IB Physics Core 2009 Draft2

IB Physics 2009: Syllabus SummaryCatherine Zhu

Table of Contents

Key: 2Topic 2: Mechanics 3

2.1. Kinematics.....................................................................................................................................32.2. Forces and dynamics......................................................................................................................32.3. Work, energy, and power...............................................................................................................52.4. Uniform circular motion................................................................................................................6

Topic 3: Thermal Physics 73.1. Thermal Concepts..........................................................................................................................73.2. Thermal Properties of Matter.........................................................................................................7

Specific Heat Capacities, Phase Changes, and Latent Heat..............................................................7Kinetic Model of an Ideal Gas..........................................................................................................8

Topic 4: Oscillations and Waves 104.1. Kinematics of simple harmonic motion.......................................................................................104.2. Energy changes during simple harmonic motion.........................................................................104.3. Forced oscillations and resonance................................................................................................114.4. Wave characteristics.....................................................................................................................114.5. Wave properties...........................................................................................................................13

Topic 5: Electric Currents 155.1. Electric potential difference, current and resistance....................................................................15

Electric potential difference............................................................................................................15Electric current and resistance........................................................................................................15

5.2. Electric Circuits............................................................................................................................16Topic 6: Forces and Fields 17

6.1. Gravitational Force and Field......................................................................................................176.2. Electric Force and Field...............................................................................................................186.3. Magnetic Force and Field............................................................................................................19

Topic 7: Atomic and Nuclear Physics 217.1. The Atom.....................................................................................................................................21

Atomic Structure.............................................................................................................................21Nuclear Structure............................................................................................................................21

7.2. Radioactive Decay.......................................................................................................................22Radioactivity...................................................................................................................................22Half-life...........................................................................................................................................23

7.3. Nuclear Reactions, Fission and Fusion........................................................................................23Nuclear Reactions...........................................................................................................................23Fission and Fusion..........................................................................................................................24

Topic 8. Energy, Power, and Climate Change 268.1. Energy Degradation and Power Generation.................................................................................268.2. World Energy Sources.................................................................................................................268.3. Fossil Fuel Power Production......................................................................................................268.4. Non-Fossil Fuel Power Production..............................................................................................27

Nuclear Power.................................................................................................................................27Solar Power.....................................................................................................................................28Hydroelectric Power.......................................................................................................................28Wind Power.....................................................................................................................................28Wave Power....................................................................................................................................29

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8.5. The Greenhouse Effect.................................................................................................................30Solar Radiation................................................................................................................................30The Greenhouse Effect....................................................................................................................30

8.6. Global Warming...........................................................................................................................30Topic 9. Motion in Fields 31

9.1. Projectile Motion..........................................................................................................................319.2. Gravitational Field, Potential and Energy....................................................................................329.3. Electric Field, Potential and Energy.............................................................................................339.4. Orbital motion..............................................................................................................................34

Topic 10. Thermal Physics 3610.1. Thermodynamics........................................................................................................................36

Gas Laws.........................................................................................................................................3610.2. Processes....................................................................................................................................36

The first law of thermodynamics....................................................................................................3610.3. Second law of thermodynamics and entropy.............................................................................38

Topic 11. Wave Phenomena4011.1. Standing Waves..........................................................................................................................4011.2. Doppler Effect............................................................................................................................4011.3. Diffraction..................................................................................................................................4111.4. Resolution..................................................................................................................................4211.5. Polarization................................................................................................................................42

Topic 12: Electromagnetic Induction 4512.1 Induced Electromotive Force......................................................................................................4512.2 Alternating current......................................................................................................................4512.3. Transmission of electrical power...............................................................................................46

Topic 13: Quantum Physics and Nuclear Physics 4713.1. Quantum Physics........................................................................................................................47

The Quantum Nature of Radiation..................................................................................................47The Wave Nature of Matter............................................................................................................48Atomic Spectra and Atomic Energy States.....................................................................................48

13.2. Nuclear physics..........................................................................................................................49Radioactive Decay..........................................................................................................................50

Topic 14: Digital Technology 5114.1. Analogue and digital signals......................................................................................................5114.2. Data Capture; digital imaging using charge-coupled devices (CCDs)......................................51Glossary..............................................................................................................................................52

Key: Not yet doneDon’t know how to doTo be refined

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Topic 2: Mechanics

2.1. Kinematics2.1.1. Define displacement, velocity, speed, and acceleration. Displacement (a vector quantity) is a measured distance in a given direction in ( ). Speed (a scalar quantity) is the rate at which a moving object covers distance in ( ). Velocity (a vector quantity) is speed in a given direction (in ). Acceleration (a vector quantity) is the rate of change of velocity in a given direction (in ). 2.1.2. Explain the difference between instantaneous and average values of speed, velocity and acceleration.

