transfer their kinetic energy to the stationary nuclei. The closer the mass of the two

colliding bodies, the greater the amount of kinetic energy transferred. In the case where the massesare equal, as in the case of a neutron colliding with a proton, 100% of the neutron’s kinetic energy will

be transferred and the neutron will stop. Electrons and uranium, on the other hand, have masses

much different from that of the neutron. The mass of the electron is too small while that of the

uranium nucleus is too large. Therefore, only a small fraction of the neutron’s kinetic energy is

transferred to these nuclei.






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State the relationship between the change in linear momentum of an object, the constant force acting

on the object, and the time for which the force acts. [1] N04/III/2

The change in linear momentum p of an object is equal to the product of the constant force acting

on it and the time for which the force acts.

Suggest with a reason why the momentum equations would not necessarily apply if the particles

concerned were traveling at speeds close to the speed of light. [1] N01/III/1

At such speeds, relativistic mechanics replaces Newtonian mechanics in predicting the behaviour of

collisions.

In an elastic collision, the two bodies become temporarily compressed and remain in contact for a

short time. Explain why both bodies have the same velocity at the time of maximum compression and

why their total kinetic energy at this time is different from the sum of their individual kinetic energiesafter they have completely separated. J87/II/9

At the point of maximum compression, the two bodies are stuck together and moving as one, hence

they must have the same velocity. Some of the kinetic energy is stored as elastic potential energy in

the compressed bodies. However, when the bodies separate, they regain their original shape and the

elastic potential energy is converted back into kinetic energy. No kinetic energy is lost since the

collision is elastic. This is unlike a perfectly inelastic collision, whereby when the two bodies are stuck

together and moving as one, kinetic energy is lost permanently as heat and sound energy, and cannot

be recovered.

In order to reduce the number of road traffic accidents, many countries conduct research into

improving road safety. a) One area of research concerns braking. State three factors that affect

braking which might be considered by researchers. b) State one other aspect of car safety that could

be researched, and suggest briefly how the research could be conducted. [5] N04/III/2

a) Frictional force between the tire and the road. Skidding due to the tires locking in abrupt braking

situations. Speed of braking action.

b) Shock absorption in the event of collision. Research can be conducted into the efficacy of the

crumple zone at the front and back of the car. The material used should be stiff enough so that the

car does not break apart, yet not so stiff as to result in an extremely large force of impact. Forcesensors placed on dummy drivers can be used to measure the force of injury in simulated collisions.

Forces






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A tennis racket hits a ball. Suggest why in practice it is impossible for a constant force to be applied to

the ball. [2] J97/III/1

As the tennis racket hits the ball, the racket strings undergo extension. The force exerted by the stringincreases as the string elongates, according to Hooke’s Law. Therefore, it is impossible for a constant

force to be applied.

Explain why, when ice floating in a jug of water melts, there is no change in the level of the water. [2]

N02/III/10

Since the ice floats, in accordance with the principle of floatation, the weight of ice is exactly equal to

the weight of the water it displaces. Therefore, the mass of the ice is equal to the mass of water it

displaces. Thus when the ice melts, it will produce the same volume of water as the water it displaces.

The water formed by the melted ice will exactly replace the water displaced by the ice. Thereforethere is no change in the level of the water.






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A mass is added to a vertical spring. The string extends according to Hooke’s Law. However, the

energy stored in the spring is only half of the loss in gravitational potential energy of the mass. With

reference to the law of conservation of energy, explain this observation. N86/II/13

When the spring first extends to its final equilibrium position, the loss in the mass’s gravitational

potential energy is equal to the sum of the spring’s elastic potential energy and the mass’s kinetic

energy. However, this kinetic energy is later lost due to damping factors such as air resistance. Thus,

when the spring settles in its final equilibrium position, it is stationary. The mass has lost all its kinetic

energy, and is left with only the spring’s elastic potential energy.

A thin plastic bag is found to have weight W when empty and pressed flat. When the bag is filled with

air at atmospheric pressure and re-weighed, the weight is again found to be exactly W. Explain why

the two results are the same. N83/I/2

When the plastic bag is inflated, it displaces a volume of air equal to its own volume. According to

Archimedes’ Principle, the bag will experience an upthrust equal in magnitude to the weight of the air

that it has displaced. Since this volume of air is exactly equal to the volume of air which filled up the

bag, the upthrust is exactly the same as the weight of the air injected into the bag. The two additional

forces, being equal and opposite, cancels out each other hence the bag weighs exactly W.

Suggest some similarities and differences between frictional forces and drag forces. J79/I/14

Similarities: Both forces are resistive forces which oppose motion.

Both forces result in heat dissipation.

Both forces increase with roughness of body’s surface texture.

Differences: Friction is independent of speed whereas drag force increases with speed.

Friction increases with body weight whereas drag force is independent of body weight.

Friction is independent of surrounding fluid medium but drag force increases with

density of surrounding fluid medium.

Friction is independent of surface area of the body, but viscous drag force increases

with surface area.

For the car, motion is impossible without friction. Discuss what is meant by friction and the direction in

which it acts on the car. In your answer, suggest another example where friction is useful. [5] N06/III/1

Friction is a type of force that exists between contact surfaces, and which resists relative motion

between the two surfaces or the tendency to such motion. In the case of the car, the frictional force

acts in the forward direction of the car. There is friction at the contact point between the tires and the

road. As the wheels rotate clockwise, the tires exert a leftward frictional force on the road surface. By

Newton’s third law of motion, the road surface will exert an equal but opposite rightward frictional

force on each of the rotating tires. This rightward force is the forward force which accelerates the car.






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Friction is also useful in braking. When the brakes are stepped on, there is a tendency for the wheels

to stop rotating and rub against the road surface. In this instance, the frictional force acts in the

opposite direction to the car’s motion. This produces a deceleration which brings the car to rest.






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A cyclist traveling at a constant speed of 15m/s exerts a power of 240W. Explain why a cyclist

traveling at a higher constant speed needs to exert a greater power. [4] It is often stated that many

forms of transport transforms chemical energy to kinetic energy. Explain why this cyclist is not making

this transformation, and explain what transformations of energy are taking. [5] N99/III/1

Resistive forces opposing the cyclist comprise friction (which is independent of speed), and air

resistance (which increases with speed according to F=kv², where k is a constant). Since acceleration is

zero, resultant force is also zero. Hence driving force is equal but opposite to resistive force. The

power exerted is given by the formula P=Fv where F is the driving force and v his speed. At the same

time, this force is exerted over a greater distance per unit time. Both increases in F and v result in an

increase in the power.

Kinetic energy = 0.5mv². When speed is constant, kinetic energy remains constant hence there is no

transformation of chemical to kinetic energy. Chemical energy (in the form of metabolic activity of thecyclist) is used to do work against resistive forces such as friction and air resistance, and dissipated as

heat and sound energy. The heat transfer raises the internal energy of the bicycle, the ground and the

surrounding air.

State the origin of upthrust.

Upthrust on a body is caused by the pressure difference between its upper and lower surfaces.

Describe a situation in which motion is produced without friction being required. [2] N06/III/1

Rockets in space which eject gas to accelerate themselves produce motion without friction being

required. The principles of their motion are the law of conservation of momentum and Newton’s third

law of motion – the backward thrust on the gas produces an equal and opposite thrust on the rocket.

Work, Energy and Power

Distinguish between gravitational potential energy, elastic potential energy and electric potential

energy.

Gravitational potential energy arises from interaction between masses, whereby forces involved arealways attractive in nature. Elastic potential energy arises from interaction between charges, whereby

forces involved can be either attractive or repulsive. Elastic potential energy arises from deformation

of a material whereby forces involved serve to stretch or compress the material.






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Discuss the energy changes which take place in the following systems. a) A mass suspended from a

spring and oscillating vertically. b) A nucleus undergoing radioactive decay. [8] N07/III/4

a) When the mass is at the top of its oscillation, it has maximum gravitational potential energy. As themass accelerates downward towards its equilibrium position, it loses GPE, gains EPE and gains KE.

Loss in GPE = Gain in KE + PE. As the mass passes its equilibrium position, it has lost half its total GPE.

Of this GPE lost, half is converted into KE and the other half stored as EPE. After the equilibrium

position, the tension in the spring decelerates the mass. The mass slows down and loses KE, continues

to lose GPE, but gains EPE. Gain in EPE = Loss in GPE + KE. Finally at the lowermost position, its GPE=0.

Its entire GPE lost is converted into EPE. In the case where resistive forces are present, the oscillating

system will experience damping and progressively lose total energy due to work done against these

resistive forces. This energy will be dissipated as heat, which then raises the internal energy of the

spring and the surrounding.

b) An unstable nucleus can undergo radioactive decay to emit an alpha particle, beta particle or

gamma radiation. In alpha and beta decay, the stationary radioactive nucleus disintegrates into two

parts: a daughter nucleus and either an alpha or beta particle. The products have a total rest-mass

energy lower than that of the radioactive nucleus. The lost mass Δm is converted into energy

according to Einstein’s mass-energy equivalence equation E=Δmc² where c is the speed of light in free

space. As mass is lost, binding energy increases hence the products have a higher binding energy and

are more stable than the radioactive nucleus. Most of this energy is released as the kinetic energy of

the products, with the remainder as electromagnetic radiation mainly in the form of gamma

radiation. The gamma radiation comes from the de-excitation of the daughter nucleus formed in

alpha or beta decay. The daughter nucleus, which is in an excited state, de-excites and falls to a lower

energy state. The energy difference is emitted as gamma radiation. The energy of the gamma ray

photon emitted is equal to the difference in the quantised energy levels within the nucleus, which are

considerably larger than those of the orbital electrons.