Average velocity: the change in displacement divided by the change in time. The slope of

the secant line of a displacement-time graph over a given interval.

Instantaneous velocity: the … as the change in time becomes infinitely small. The

derivative of the displacement-time graph function at a given point. Speed and acceleration work in similar ways. 2.1.3. Outline the conditions under which the equations for uniformly accelerated motion may be applied. Objects must be uniformly accelerated. Objects must be in linear motion (traveling in a straight line). 2.1.4. Identify the acceleration of a body falling in a vacuum near the Earth’s surface with the acceleration g of free fall. Constant acceleration at . 2.1.5. Solve problems involving the equations of uniformly accelerated motion.

€

v = u + at (definition of acceleration)

€

s = ut +1

2at 2

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v 2 = u2 + 2as2.1.6. Describe the effects of air resistance on falling objects. Air resistance provides a drag force to objects in free fall. The drag force is directly proportional to the speed of the object. When the drag force reaches the magnitude of the force providing the acceleration, the falling

object will stop accelerating and fall at a constant velocity. This is called the terminal velocity. 2.1.7. Draw and analyze distance-time graphs, displacement-time graphs, velocity-time graphs and acceleration-time graphs. Use calculus as Cathy is too lazy to write otherwise. 2.1.8. Calculate and interpret the gradients of displacement-time graphs and velocity-time graphs, and the areas under velocity-time graphs and acceleration-time graphs.

Displacement-Time Velocity-Time Acceleration-TimeGradient Velocity Acceleration JerkArea Nothing Displacement Velocity2.1.9. Determine relative velocity in one and in two dimensions. Relative velocity is determined by different frames of reference.

2.2. Forces and dynamics2.2.1. Calculate the weight of a body using the expression . Quite a retarded requirement…

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2.2.2. Identify the forces acting on an object and draw free-body diagrams representing the forces acting. ** Picture needed. 2.2.3. Determine the resultant force in different situations. ** Picture needed. 2.2.4. State Newton’s first law of motion. Every object continues in a state of rest or uniform motion in a straight line unless acted upon by

an external force. 2.2.5. Describe examples of Newton’s first law. A ball rolling down a ramp onto a smooth (frictionless) surface will continue to roll forever unless

an external force acts on it. 2.2.6. State the condition for translational equilibrium. Objects can be in equilibrium at either static (not moving) equilibrium or dynamic (moving at

constant speed) equilibrium. The condition for translational equilibrium is that the net force acting on the object is zero.

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F = 0∑ Static equilibrium: book resting on table. Dynamic equilibrium: book pulled along table at constant speed. 2.2.7. Solve problems involving translational equilibrium. * 2.2.8. State Newton’s second law of motion. Acceleration is directly proportional to the force acting and is in the same direction as the applied

force. The rate of change of linear momentum of a particle is directly proportional to the impressed force

acting upon it and takes place in the direction of the impressed force. 2.2.9. Solve problems involving Newton’s second law. * 2.2.20. Define linear momentum and impulse. Linear momentum is defined as the product of an objects mass and its velocity. Impulse is defined as a change in momentum.

A body acted on by a force F will have the acceleration

€

a =F

m. After time t, it will have a velocity

of

€

v = at =Ft

m. Thus

€

Ft = mv . The product of the body’s mass and its velocity gained is equal to the

product of the force acting on it and the time taken. Impulse （冲量） is

€

I = Ft , in units of .