Circular Motion

Use Newton’s laws of motion to explain why a body moving with a uniform speed in a circle must

experience a force towards the center of the circle. J78/I/14

When a body moves in a circle, even though the speed remains uniform, its velocity is continuouslychanging due to the changing direction. Newton’s first law of motion states that a body will continue

in its state of rest or uniform motion in a straight line, unless acted upon by an external net force. An

external net force is thus required to change the direction of its motion. The direction of change is

always towards the center of the circle. Newton’s second law of motion states that the net force

produces an acceleration in the same direction. Since the acceleration is towards the center of the






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circle, the force must also be towards the center of the circle. They are known as the centripetal

acceleration and centripetal force, respectively.

“An aeroplane circling the Earth above its equator is said to orbit the Earth.” Discuss the validity of his

statement. [2] YJC Prelims 08/III/6

It is not valid. To be in orbit, the acceleration of the aeroplane must be equal to the gravitational field

strength. The aeroplane would be falling freely but here, it has a thrust force due to its engine.

A table fan’s blades broke and you glued them back. Use Newton’s laws to explain why the blades

might break off again at high angular velocities. [4] N89/II/9

Newton’s first law of motion states that a body will remain in its state of rest or uniform motion in a

straight line, unless acted upon by an external net force. When the blades undergo circular motion,

their direction is continuously changing. To change the direction of their velocity, a net external force

has to be applied. This is the centripetal force, which is provided by the holding force of the glue

between the blade and the axle of the fan. Centripetal force increases with angular velocity. At high

angular velocities, the centripetal force required exceeds the holding force of the glue. The blade thus

breaks and flies off tangential to its circular motion, in a straight line uniform motion according to

Newton’s first law of motion.

Using energy considerations, suggest why it is difficult to drive a fairground ride to whirl people on a

platform in circular motion at a constant speed. [4] N02/III/2

As the panel rises and falls, it gains and loses gravitational potential energy respectively. There is a

tendency for the platform to lose kinetic energy and slow down on the way up, and gain kinetic

energy and speed up on its way down. To avoid this, the motor’s power output has to be increased on

its way up and reduced on its way down. To complicate matters, the rate of gain or loss in

gravitational potential energy is not uniform throughout the motion, varying from zero when the

arms are vertical, to maximum when they are horizontal. To maintain a constant speed would require

very precise control of motor power output using computerized controllers.

Forces acting on bodies which travel in a circle are responsible for the following. Suggest an

explanation for each. a) A string may snap if it is attached to an object and the object is spun around a

vertical pole. b) The rings of Saturn are centered on the center of the planet. [4] N06/III/3

a) As the string wraps round the pole, the radius of the circular orbit becomes progressively smaller.

Assuming no loss in kinetic energy of the object due to air resistance, its speed will remain constant.

The tension in the string, which provides the centripetal force for the object’s circular motion is given






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by T=mv²/r. With a constant mass m and speed v but a progressively smaller orbital radius r, the

tension becomes progressively greater. The string may snap if this tension exceeds the string’s

breaking strength.

b) The gravitational force acting on the rings provides the centripetal force for their circular motion

about the planet. Since the gravitational force acts towards the center of the planet while the

centripetal force acts towards the center of the orbit , the plane of the ring’s orbit must contain the

center of the planet. Any asteroid which orbits about a circle not centered on the center of the planet

will experience a force which moves it towards the equatorial plane.

Gravitation

Why is it incorrect to call g “gravity”? [2] J94/II/2

“Gravity” refers to the gravitational force acting on a body. “g” is not a force, but the acceleration due

to this gravitational force F. Since F=ma, this acceleration a=F/m.

The Moon orbits about the Earth with a centripetal acceleration of 0.00271m/s² towards the Earth.

Since the Moon is accelerating towards the earth, why does the Moon not fall and hit the Earth?

J91/III/1

The Moon has a tangential momentum which is perpendicular to the gravitational pull that the Earth

exerts on it. The gravitational pull of the Earth on the Moon is just sufficient to provide the centripetalacceleration required to keep the Moon in circular motion. The centripetal acceleration keeps altering

the direction of the Moon’s velocity so that it is always tangential to its circular path, and the

continual falling simply results in a change in the Moon’s direction of motion. Since the Earth is round,

as the moon accelerates towards it, the Earth’s surface curves away at the same angular rate, thus

maintaining a constant distance between the Moon and the Earth’s surface. Therefore, the Moon will

never hit the Earth’s surface.

Explain why the center of the Earth is expected to lie on the plane of the moon’s orbit. [2] AJC Prelims

08/III/1

The only force acting on the moon is the gravitational force directed towards the center of the Earth.The moon will only move in the plane where this force lies.

Explain why gravitational potential has a negative value? [2] N94/III/1

Due to the attractive nature of the gravitational force, an external agent has to exert a force in the

opposite direction to the displacement of the mass, in order not to cause it to accelerate when






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bringing it from infinity to the point in question. Since the applied force and the displacement are in

opposite directions, the work done by the external agent is negative. Since potential is defined as

work done per unit mass by the external agent, potential is negative.

Explain why gravitational field strength at the poles is greater than that at the equator.

Part of the gravitational field strength at the equator is used to provide centripetal force for circular

motion.

Explain why a geostationary satellite is often used in telecommunications.

Its radius of orbit is always fixed at 4.23x107m. Therefore its position can be predicted accurately at all

times.

What are the advantages of a low orbit satellite?

Time of transmission is shorter. Less energy is required to bring the satellite to orbit. Signal of

transmission is higher.

Why must a geostationary satellite be above the earth’s equatorial orbit?

The center of earth is approximately the center of the satellite’s orbit. All gravitational force exerted

by the satellite provides centripetal force required for circular motion. There is no net force acting on

the satellite.

Explain why the energy at infinity is normally taken to be zero. [1] I JC Prelims 08/III/4

The force between the respective two entities is negligible. Thus, the potential energy at infinity is

zero and it is used as a reference for other potential energy.

State the condition(s) under which the equations to find the gravitational potential energy U=mgh and

U=-GMm/r may be used. [2] MJC Prelims 08/II/2

The first equation can be used to find the change in gravitational potential energy due to a change in

the distance h when distance h is << the radius of the planet, meaning it is very close to the surface of

the planet. The second equation can be used to find the gravitational potential energy associated with

an object of mass m at a distance r from the centre of another object M, regardless of this distance.






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Suggest two advantages of low polar orbits and two advantages of geostationary orbits. [4] N07/III/5

Satellites in low orbits are closer to the Earth hence their signals are received more strongly. These

satellites can fly over and serve every part of the world equally. A geostationary satellite allowscontinuous transmission between the ground station and the satellite, since they are always at the

same spot above the equator. Less energy is also required to launch and maintain it.

Communications satellites lose speed due to friction. Discuss this consequence in its motion of not

correcting for this loss. [2] YJC Prelims 08/III/6

As the satellite loses speed, it would drop to a lower height and it will increase in speed.

Thermal Physics

State why the thermodynamic scale of temperature is called an absolute scale. [2] J90/II/6

This means that the temperature on such a scale is not dependent on the thermometric property of

any particular substance and has absolute zero as its minimum temperature. Its fixed point, absolute

zero, is not dependent on any particular substance but rather is the temperature at which all

substances have a minimum internal energy.

List the basic assumptions of the kinetic theory of gases. J77/I/16

A gas consists of a large number of molecules in constant random motion and which obey Newton’s

laws of motion.

Inter-molecular forces of attraction are negligible.

Collisions are elastic on average.

The volume of the molecules is negligible compared to the volume occupied by the gas.

Collisions are of negligible duration compared to the duration between collisions.

What experimental evidence is there that the assumption that the collisions of the molecules with the

walls of the container are elastic is reasonable? N84/I/17

Collisions are elastic as the temperature of the insulated cylinder of gas is constant. The temperatureof an insulated cylinder of gas remains constant provided no heat lost to surrounding. Temperature is

proportional to the average kinetic energy of gas molecules. The fact that temperature remains

constant shows that collision is elastic. Otherwise, the temperature will keep falling with time as

molecules lose their kinetic energy.

How may an isothermal compression of a gas be achieved in practice? N78/I/15






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Heat is removed from the system at the same rate that work is being done on it.

Two different gases at the same temperature have molecules with different mean square speeds.Explain why is this possible. [2] ACJC Prelims 08/III/2

Gases at the same temperature have the same average translation kinetic energy. However, different

gases have different masses, therefore mean square speed is different.

In the upper atmosphere, a large fraction of the hydrogen molecules travel so fast that they are able

to escape from the Earth. There may also be some loss of helium, but for all other heavier molecules

escape in negligible. Explain a) fast molecules are able to escape form the Earth’s atmosphere but slow

molecules are not; b) molecules of smaller mass are able to escape whereas more massive ones are

not; c) some molecules escape even though the speed required for escape is very much greater thantheir root-mean-square speed. J89/II/10

a) Fast molecules have sufficient kinetic energy to overcome their potential energy due to Earth ’s

gravitational pull. They will escape if their speed exceeds the escape speed of the Earth, which is

approximately 11km/s.

b) For the same temperature, root-mean-square speed is inversely proportional to the square-root of

a molecule’s mass. Smaller molecules thus have greater rms speeds and thus more likely to exceed

the escape speed.

c) Root-mean-square speed is juts a form of average speed. Even at the same temperature, there are

molecules with speeds much greater and much less than the rms speed. Those that are much faster

may exceed the escape speed, and thus escape.






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If two sufficiently energetic sodium atoms collide, an electron in one of them may be raised to a higher

energy level. a) Explain why such a collision is called an inelastic collision. b) Briefly explain why such

inelastic collisions are not consistent with basic assumptions of the kinetic theory of gases. J90/III/3

a) When the sodium atom is raised to a higher energy state, the energy is gained from the kinetic

energy of the colliding sodium atoms. The colliding atoms thus lose part or all of their kinetic energy.

Since kinetic energy of the system is not conserved, the collision is inelastic.

b) Kinetic theory of gases assumes that molecules make elastic collisions so that their average kinetic

energy, and hence temperature, remains constant. If collisions are inelastic, then colliding molecules

progressively lose their kinetic energy and gradually slow down. The temperature of the gas thus

progressively decreases, even though no heat is supplied / removed or work done on / by the system.

Explain why the specific latent heat of vaporization of a substance is much larger than the specificlatent heat of fusion. N97/III/5

During boiling, the liquid absorbs heat known as the latent heat of vaporization. This heat breaks the

intermolecular bonds between molecules and separates them to a great distance apart, as well as

pushes back the atmosphere. During melting, the heat absorbed, known as the latent heat of fusion,

does not break the intermolecular bonds completely or separate the molecules to a great distance

apart. The heat merely modifies the bonds from a rigid structure to a form that allows relative motion

amongst molecules. Less energy is required. Furthermore, the change in volume in the substance is

negligible during melting hence little work is done on or by the system.

Explain the following observations a) when pumping up a bicycle tyre the pump barrel gets warm; b)

when a gas at high pressure in a container is suddenly released, the container cools. [2] CJC Prelims

08/III/2

a) External work done on the gas during compression causes the internal energy to increase. Since the

internal energy is proportional to the temperature, the temperature increases.

b) The gas undergoes sudden expansion and internal energy is used do work against external

pressure. This causes the internal energy of the gas to decrease, hence the temperature decreases

and the container cools.

“Internal energy is determined by the state of the system”. Expla in what this means. [2] PJC Prelims

08/III/1

A system is at a definite state when it is at equilibrium under a given set of conditions. The system has

a specific pressure, volume, number of moles and molecules and thermodynamic temperature values

that correspond to that state. Internal energy is determined by the values of the current state and is






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independent on how the state is arrived at. If a system undergoes a series of change from one state to

another, its increase in internal energy is the same, regardless of which path it has taken.

Suggest how an isothermal expansion can be achieved in practice. [2] HCI Prelims 08/III/2

The process must be carried out very slowly so that heat has time to flow in or out to maintain

constant temperature. The walls of the container must be a good conductor.

Bubbles are formed in water when water boils. Explain why the bubbles in boiling water get larger as

they approach the surface. [1] PJC Prelims 08/III/1

The pressure of water decreases with a decrease in depth of water. The bubble experiences less

pressure as it approaches the surface. Since PV=nRT, the volume of the air bubble is inverselyproportional to the pressure it experience. Therefore the volume increases as it approached the

surface.

Explain why the melting of ice takes place without a change in temperature. [3] TPJC Prelims 08/II/1

Heat energy that ice absorbs from the surrounding when it is melting is used to increase potential

energy of water molecules. Heat energy has not been used to increase the average kinetic energy of

the water molecules. Thermodynamic temperature of matter is directly proportional to its average

kinetic energy, hence melting of ice takes place without a change in temperature.

Explain what is meant by an ideal gas. N07/III/6

An ideal gas is a hypothetical gas that obeys the equation of state of an ideal gas perfectly at all

temperatures and pressures. A real gas approaches ideal behaviour at very low pressures and high

temperatures.

Outline how molecular movement causes the pressure exerted by a gas. [2] N99/III4

Gas molecules are in continuous random motion. When a molecule collides with the walls of a

container, it exerts a force which is proportional to its mass, speed and frequency of collision. The

force by all molecules acting per unit surface area is the pressure exerted by the gas.

Outline an electrical method to determine the specific latent heat of vaporization of water. [4]

N98/III/5

An electric kettle, with voltage rating V and current rating I, contains some water and is placed on a

balance. The kettle is switched on and when the water is boiling, the reduction in the balance m

within a time interval t is recorded. The specific latent heat of vaporization l v can be calculated from






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the following equation: lv=IVT/m. Errors resulting from re-condensation of steam at the mouth of the

kettle, as well as heat loss to the surrounding, should be minimized with appropriate measures.

Outline the principles involved in measuring the specific heat capacity of a liquid using an electrical

method. [4] N01/III/5

An insulated container contains the substance which specific heat capacity is to be measured. An

electric heater is placed in the liquid. A thermometer is used to measure the temperature of the liquidand a stirrer ensures the temperature is evenly distributed throughout the liquid. The heater is

switched on for a predetermined period of time t. The rise in temperature Δθ of the liquid within this

time interval is recorded. The voltage V and current I is recorded from the voltmeter and ammeter

respectively. The specific heat capacity of the liquid can be found from the equation c=IVT/(m Δθ).

State two reasons why the temperature of a body is not a measure of the quantity of thermal energy

in the body. [2] N06/II/4

Temperature is a measure of the average kinetic energy of the molecules whereas the thermal energy

in a body is its total energy. Temperature only measures the kinetic energy of the molecules whereasthermal energy includes both their kinetic and potential energy.

Superposition

An experiment is conducted to obtain the displacement-time graph and displacement-distance graph

of a sound wave. Suggest an experimental method for obtaining the displacement-time graph. Discuss

whether the same method could be used for the displacement-distance graph. [6] N96/III/2

The displacement-time graph can be obtained by placing a microphone in the path of the sound wave,

and connecting the output from the microphone to an oscilloscope. The microphone acts as a

transducer to convert sound energy into electrical energy, such that the amplitude of the

microphone’s voltage output is proportional to the amplitude of the sound wave. The x-axis of the

oscilloscope is the time base. The oscilloscope displays voltage-time graph of the microphone output,

and thus the displacement-time graph of the sound wave.






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The same method cannot be used for the displacement-time graph because the oscilloscope’s

horizontal axis is time and not distance. Displacement-distance graph shows the displacement of all

the particles along the wave at one instant in time. To produce the displacement-distance graph,

multiple microphones must be placed along the sound wave, and all the microphone outputsconnected to a data-logger which records all of their voltage outputs simultaneously. Their values are

then plotted against distance to obtain the displacement-time graph.






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It is possible to use two separate oscillators feeding two loudspeakers to demonstrate interference of

sound. It is not possible to use two filament lamps, however similar, to produce interference of light.

Explain the difference. How could you modify the experiment in order to show interference of light? [4]

J91/III/2

Provided the two sound oscillators are identical, they will maintain a constant phase difference. This

ensures that both waves are coherent – a condition for interference to occur. Light from a filament

lamp is emitted in random pulses, with different phases emitting from different parts of the filament.

Even if two filament lamps emit the same frequency of light, their wave trains are not able to

maintain a constant phase difference between each other. Since they are not coherent, the two

sources of waves are not able to produce interference. Use a single light source and place a third slit

behind the double slits. The third slit ensures that the light waves arriving at the double slits are from

a single point source and thus coherent. Alternatively, laser light can be used since laser light is

coherent.

Describe an experiment by which the frequency of a stationary wave can be accurately determined. [5]

N90/III/3

Place a light gate transmitter-received pair across an antinode of the vibrating string. Connect the

output of the light gate’s receiver to a CRO. When the string is not blocking the light gate, the light

gate receiver’s output is high hence the CRO displays a high voltage. When the string passes through

the equilibrium position and comes between the light gate’s transmitter and receiver, the light is

blocked. As a result, there is a brief drop in the light gate receiver’s output, resulting in a dip in the

CRO’s voltage display. The time-interval between two successive voltage drops is half a period. From

the period T, the frequency f=1/T.

Explain what is meant by interference with reference to a stationary wave on a stretched spring. [3]

N95/III/3

When the string is plucked in its center, progressive waves emerge in both directions from the center

of the string. When the waves reach the ends of the string, they are reflected by a phase angle of 180˚

due to the ends being fixed. These reflected waves, traveling in opposite directions, superpose with

each other to produce a stationary wave. At locations where the reflected waves are in phase with

each other, they undergo constructive interference to produce antinodes with twice the amplitude of

vibrations of each wave. At locations where they are 180˚ out of phase with each other, they undergodestructive interference to produce nodes with zero amplitude of vibration. Energy is redistributed

from the minima to the maxima.