Momentum （动量） is

€

p = mv in units of

€

kg ⋅ms−1. Suppose a body with mass and initial momentum is acted on by a force for a time interval

. The impulse

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Ft = m ⋅a ⋅ t = m v '−v( ) / t ⋅ t = mv'−mv = p'−p . The impulse of a net force acting on a body equals the change of its momentum. 2.2.11. Determine the impulse due to a time-varying force by interpreting a force-time graph. The impulse of a time-varying force is represented by the net area under the function (the integral)

of the force-time graph. 2.2.12. State the law of conservation of linear momentum. Let two bodies

€

m1 and

€

m2 separately with the velocities

€

v1 and

€

v2 collide. Their total initial momentum can be represented by

€

pT = m1v1 + m2v2 . According to Newton’s second law, the force exerted on each body is equal and opposite to the force exerted on the other

€

F1 = −F2. Thus…

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F1t = −F2t

m1 ⋅ v1'−v1( ) / t ⋅ t = −m2 ⋅ v2 '−v2( ) / t ⋅ t

p1'−p1 = p2 − p2 '

p1 + p2 = p1'+ p2 '

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The total initial momentum is equal to the total final momentum. The total momentum of a system remains constant when there are no external forces (or when

the net external force is equivalent to zero) acting on the system. 动量守恒定律：一个系统不受外力或者所受外力之和为零，这个系统的总动量保持不变。2.2.13. Solve problems involving momentum and impulse. *2.2.14. State Newton’s third law of motion. When a force acts on a particle, an equal and opposite force acts on another particle somewhere in

the universe. When two bodies A and B interact, the force that A exerts on B is equal and opposite to the force

that B exerts on A. 2.2.15. Discuss examples of Newton’s third law. Two ice skaters push off of each other. They both slide backwards.

2.3. Work, energy, and power2.3.1. Outline what is meant by work. Work is the product of the magnitude of force and the displacement in the direction of the force. Work is also the scalar (dot) product of force and displacement. 2.3.2. Determine the work done by a non-constant force by interpreting a force-displacement graph. The work done by a non-constant force is represented by the net area under the function (the

integral) of the force-displacement graph. 2.3.3. Solve problems involving the work done by a force. *2.3.4. Outline what is meant by kinetic energy. Energy is the ability to do work. Kinetic energy is the energy an object possesses due to motion.

€

Ek =1

2mv 2

2.3.5. Outline what is meant by change in gravitational potential energy. Potential energy is stored energy.

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ΔEP = mgΔh2.3.6. State the principle of conservation of energy. Energy cannot be created or destroyed; it can only be changed from one form to another. 2.3.7. List different forms of energy and describe examples of the transformation of energy from one form to another. Thermal energy – the kinetic energy of atoms and molecules. Chemical energy – the energy associated with the electronic structure of atoms and therefore

associated with electromagnetic force. Nuclear energy – the energy associated with nuclear structure of atoms and therefore associated

with the strong nuclear force. Electrical energy – the energy associated with an electric current. 2.3.8. Distinguish between elastic and inelastic collisions. Elastic collisions are collisions in which mechanical energy is not lost. Inelastic collisions are collisions in which mechanical energy is lost. 2.3.9. Define power. Power is the rate at which work is performed or the rate at which energy is transmitted.

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P =W

t2.3.10. Define and apply the concept of efficiency. Efficiency is the percentage of useful work out of total work done.

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Efficiency =Useful Work

Total Work Done2.3.11. Solve problems involving momentum, work, energy and power. *

2.4. Uniform circular motionFor a particle traveling at uniform speed in the path of a circle with radius r, the distance traveled is

(where is the angle swept out).

Therefore the (traveling) velocity is given by

€

v =s

t=

rθ

t.

We also define a quantity called the angular velocity:

€

ω =θt

.

The relationship between the two velocities is given by:

€

v = r ⋅θ

t= r ⋅ω

2.4.1. Draw a vector diagram to illustrate that the acceleration of a particle moving with constant speed in a circle is directed towards the centre of the circle.

2.4.2. Apply the expression for centripetal acceleration.

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a =v 2

r For a swept angle the change in v is a vector at right angles to v and of magnitude

€

vdθ , which in turn means that the magnitude of the acceleration is given by

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a =vdθ

dt=

vω ⋅dt

dt= v ⋅ω =

v 2

r.

2.4.3. Identify the force producing circular motion in various situations The force causing the circular motion is called the centripetal force.

€

F = ma =mv 2

r2.4.4. Solve problems involving circular motion.

You wish to have a toy car go in a loop-the-loop around a circular track with radius R. What is the minimum speed the car must have at the top of the loop?