If Young’s double-slit experiment were conducted underwater, how would the observed interference

pattern be affected?






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The speed of electromagnetic radiation underwater will be much slower than that in a vacuum. The

wavelength of the wave will decrease and fringe spacing of observed interference pattern will

decrease.






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The speed v of a progressi ve wave is given by the expression v=fλ. A stationary wave does not have a

speed. By reference to the formation of a stationary wave, explain the significance of the product fλ

for a stationary wave. [3] N04/II/4

A stationary wave is formed by the superposition of two progressive waves of the same type with

equal speed, frequency, wavelength and amplitude traveling in opposite directions. The product fλ in

a stationary wave refers to the speed of the two progressive waves that superpose to form the

stationary wave. Due to the two waves having the same speed fλ but different directions, their

velocity vectors cancel out resulting in the stationary wave not traveling in either direction.

Explain why it is usually necessary to adjust either the vibrating length of the string or the frequency of

the vibrator in order to obtain observable stationary waves on the string. N95/III/3

Both ends of a stretched string are nodes since they are fixed in position and not able to move. Inorder for a stationary wave to be set up in a stretched string, the length of the string must be an

integer multiple of 0.5λ. If the frequency, and thus wavelength, is fixed, then the length of the

vibrating string must be adjusted to accommodate the condition that its length is an integer multiple

of 0.5λ. However, if the vibrating length of the string is fixed, then the wavelength can be adjusted to

accommodate the condition, by varying the frequency of vibration, since λ=v/f.

Suggest why two-source interference of water waves, using a double-slit arrangement, may not be

observed when the slits are wide but, when the slits are narrow, interference is observed. J96/III/3

When the slits are wide, the water waves do not diffract much. Their wavefronts pass straight through

the slits and their paths do not cross. Since their wavefronts do not meet, the two waves are not able

to interfere with each other. When the slits are narrow, the water waves diffract significantly. Their

wavefronts spread out in a semi-circular profile. Where their wavefronts meet, the two waves are

able to interfere. At locations where the waves are in phase with each other, they interfere

constructively to produce intensity maxima. Where the waves are 180˚ out of phase, they interfere

destructively to produce intensity minima.

Diffraction gratings can be used to determine the wavelength of electromagnetic radiation. Suggest

one advantage and one disadvantage of obtaining the wavelength by using observations of the

second-order diffracted light rather than the first-order diffracted light. N95/III/3

Second order diffracted beams make larger angles with respect to the central axis. The percentage

uncertainty in the measured angle will thus be lower. Second order diffracted light has a lower

intensity due to the diffraction envelope constraint resulting from diffraction of light from each

individual slit. This causes the diffracted beam’s intensity to be progressively lower the further it is

from the central axis, making observation of the maxima more difficult.

Describe briefly how you would confirm that the laser beam is plane-polarised. [2] JJC Prelims 08/III/2






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Pass the laser beam through a polariser. As the polariser is rotated in plane perpendicular to the

beam, the intensity of the emerging beam should vary from a maximum to zero or vice versa.

Both diffraction and superposition of waves occur when a diffraction grating is used to produce a

spectrum. The same principles are involved when a compact disc is viewed in white light and is seen to

produce multicoloured streaks of light. Explain how a diffraction grating produces a spectrum and

suggest what this implies about the nature of the surface of the CD. [5] N94/III/2

When white light passes through a diffraction grating, the light waves diffract and spread out from

each of the many slits. The spreading wave fronts then interfere with one another. At certain angles

where the light waves are in phase, they interfere constructively to produce intensity maxima. Theseangles where the maxima occur depends on the wavelength of the light according to the equation

dsinѳ=nλ where d is the slit separation and n the order of the maxima. Since white light comprises a

whole range of wavelengths, each wavelength of light will have its maxima at a different angle, thus

producing a spectrum.

The fact that the CD is seen to produce a spectrum suggests that the surface of the CD has a

diffraction grating-like structure. The indentations on the surface of the CD must be regularly spaced

just like a diffraction grating. Each indentation is a small mirror and reflects white light incident upon

it. The reflected light from all the indentations is similar to the multiple source of light wave spreading

out from the slits of the diffraction grating. They interfere with one another to produce a spectrum asin the case of a diffraction grating.

Light from a laser is produced via stimulated emission, whereas light form a fluorescent tube is

produced via spontaneous emission. Compare the light from these two sources in terms of phase

difference and deduce the effect this has on the experimental setup for a double-slit interference

experiment using laser light. [2] YJC Prelims 08/II/3

All photons produced by stimulated emission in a laser have the same phase difference, whereas

those produced by spontaneous emission do not. Thus for a double-slit experiment, light from a single

laser source incident on the double slits will produce an interference pattern.

Explain why a stationary sound wave set up in a closed tube looks like a transverse wave although

sound waves are longitudinal waves. [2] N06/III/4

This is only a schematic graphical representation of the displacement of the air molecules in the

sound wave. Since sound wave is a longitudinal wave, the air molecules vibrate parallel to the axis of

the pipe. The air molecules actually vibrate in a horizontal direction (left and right) but the schematic






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graphical representation is such that a rightward displacement is represented as positive while a

leftward displacement is represented as negative.

The band is practicing in the band room down the corridor with the door left slightly ajar. Explain why

notes of a certain range of frequencies can be heard more clearly than others at the end of the

corridor. [2] HCI Prelims 08/III/7

Low-pitched notes have longer wavelengths and undergo more diffraction through the door.

Oscillations

Some sand is placed on a flat horizontal table and plate is made to oscillate with simple harmonic

motion in a vertical direction. With the frequency of oscillation kept constant at 13Hz, the amplitude of

oscillation of the plate is gradually increased. Explain at which point the sand loses contact. [3]

J99/III/4

The sand starts to lose contact with the oscillating table when the maximum downward acceleration

of the table exceeds the acceleration of free fall of the sand. Maximum downward acceleration occurs

at the maximum upward displacement position. When the amplitude of oscillation exceeds 1.47mm,

the maximum acceleration exceeds that of free fall. When this happens, at its maximum displacement

position, the table accelerates downwards with greater magnitude than the sands’ acceleration dueto free fall. This will cause the subsequent downward velocity of the table to exceed that of the sand.

The contact force between the sand and table falls to zero and the sand loses contact with the table.

A block of wood of mass m floats in still water. When the block is pushed down into the water, without

totally submerging it, and is then released, it bobs up and down in the water with a frequency f.

Surface water waves are then incident on the block. These cause resonance in the up-and-down

motion of the block. Describe and explain what happens to the amplitude of the vertical oscillations of

the block after the following changes are made. a) Water waves of larger amplitude are incident on

the block. b) The distance between the wave crests increases. c) The block has absorbed some water.

[6] N94/II/2

a) The amplitude of the block increases. The energy of a wave is proportional to the square of its

amplitude. Waves of larger amplitude possess greater energy, thus transferring a greater amount of

energy to the block.

b) Resonance no longer occurs hence the amplitude of oscillation decreases. Distance between wave

crests is the wavelength λ. Since speed of wave v=fλ and v is constant, a larger λ means a lower






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frequency f. The frequency f of the driving force drops below that of the natural frequency of the

block.

c) Resonance no longer occurs hence the amplitude of oscillation decreases. When the blockabsorbed some water, its mass increases. The natural frequency decreases. The frequency of the

driving force is now above the natural frequency of the system.

State one situation in which resonance is used to advantage. [1] J97/II/2

Radio tuner’s natural frequency adjusted to resonate with frequency of radio wave of the station it

intends to receive.






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A mass-spring system is used to demonstrate the effects of damping on the oscillation of the mass.

Suggest how light damping of the oscillations may be achieved and how the degree of damping may

be increased. [4] N2000/II/3

Light damping may be achieved by attaching a light piece of cardboard to the mass thus increasing its

effective area and air resistance experienced by it. The degree of damping may be increased by

immersing the mass in a viscous liquid such as glycerine, which provides a large viscous drag force

against the motion. This causes large amounts of energy to be dissipated from the body.

Discuss the behaviour of a car when the shock absorber mechanism is working correctly. N78/III/1

A shock absorber mechanism should be critically damped. When a car goes over a hump, there is an

immediate compression of the suspension springs. A properly working mechanism should then return

the spring to its uncompressed position in the shortest time, without overshooting the equilibriumposition.

Resonance can cause considerable engineering problems. Explain one such problem and suggest ways

in which it can be overcome. [4] N98/III/2

When resonance occurs, the system vibrates with maximum amplitude and energy. This vibration

creates tremendous stress on mechanical structures and may cause them to breakdown. One such

problem is in building and bridge structures. If the frequency of the gusts due to high speed winds

coincides with the natural frequency of the bridge, the bridge may resonate and vibrate with

maximum amplitude. This problem can be overcome by increasing the damping of the system

through the use of shock absorbers.

Describe 2 practical examples of forced oscillations and resonance.

Microwave oven – Microwaves will cause the water molecules in the food to vibrate. If the frequency

of the microwave is the same as the natural frequency of the water molecules, resonance occurs and

the water molecules will vibrate with maximum amplitude, hence heating up the food.

Breaking of a glass by a singer – sound waves from the singer will cause the glass molecules in the

glass to vibrate. If the frequency of the sound wave is the same as the natural frequency of the glass

molecules, resonance occurs and the glass molecules will vibrate with maximum amplitude, andhence may break the glass.

If a truck travels at a certain speed over a series of speed bumps, the vertical oscillations can be very

large. Explain why this is so. [2] MJC Prelims 08/II/2

Resonance occurs. The frequency of passing over the bumps matches the natural frequency of the

truck.






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Damping is very often necessary when unwanted oscillations occur in machinery such as a washing

machine or a dishwasher. Describe the factors that determine the frequency at which unwanted

oscillations occur and the principles that are used in damping out these oscillations. [5] H2 Specimen

Paper 07/III/6

The frequency of unwanted oscillations is the natural frequency of the system. The natural frequency

of a system is determined by factors such as the inertia of the system (mass), the elastic restoring

force acting on it (spring constant) and the dimensions of the system. For machinery like washingmachines and dishwashers, their mass, springiness of their metal frames and dimensions of their

casings determine their natural frequency and frequency of unwanted oscillations. Damping involves

the reduction of amplitude of an oscillating system through the application of external resistive forces

that results in energy being dissipated from the system. This can be achieved by using dampers.

Dampers can be in the form of viscous fluids or solid material with dissipative properties attached to

the parts of the machine that are likely to experience the most vibrations.

Waves

The wavelength of sound in air is of the order of one million times greater than the wavelength of light

in air. Describe how you could check this statement experimentally. [8] N04/III/3

The wavelength of a wave can be determined using two-source interference experiments. To

determine the wavelength of sound, connect two loudspeakers to a single sound oscillator. Face the

two speakers towards a wall several metres away. Move a microphone along the wall to detect

variations in sound intensity. There will be intensity maxima corresponding to constructive

interference of the two sound waves, and minima corresponding to destructive interference. Select a

maximum that is nth

order from the central axis maximum. Measure the distance from each speaker

to this maximum and subtract them to obtain the path difference. The path difference divded by ‘n’

will be the wavelength of the sound.

To determine the wavelength of light, use Young’s double-slit experiment. A monochromatic light

source is placed behind the double slits, with a third slit between them to ensure coherence. Bright

and dark fringes will be observed on the screen. Since the angle of diffraction is small in this

experiment, the Young’s double-slit formula y=λD/d can be used to calculate the wavelength λ of the






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light. The experimental results will show that the wavelength of sound waves is in the order of

metres; while that of light waves in the order of micrometres.

Distinguish between the displacement of a vibrating object and the amplitude of vibration. [3] J99/III/4

Displacement is the shortest distance from the equilibrium position to the object at any instant in

time. Amplitude is the maximum displacement of the object from its equilibrium position, in either

direction.

What phenomenon associated with transverse waves is not observed with longitudinal waves? N90/III/3

Polarisation. Transverse waves vibrate perpendicularly to its direction of propagation, and possess

many possible planes of vibration. Polarisation eliminates all planes of vibration except the plane

which is parallel to the allowed axis of transmission of the polarizer. Longitudinal waves vibrate

parallel to its direction of propagation, and possess no plane of vibration parallel to the allowed axis

of transmission of the polarizer. Therefore, longitudinal waves cannot be polarized.

Electricity

Discuss briefly whether it is practicable to suggest that power losses as heat can be reduced

indefinitely by a suitable choice of generator pd. N81/1/7

Theoretically, power loss can be reduced infinitely by increasing the generator pd by using step-up

transformers at the generator output. However, extremely high voltages tend to cause insulation

breakdown between live and neutral wires / insulation breakdown between windings in the high-

voltage secondary coil of the transformer / electromagnetic interference with the telecommunication

equipment. Hence, there is a limitation to how high the voltage can be stepped up.

Why do the I-V graphs of a filament of a torch bulb and a piece of intrinsic semiconductor differ in

shape? N89/III/5

The resistance of a metallic conductor increases with temperature. As the voltage and current

increase, the power dissipated increases causing significant heating. This increases the ionic lattice

vibration within the metal, causing increasing collisions with the drifting free electrons. The drift






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velocity of the electrons decreases; the filament’s conductivity falls; and resistance rises. Since R=V/I,

this ratio increases thus causing the graph to concave downwards.

The resistance of a semiconductor decreases with temperature. As the voltage and current increase,the power dissipated increases causing significant heating. This energy causes more electrons to be

released from their bonds. The charge carrier density of the semiconductor increases; its conductivity

rises; and resistance falls. Since resistance R=V/I, this ratio decreases causing the graph to concave

upwards.

By taking the average value of power dissipated at different temperatures, energy supplied by battery

during period which temperature changes can be calculated. However, this calculation is only an

estimate. Explain.

Since power does not vary linearly with resistance, this method will not yield an accurate value of power dissipated when resistance changes.






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Explain why power is required to maintain an electric current through a metallic conductor. [4]

J98/III/2

The flow of current is a result of electrons drifting in the opposite direction. Electrons drifting throughthe conductor constantly collide with the metal ions in the lattice, passing energy to the ions, causing

them to vibrate, and resulting in a rise in the temperature of the conductor. In order to prevent the

electrons from slowing down after the collision, a continuous amount of energy must be supplied by

the potential difference across the conductor. This potential difference creates an electric field which

immediately accelerates the electrons back to their terminal drift velocity after each collision with the

ionic lattice. In this way, the power supplied by the potential difference balances the power dissipated

as heat by the vibrating ionic lattice, in accordance with the law of conservation of energy.

In using a simple slide-wire potentiometer circuit, a large protective resistance is sometimes connected

in series with the galvanometer. Why is this done? Explain how the presence of this resistance affectsa) the position of the balance point, b) the precision with which it may be found. J84/I/7

This resistance limits the current flowing through the galvanometer, preventing it from being

damaged. When the potentiometer is still far from its balance point, there could be a large potential

difference across the galvanometer. Since the galvanometer’s resistance is low, the current flowing

through it could be extremely high if not limited by the protective resistance. This protective

resistance does not affect the position of the balance point. At the balance point, there is no potential

difference across the galvanometer. The current will thus be zero whether or not the protective

resistance is present. However, this protective resistance reduces the precision with which the

balance point may be found. This resistance reduces the current through the galvanometer, thus

making it less sensitive to small changes in potential difference. To overcome this problem, a dual-

resistor system is used whereby the protective resistance is switched to a lower value when the

jockey is near the balance point. By then, the potential difference across the galvanometer will be

quite small.

Explain the use of a thermistor and a light-dependent resistor in potential dividers to provide a

potential difference which is dependent on temperature and illumination respectively.

A thermistor is sensitive to temperature changes. When temperature increases, resistance decreases.

Hence current from the DC source will increase. Hence, the potential difference across the resistor

increases. A light dependent resistor is sensitive to illumination. When illumination increases,resistance decreases. Current from the DC source will increases. Hence, the potential difference

across the resistor will increase.

Use Faraday’s law of electromagnetic induction to explain why a transformer will operate for an

alternating voltage input but not for a direct voltage input. [2] AJC Prelims 08/III/3






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An alternating voltage input causes a changing magnetic flux which links the primary coil to the

secondary coil. As a result of electromagnetic induction, a changing emf is produced in the secondary

coil. A direct voltage input does not provide a changing magnetic flux and thus, no emf is induced in

the secondary coil.

In a potentiometer setup, the instructions suggested that the galvanometer be set to different

resistance levels (high or low) for the initial estimation of balance length and for the final, more

accurate verification. Suggest which resistance levels should be chosen for each measurement. Explain

your answer. [4] AJC Prelims 08/III/6

Initially, high resistance is necessary to protect the meter against possible high current. For final

verification, a change from high to low resistance means that there will be a current flowing through

the galvanometer even at the balance point that has been determined initially. Hence, a more

accurate balance point can be determined with fine adjustment till the galvanometer reflects nulldeflection again.

If the equation V=IR is used to define resistance, why is it not possible then to use the same equation

to define potential difference? [1] CJC Prelims 08/II/4

Resistance of a resistor is defined as the ratio of potential difference across the resistor to the current

through it. Therefore, potential difference cannot be defined using resistance. This is because physical

quantities must be defined in sequence.

Explain why a railway employee who touches the track through which there is a current of 180A does

not get an electric shock. [2] N98/III4

This is because there is no potential difference between the railway employee and the track. Electric

current flows from a region of higher to lower electric potential. Both the railway employee and the

track are in contact with the earth, and thus are grounded at the same earth potential. Since the

employee and the track are at the same potential, current will not flow either way.

Explain why a high voltage supply is essential for a railway system. [2] N98/III/4

High voltages result in lower transmitted current, since I=P/V where transmitted power is a constant.