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€

F =mv 2

R= mg

€

v 2

R= g

€

v = gR

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Topic 3: Thermal Physics

3.1. Thermal Concepts3.1.1. State that temperature determines the direction of thermal energy transfer between two objects. Temperature is a scalar quantity that gives indication of the degree of hotness or coldness of a

body. Temperature determines the direction of thermal energy transfer between two bodies in contact

from the body at higher temperature to the body at lower temperature. Thermal equilibrium occurs when all parts of the system are at the same temperature. There is no

exchange of heat. 3.1.2.

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T /K = t /°C + 2733.1.3. State that the internal energy of a substance is the total potential energy and random kinetic energy of the molecules of the substance. Thermal energy of a system is referred to as internal energy—the sum total of the potential energy

and kinetic energy of the particles making up the system. Potential energy of the molecules arises from the forces between them. Kinetic energy of the molecules arises from the translational, rotational, ad vibrational motion of

the particles. 3.1.4. Explain and distinguish between the macroscopic concepts of temperature, internal energy, and heat. Temperature is a measure of the average kinetic energy of the molecules of a substance. Internal Energy is the thermal energy of a system—the sum total of the potential energy and

kinetic energy of the particles making up the system. Heat is the thermal energy that flows from one (high temperature) body to another (of lower

temperature). 3.1.5. Define the mole and molar mass Relative atomic mass is the mass of an atom in units of 1/12 of the mass of a carbon-12 atom. The mole is the amount of substance that contains as many elementary particles as there are in

0.012 kg of carbon-12. Molar Mass is the mass of one mole of a substance (unit is g/mol). The amount of substance is related to the mass and the molar mass according to the following

equation: where n stands for the number of moles of the substance, m stands for the mass of

the substance in grams, and M stands for the molar mass of the substance in g/mol. 3.1.6. Define the Avogadro’s Constant Assumption: equal volumes of gases at the same temperature and pressure contained the same

number of particles. Avogadro’s Constant: one mole of a gas occupies 22.4 at 0 and 101.3kPa pressure and

contains particles.

3.2. Thermal Properties of Matter

Specific Heat Capacities, Phase Changes, and Latent Heat3.2.1. Define specific heat capacity and thermal capacity. Thermal Capacity (also heat capacity) is the amount of heat needed to raise the temperature of a

substance one degree Kelvin (or Celsius). Specific heat capacity is the quantity of thermal energy required to raise the temperature of one

kilogram of a substance by one degree Kelvin.

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The difference is that specific heat capacity does not take into account the mass of the substance. Whereas thermal capacity measures the substance’s ability to absorb heat as an entire object, specific heat capacity measures the substance’s ability to absorb heat per unit mass.

3.2.2. Solve problems involving heat capacities and thermal heat capacities.

€

Heat Capacity =ΔQ

ΔT

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ΔQ = cmΔT3.2.3. Explain the physical differences between the solid, liquid and gaseous phases in terms of molecular structure and particle motion.

Characteristic Solid Liquid GasKinetic Energy Vibrational Vibrational, rotational,

(translational)Mostly translational, higher rotational and vibrational

Potential Energy

High Higher Highest

Mean molecular Separation

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3.2.4. Describe and explain the processes of phase changes in terms of molecular behavior. While melting, vibrational kinetic energy increases and particles gain enough thermal energy to

break from fixed positions. Potential energy of system increases. While freezing, particles lose potential energy until thermal energy of the system is unable to

support distance between particles and is overcome by the attraction force between them. Kinetic energy changes form from vibrational, rotational and part translational to merely vibrational. Potential energy decreases.

While evaporating, certain particles in the liquid gain enough potential energy to escape the intermolecular bonds as a gas. The escape of the higher-energy particles will lower the average kinetic energy and thus lower the temperature.

While boiling, substance gains enough potential energy to break free from inter-particle forces. Similar to evaporation, the only difference being that energy is supplied from external source so there is no decrease in temperature.

While condensing, the energy changes are opposite to that of boiling. 3.2.5. Explain in terms of molecular behavior why temperature does not change during a phase change. During a phase change, the thermal energy gained or lost will go towards increasing or

decreasing the potential energy of the particles to either overcome or succumb to the inter-molecular force that pulls particles together. In the process, the average kinetic energy will not change.