A lower current reduces the power loss as P loss=I²R where R is the resistance of the transmission cable.A lower current either increases the efficiency of transmission or, if efficiency is to be maintained,

allows a thinner wire with higher resistance to be used, thus saving on cabling costs.

Explain why a different current is needed when the train is climbing a hill from that required when

traveling at the same speed on the flat. [2] N98/III/4






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When climbing a hill, additional work needs to be done against gravity which is converted into

potential energy of the train. Engine power P=IV=Fv where F is force exerted and v the speed of the

train. Since speed v is constant but a greater force F has to be exerted to overcome gravity, a greater

current I has to be drawn to provide the additional power required. This is in accordance with the lawof conservation of energy.

Describe electrical conduction in a metal. [1] N99/III/5

When a potential difference is applied across the ends of a metal, an electric field is set up. This field

exerts an electric force on the free electrons, causing them to drift towards the higher potential end.

Discuss two factors which affect the magnitude of the current and hence result in the possible danger

of electric shock. One obvious safety precaution is to keep live wires well insulated. What other safety precautions do you suggest? [4] N2000/III/4

One factor is the resistivity of the skin, which is affected by its moisture. Wet skin has lower resistivity

and hence resistance, thus increasing the danger from electric shock. Another factor is the thickness

of the skin. If the skin is thinner, the resistance will also be lower, increasing the danger from electric

shock.

The other safety precautions are 1) wear thick rubber boots to reduce current flowing through the

body into the earth in the event of an electric shock; 2) connect an Earth Leakage Circuit Breaker in

the electric circuit to cut off the power supply the moment current is diverted into the earth wire.

Electric Fields

Explain why the electric potential on the surface of an isolated charged conductor is the same

everywhere. [4] J88/III/5

The surface of a conductor has zero resistance, hence charges on it can flow freely. Any potential

difference which develops between two points on the surface will create an electric field between the

two points. The field will produce a force which causes the charges to move and redistribute

themselves until there is no more potential difference between the two points. Hence the electric

potential on the surface must be the same everywhere.

Explain to what extent an isolate, positively charged conducting sphere may be considered to act as a

point charge. [3] J89/III/12






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An isolated, positively charged conducting sphere may be considered to act as a point charge at

distances equal to or greater than the radius of the sphere. On the surface as well as outside the

sphere, the electric field strength E=Q/4πε0d²and electric potential V=Q/4πε0d, where d is the

distance measured from the center of the sphere. Hence, the sphere behaves like a point charge of magnitude Q located at its center. Within the sphere, however, E=0 and V=Q/4πε0R everywhere in the

sphere, where R is the radius of the sphere, which is a constant. Hence within the sphere, it does not

behave as a point charge. The reason behind this is that the resistance of a conductor is zero and

there can be no potential difference between any two points in the sphere. Since electric field

strength is the negative of the potential gradient, the electric field must be zero everywhere inside

the sphere.

Distinguish qualitative and quantitative aspects of electric field and gravitational field.

Both are inverse square law fields. Electric field acts on charges while gravitational field acts onmasses. Field lines in an electric field are always directed away from a positive point charge and

towards a negative point charge. Field lines in a gravitational field are always directed to a point mass.

Electric forces can be attractive or repulsive while gravitational forces are always attractive.






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Suggest why, in the alpha-scattering experiment, a) gravitational effects are ignore; and b) when

calculating electric potential, the direction of approach of the alpha-particle to the nucleus need not

be considered. [2] N98/II/2

a) The potential energy and force due to a gravitational field are many orders of magnitude smaller

than the potential energy and force due to an electric field, respectively.

b) Electric potential is a scalar quantity which has only magnitude but not direction. It is hence

independent of the direction of approach.

Explain why lightning is more likely to strike the tip of the lighthouse than any other places close to it.

[1] IJC Prelims 08/III/4

Near the tip of the lighthouse, the equipotential surfaces are very close to one another. This meansthat the potential gradient there is very strong and it is more likely to reach the threshold potential

gradient before any other places for an electric discharge to occur. There is a high concentration of

charges at the tip of the lighthouse.

Explain the shape of the path followed by electrons as they pass between the deflecting plates.

A uniform electric field acts from the upper plate to the lower plate, hence a constant force exerted

on the electron beam causes it to curve up. The curve is parabolic.

State how the magnitude and direction of the electric field strength at any point between two charges

can be determined by their electric potential-distance graph. [2] RJC CT1 08/16

The magnitude of the electric field strength at any point between the two charges can be obtained

from the gradient of the potential-distance graph. The electric field strength acts from region of high

to low potential.

Magnetism

A copper disc spins freely between the poles of an unconnected electromagnet. Describe and explain

what will happen to the speed of rotation of the disc when direct current is switched on in theelectromagnet. [4] J91/II/5

The copper disc will slow down and then come to a halt. When a direct current is switched on, a

magnetic field is created perpendicular to the plane of the copper disc. The rotation of the disc causes

the disc to cut these magnetic field lines. According to Faraday’s law of electromagnetic induction, a

change in the magnetic flux linking the disc will result in an emf induced across its axle and rim. This






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emf will cause a current to flow in the disc. According to Lenz’s Law, this current will flow in such a

direction as to oppose the change in magnetic flux linkage, hence creating an opposing force. This

opposing force will slow down the disc. By the Law of Conservation of Energy, the mechanical energy

of the rotating disc is converted into electrical energy and then dissipated as heat in the disc.

State the effect on the magnetic flux density along the axis of a solenoid in the presence of a ferrous

core. [1] H1 Specimen Paper 06/II/4

In the presence of a ferrous core, the magnetic flux density will be increased a few thousand times

since the permeability of iron is approximately 5000 times that of free space. There will be many

more magnetic field lines which are more closely spaced compared to before.

A step-down transformer is used to charge a rechargeable battery. The secondary circuit consists of a

diode, a resistor, and the battery to be recharged. a) Suggest why the diode is necessary in thesecondary circuit. b) Suggest why the resistor is necessary in the circuit. [4] J2000/II/5

a) The diode ensures current is always in one direction so that battery will not discharge. There will be

times when the charging voltage falls below the emf of the battery. During such instances, the diode

prevents the current from reversing, out of the battery into the transformer which will cause the

battery to be discharged.

b) The resistor limits the current in the circuit to protect the battery and the diode. This is because the

resistance of the diode and internal resistance of the battery are both very small. If there is no resistor

to limit the current, the current could become very high, causing damage to the battery and diode.

A long bar magnet is suspended from a helical spring so that one pole of the magnet lies within a short

cylindrical coil. The magnet is given a small vertical displacement and is then released so that one pole

of the magnet oscillates within the coil. Explain the nature of the magnet’s oscillations when no

resistor is connected; a large resistor is connected and a low resistor is connected. J94/III/3

With no resistor, although an emf is induced across the coil due to Faraday’s law of electromagnetic

induction, the current cannot flow hence no magnetic field can be created to oppose the motion of

the oscillating magnet. The magnet thus oscillates freely with constant amplitude.

With a large resistor, the induced emf is able to drive a small current through the coil. According to

Lenz’s Law, the current will flow in such a direction as to oppose the change in magnetic flux linkage.This opposing field slows down the oscillating magnet. Light damping occurs.

With a small resistor, a large current is able to flow. The opposing field is strong, and the magnet

experiences heavy damping.






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In the second and third case, the mechanical energy of the oscillating magnet is converted into

electrical energy, then dissipated as heat in the resistor in accordance with the Law of Conservation of

Energy.

Describe and analyse deflections of beams of charged particles by uniform electric and uniform

magnetic fields.

Beams of charged particles entering a perpendicular uniform electric field are deflected in parabolic

paths. Beams of charged particles entering a perpendicular uniform magnetic field are deflected in

circular paths. The direction of the centripetal force is given by Fleming’s left hand rule.






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A coil, consisting of many turns of insulated metal wire wrapped around a soft-iron core, is connected

in series with a battery, a switch and a lamp. State what happens to the magnitude of the magnetic

flux in the coil as the current increase from zero when the switch is closed. Hence explain why an emf is

induced in the coil as the current increases. Hence explain why there is noticeable delay before thelamp lights up after the switch is closed. State and explain what will happen to the length of the delay

if the soft-iron core is replaced by one made of wood. [6] J95/II/14

The magnetic flux increases.

According to Faraday’s law of electromagnetic induction, an emf will be induced in the coil when

there is a change in the magnetic flux linking the coil.

According to Lenz’s law, the induced emf will be in such a direction as to oppose the change. The

induced emf is initially equal but opposite to the battery’s emf , thus canceling it out, resulting in therebeing no net emf in the circuit. Gradually, this induced emf decreases due to the reduction in the rate

of change of magnetic flux, thus allowing the battery to drive a current through the circuit.

The delay will be shorter. Wood does not encourage magnetic flux as well as soft-iron. Therefore, the

change in the magnetic flux linkage in the coil will be lower. This induced emf which opposes the

battery’s emf will be thus lower. Hence the delay will be shorter.

An electron is projected in a vacuum along the axis of a current-carrying solenoid. Describe and explain

its motion. N81/I/8

The electron will pass straight through undeflected, without any change in speed. The magnetic field

in a solenoid is parallel to its axis. When an electron travels along the axis of the solenoid, the angle

between the direction of the magnetic field and that of the electron’s velocity is zero. Therefore, the

force acting on the electron will also be zero. With no resultant force acting on the electron, it will not

undergo any acceleration and thus will travel with uniform speed in the same direction, in accordance

with Newton’s first law of motion.

Explain the forces between current-carrying conductors and predict the direction of the forces.

Two parallel current-carrying conductors are placed near to each other. Current in the first conductor

generates a magnetic field in its vicinity whose direction is given by the right hand grip rule. Thesecond current carrying conductor within this field would experience a magnetic force, whose

direction is given by Fleming’s left hand rule. 2 parallel conductors with currents flowing in the same

direction will attract each other. 2 parallel conductors with currents flowing in opposite directions

with repel each other.

Briefly explain the working principles of a current balance. [2] NJC Prelims 08/III/6






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The magnetic field produced a magnetic force which results in an anti-clockwise moment about XY to

counter the anti-clockwise moment due to the weight of the rider.

Explain simple applications of electromagnetic induction.

Turbine generator – the coil of the turbine is positioned in a strong magnetic field. The turbine uses

force to turn its coil. Hence, its coil experiences changing magnetic flux linkage. According to

Faraday’s law, emf is induced.

Electric guitar – the vibrating string induces an emf in the coil. The pickup coil is placed near the

vibrating guitar string which is made of a metal that can be magnetized. The permanent magnet

inside the coil magnetizes the portion of the string nearest the coil. When the guitar string vibrates atsome frequency, its magnetized segment produces a changing magnetic flux through the pickup coil.

The changing flux linkage induces emf in the coil. Subsequently the emf is fed to the amplifier and

speaker system to produce sound.

By considering the Earth’s magnetic field, suggest with reasons why Aurorae are mostly seen in the

polar region rather than in the equatorial region. [2] ACJC Prelims08/II/7

The direction of the entry of the solar wind (or charged particles) and the Earth’s magnetic field are

almost perpendicular at the Equator, hence deflected away from the Earth. However, the direction of

solar wind is almost parallel to field lines at the poles. Hence it is not deflected. Thus Aurora sightingsat the equator is rare but not at the poles.

A charged particle enters a region of uniform magnetic field directed into the plane of the paper. The

tracks of such particles can be made visible by an apparatus known as a bubble chamber, in which the

particle is made to pass through a liquid close to its boiling point. Thus tiny bubbles are formed along

the path of the particle’s motion, allowing us to observe the particle’s trajectory. Such a track is

observed to spiral. Briefly explain why the path deviates from uniform circular motion. [2] HCI Prelims

08/III/6

Due to collisions between the particle and the medium of the bubble chamber, the particle loses

kinetic energy and thus slows down. Since r=mv/Bq, the decrease in speed results in a decrease in r,thus resulting in the inward spiraling trajectory.

A beam of electrons of speed v passes undeflected through superimposed uniform magnetic and

electric fields of magnitudes B and E respectively. How must the fields be related in both magnitude

and direction? N98/III/6






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In order for there to be no deflection, the force exerted by the electric field must be equal but

opposite to that exerted by the magnetic field. The two fields must be crossed fields. They must be

placed perpendicular to each other, and both fields must be perpendicular to the direction of the

electron’s velocity. If the electric field is downwards, the magnetic field should be into the plane of the paper. If the electric field is upwards, the magnetic field should be out of the paper. Since

magnetic force = electric force, Bqv=qE thus v=E/B. The ratio of the electric field to magnetic field

should be equal to the velocity of the electron.

Explain why a charged particle moves in a spiral path when it is projected into a magnetic field.

When it enters the uniform magnetic field at an angle, instantaneous velocity can be resolved into 2

components – one parallel to the magnetic field and the other perpendicular to the magnetic field.

The parallel component remains unchanged because there is no force along the magnetic field,

resulting in a translational motion. The perpendicular component causes a magnetic force to act

perpendicular to both the magnetic field and velocity which compels the particle to move in a c ircular

path. The resultant motion is a spiral path.

Quantum Physics

What are the 4 results of the photoelectric effect experiments?

Result 1: Current is proportional to intensity. This result can be explained using wave nature and

particulate nature of light.

Result 2: For every material of cathode irradiated, there is a threshold frequency below which no

electrons would be emitted from the cathode regardless of light intensity. This result can be explained

using the particulate nature of light only.

Result 3: The maximum kinetic energy of emitted photoelectrons depends only on the frequency of

the incident radiation, and not its intensity. This result can be explained using the particulate nature

of light only.

Result 4: The emission of photoelectrons starts with no observable time lag, even for very low

intensity of incident radiation. This result can be explained using the particular nature of light only.






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Explain why, for a particular metal and for incident light of suitable frequency, emission of

photoelectrons begins almost instantaneously even if the light has low frequency. [2] ACJC Prelims

08/II/4

For light of different intensity but same frequency, the energy of the photon remains the same.

Photoelectron emission is the result of direct interaction between each photon and an electron and

the entire energy hf of the photon is absorbed by the electron instantaneously. The photon then

ceases to exist. Hence, instantaneous emission of photoelectrons occurs.

Explain why not all photons emit photoelectrons.

The metal surface is reflective. Electrons beneath the surface require more energy in order to be

emitted. Before emission, electrons may collide with other electrons thus losing all its energy.






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Describe and interpret qualitatively the evidence provided by electron diffraction for the wave nature

of particles.

When a beam of electrons passed through a thin film of crystal, the dispersion pattern of theemergent electrons produced on a screen is observed to be similar to the diffraction pattern

produced by a beam of X-ray. This phenomenon provides evidence for the wave nature of particles

like electrons.

Distinguish between ionization energy and work function energy.

Work function energy is the minimum amount of energy required to remove a free electron from the

surface of a metal. Ionisation energy is the minimum amount of energy required to remove an

electron from an isolated atom.

Explain how spectral lines show discrete energy levels in an atom.

An emission spectrum consists of a set of discrete wavelengths. A photon is emitted from an isolated

atom when one of its electrons transits from a higher to a lower energy level. Energy of the photon is

equal to the energy difference between the two levels involved in the transition.

Distinguish between emission and absorption line spectra.

An emission line spectrum of an element consists of coloured lines on a dark background while an

absorption spectrum consists of dark lines on a coloured background at the same discrete wavelength

positions for the same element. For emission spectra, electrons transit from a higher energy level to a

lower energy level. For absorption spectra, electrons transit from a lower energy level to a higher

energy level.

Explain the origins of the features of a typical X-ray spectrum using quantum theory.

It is produced in an X-ray tube where fast electrons strike a metallic target. The spikes are due to

characteristic radiation of the target metal in which electrons transit from very high to low energy

levels. The continuous spectrum is due to losses of various energies when fast moving electrons

collide with atoms of the metallic target.

Explain qualitatively the phenomenon of quantum tunneling of an electron across a potential barrier.

An electron is considered as a wave function. The probability of finding an electron is directly

proportional to the square of the amplitude of the wave function. When the wave function of an

electron encounters a potential barrier, its amplitude decreases exponentially. For a narrow barrier,

the wave amplitude may not become zero after the electron passes through the barrier. Hence, there






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is a non-zero probability that the electron will be found beyond the barrier. This process is called

quantum tunneling.






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Explain how the photoelectric equation expresses the application of the principle of conservation of

energy to this process. [2] SAJC Prelims 08/II/6

The energy of the incident photon is used to do work to release an electron from the atom and toprovide the electron with kinetic energy.

Describe the application of quantum tunneling to the probing tip of a scanning tunneling microscope.

The probing tip of an STM is positioned at a very small distance above the conducting sample surface

which represents the width of the potential barrier. Electrons can cross the potential barrier between

the tip and the surface through the process of quantum tunneling. A small potential difference is

applied between the tip and the surface to produce tunneling current. The tunneling current I

decreases exponentially with the tip surface distance d, so a small change in d will induce a large

change in I.

Explain whether protons of identical kinetic energy as the electron would make a more or less effective

probe of small-scale structures. [2] HCI Prelims 08/II/5

Protons are more effective. They have a larger mass and thus a smaller de Broglie wavelength. The

associated wavelength should be of the same order of magnitude as the dimensions of the observed

object for good resolution of image. Thus for small objects, we need the associated wavelength to be

small as well.

At low temperatures, the absorption line spectrum of hydrogen shows only the spectral lines of the

Lymen series. At higher temperatures, it also displays other series. Explain the above observation. [2]

IJC Prelims 08/II/6

At low temperatures, the hydrogen atoms are mostly in the ground state. Hence only transitions

corresponding to the Lymen series are obtained. At higher temperatures, hydrogen atoms in higher

excited states are present. Hence transitions corresponding to the Balmer and Paschen series are

obtained.

Why is it that sound waves are not normally considered as having particle-like properties, nor

raindrops as having wave-like properties? [6] J89/II/12

The wavelength of a wave is related to its momentum and the Planck constant by the equation

=h/mv. For sound waves, their wavelength is too long hence the sound particles have too little

momentum to exhibit particulate properties. For raindrops, due to their large mass and hence

momentum, their wavelength is too short for them to undergo significant diffraction. Diffraction can

only be observable if the dimension of the aperture is comparable to the wavelength of the wave.






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It has been said that the ground-state energy in the hydrogen atom can be precisely known but that

the excited states have some uncertainty in their values. Is this consistent with the energy-time

uncertainty principle? Explain. [3] PJC Prelims 08/III/5

Electron in the ground state is stable and stays there for a long time. Hence the lifetime t is large and

from the expression Eth/4, E will be small. However, in the excited state, electron is unstable

and stays here for a short time. Lifetime t will be small and hence E will be large. Hence the

statement is consistent with the uncertainty principle.

Discuss the relationship between ground-state energy and the uncertainty principle. Serway Q41-3

Consider a particle bound to a restricted region of space. If its minimum energy were zero, then the

particle could have zero momentum and zero uncertainty in its momentum. At the same time, the

uncertainty in its position would not be infinite, but equal to the width of the region. In such a case,

the uncertainty product xp would be zero, violating the uncertainty principle. This contradiction

proves that the minimum energy of the particle is not zero.

It is said that a helium atom in state E 3 can collide with a neon atom in its ground state and raise the

neon atom to state E 2. The energy of helium state E 2 (20.61ev) is close to, but not exactly equal to, theenergy of neon state E 2 (20.66ev). How can the energy transfer take place if these energies are not

exactly equal? Halliday Q40-13

In addition to quantized energy, a helium atom has kinetic energy; its total energy can equal 20.66eV.

The absorption or emission spectrum of a gas consists of lines that broaden as the density of gas

molecules increases. Why do you suppose this occurs? Serway Q42-19

At low density, the gas consists of essentially separate atoms. As the density increases, the atoms

interact with each other. This has the effect of giving different atoms levels at slightly different

energies, at any one instant. The collection of atoms can then emit photons in lines or bands,narrower or wider, depending on the density.

Lasers and Semiconductors






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With reference to conduction electrons and holes, explain why electrons in solids are represented by

energy bands, whereas those in isolated gas atoms are represented by energy levels. [2] ACJC Prelims

08/III/7

As isolated atoms are far apart, interatomic interactions are negligible. An isolated atom has a well-

defined set of energy levels that electrons can occupy. When the atoms are closer together, the

energy level splits and curves, either upwards or downwards and by varying amounts. Hence, these

energy levels combine to form a set of energy bands.






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Explain how does stimulated emission occur. [2] ACJC Prelims 08/III/4

Incoming photons of suitable frequency f stimulates the transition of an electron from an excited

state to a lower energy one. The result is two photons of exactly the same frequency, phase andpolarization that move in the same direction.

Using the ideas of population inversion and stimulated emission, explain how a laser could deliver an

intense and directed light beam. [4] HCI Prelims 08/II/4

When more atoms are in an upper state than in a lower state, population inversion occurs. Population

inversion is a necessary condition for stimulated emission to dominate. Light and electricity are

commonly used to selectively transfer energy to atoms, exciting them to higher energy levels, most of

the time, a metastable state. The photon that any atom releases has a certain wavelength that is

dependent on the energy difference between the excited state and the ground state. If this photonshould encounter another atom that has an electron in the same excited state, stimulated emission

can occur. The first photon can induce atomic emission such that the subsequent emitted photon

vibrates with the same frequency and direction as the incoming photon. When a stimulated emission

happens, one photon results in two in-phase photons. The other key to a laser is a pair of mirrors, one

at each end of the lasing medium. Photons, with a very specific frequency and phase, reflect off the

mirrors to travel back and forth through the lasing medium. In the process, they stimulate other

electrons to make the downward energy jump and can cause the emission of more photons of the

same frequency and phase. The initial two in-phase photons will create two simulated emissions,

resulting in four in-phase photons and so on. A cascade effect occurs, and soon we have propagated

many photons of the same frequency and in exactly the same direction in phase with the incident

photon. Thus, the light is amplified, resulting in an intense and directed light beam.

Explain why a metal is a better electrical conductor than an insulator?

The conduction band of a metal is partially filled. Hence, electrons are free to move in metal. For an

insulator, the band gap between the conduction band and valence band is wide. Thermal excitation

can only produce an insignificant number of electrons in the conduction band. Hence, it is a poorer

conductor.

Why is a semiconductor a better electrical conductor than an insulator?

For a semiconductor, the band gap between the conduction and valence bands is narrow. At finite

temperatures, thermal excitation will excite a significant number of electrons from the valence to

conduction band.

The energy gap for Silicon is 1.17eV at 0K and 1.14eV at 300K. What do you suppose accounts for the

decrease in energy gap with increasing temperature? Serway Q43-4






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Thermal excitation increases the vibrational energy of the molecules. It makes the crystal lattice less

orderly. We can expect it to increase the width of both the valence band and the conduction band, to

decrease the gap between them.






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Briefly describe the formation of energy bands. [1] CJC Prelims 08/III/5

Electrons in isolated atoms are restricted to discrete energy levels within the atom. When the atoms

are brought closer together, electrons from one atom could also be influenced by the neighbouringatoms. The effect of the overlapping influence of many atoms results in the discrete energy levels

broadening into bands of allowed values. The allowed values in a band are usually closely spaced and

resemble a continuous band.

Using band theory, explain how p-type and n-type extrinsic semiconductors are produced from

intrinsic semiconductors for better electrical conduction. [3] ACJC Prelims 08/III/7

For a p-type semiconductor, when acceptor atoms are added, they provide an acceptor level which is

just above the valence band. The valence electrons of the pure semiconductor can easily be excited to

this level, leaving behind a hole in the valence band. When a potential difference is applied, theseholes will move within the valence band to conduct current.

For a n-type semiconductor, when donor atoms are added, they provide a donor level which is just

below the conduction band. The donor electron can easily be excited to the conduction band, thus

becoming one of the conduction electrons moving freely through the semiconductor. When a

potential difference is applied, these electrons will move in the conduction band in a direction

opposite to that of the electric field to produce current flow.

Discuss qualitatively the origin of the depletion region at a p-n junction and use this to explain how a

p-n junction can act as a rectifier.

Diffusion of the electrons occurs from the n to p-type region of a p-n junction. Holes diffuse in the

opposite direction. They meet and recombine to form a depletion region consisting of positive and

negative immobile ions. An electric field is set up in the depletion region directed from n to p-type

region.

Under forward bias, the external electric field opposes the junction’s electric field. Hence, the

majority charge carriers flow across the junction, resulting in a considerable electric current. Under

reverse bias, the external electric field reinforces the junction’s electric field. Hence, only the minority

charge carriers flow resulting in negligible current flow.

Suggest qualitatively how the presence of a forward-bias voltage sustains a population inversion in the

semiconductor laser.

The forward bias voltage ensures a constant source of free charge carriers, thus there is an increased

number of excited electrons in the conduction band which releases photons when they fill up the

holes in the valence band, sustaining population inversion.






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Nuclear Physics

State and explain if mass if conserved in radioactive decay processes. [2] N01/III/6

Mass is not conserved as shown by the mass defect because some of it is converted into energy.

However, mass-energy is conserved.

State and infer from the results of the alpha-particle scattering experiment the properties of an atom.

N86/II/12

The atom is mostly empty space with a small nucleus at its centre – this accounts for most of the

alpha particles passing straight through. The nucleus is massive – this accounts for its ability to deflect

the high-speed alpha particles. The nucleus is positively-charged – this accounts for its ability to repel

the high-speed alpha particles backwards resulting in a detectable count rate beyond 90 degrees fromthe straight-through axis.

Explain the relevance of binding energy per nucleon to nuclear fission and fusion.

The higher the binding energy per nucleon of a nuclei, the more stable the nuclei is. In nuclear fission

or fusion, the products have higher binding energy per nucleon than the reactants. Hence, they are

more stable than the reactants. Therefore, these processes release energies.

Explain why more energy per nucleon is released in the fusion process than in the fission process.

Energy released in a nuclear reaction is equal to the difference in binding energy between products

and reactants. As indicated by the steep slope of the binding energy curve for light nuclei, the change

in binding energy is much larger for fusion reactions involving lighter nuclei, as compared to that for

fission processes that involve larger nuclei. Therefore more energy per nucleon is released in a fusion

reaction than in fission reaction.

What are the applications and dangers of radioactivity?

Radiation therapy. Tracers and imaging in research and medicine. Damage in biological organism due

to ionization produced in cell. Damage to DNA. Metal and other structural material becomes brittle

and their strength is weakened if the radiation is very intense.

Describe how you would demonstrate that radioactive decay is a random process. [1] CJC Prelims

08/III/8

It may be demonstrated by placing a detector such as a Geiger-Muller tube connected to a counter

near a radioactive source. The fluctuations in count rate show that decay is random.






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Why are gamma emitters preferred over alpha / beta emitters for medical purposes?

Gamma photons are more penetrating, so the radiation can be easily detected by detectors outside

the body and so less amount of radioisotopes are required.

Final Qualitative List

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