3.2.6. Distinguish between evaporation and boiling. Evaporation is a change from the liquid state to the gaseous state that occurs at a temperature

below the boiling point. See 3.2.4. 3.2.7. Define Specific Latent Heat. Latent heat is the thermal energy that a substance gains or loses during a phase change at

constant temperature. Specific latent heat is the heat required for a unit mass of a substance to undergo a phase change. 3.2.8. Solve problems involving specific latent heat.

Kinetic Model of an Ideal Gas3.2.9. Define pressure. Air / gas pressure is the force gas molecules exert due to their collisions (with an object). 3.2.10. State the assumptions of the kinetic model of an ideal gas. Gases consist of tiny particles called atoms or molecules. 9


The total number of molecules in any sample of a gas is extremely large. The molecules are in constant random motion. The range of the intermolecular forces is small compared to the average separation of the

molecules. The size of the particles is relatively small compared with the distance between them. Collisions of short duration occur between molecules and the walls of the container and the

collisions are perfectly elastic (no loss of kinetic energy). No forces act between particles except when they collide, and hence particles move in straight

lines. Between collisions the molecules obey Newton’s Laws of motion. 3.2.11. State that the temperature is a measure of the average random kinetic energy of the molecules of an ideal gas. Temperature is a measure of the average random kinetic energy of the molecules of an ideal gas. 3.2.12. Explain the macroscopic behavior of an ideal gas in terms of a molecular model. Increase in temperature is equivalent of an increase in average kinetic energy (i.e. a greater

average speed of particle movement). This leads to more collisions and collisions with greater impulse. Thus resulting in higher pressure.

Decrease in volume results in a smaller space for gas particles to move, and thus a greater frequency of collisions. This results in an increase in pressure. Also, depending on the speed at which the volume decreases, particles colliding with the moving container wall may bounce back at greater speeds. This would lead to an increase in average kinetic energy and thus an increase in temperature. An increase in volume would have an opposite effect.

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Topic 4: Oscillations and Waves

4.1. Kinematics of simple harmonic motion4.1.1. Describe examples of oscillations.

Swings of a pendulum A mass attached to a spring attached to a wall that vacillates back and forth.

4.1.2. Define the terms of displacement, amplitude, frequency, period and phase difference. Displacement is the directed distance of an object from its equilibrium position. Amplitude is the magnitude of the maximum displacement, or the maximum distance of an object

from its equilibrium position. Period is the time for one complete cycle of motion. Frequency is the number of cycles per unit time (usually per second). Phase difference is the difference between the phase of a sinusoidally varying quantity and the

phase of a second quantity, which varies sinusoidally at the same frequency (also known as phase angle).

4.1.3. Define simple harmonic motion and state the defining equation as

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a = −ω2x . Simple Harmonic Motion is periodic motion in which the restoring force is proportional to and in

opposite direction of the displacement. General equation for the position of a particle undergoing simple harmonic motion:

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x t( ) = Asin 2π f t + δ( ). A – amplitude. – frequency. – phase of oscillation (initial displacement from equilibrium). As angular velocity , we can substitute

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x t( ) = Asin ω t + δ( ).

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v t( ) =dx

dt= ωAcos ωt + δ( )

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a t( ) =dv

dt= −ω2 sin ωt + δ( ) = −ω2x t( )

4.1.4. Solve problems using the defining equation for SHM.

4.1.5. Apply the equations

€

v = v0 sinωt ,

€

v = v0 cosωt ,

€

v = ±ω x02 − x 2

( ) ,

€

x = x0 cosωt , and

as solutions to the defining equation for SHM.

and respectively represent SHM with an initial position at and 0. The velocity equations are just their derivatives. 4.1.6. Solve problems, both graphically and by calculation, for acceleration, velocity and displacement during SHM.

4.2. Energy changes during simple harmonic motion4.2.1. Describe the interchange between kinetic energy and potential energy during SHM. In an ideal situation, total mechanical energy is conserved.

€

ETotal = EPotential + EKinetic

€

EP =1

2kx 2 =

1

2kA2 cos2 ωt + δ( )

€

EK =1

2mv 2 =

1

2mω2A2 sin2 ωt + δ( ) =

1

2kA2 sin2 ωt + δ( ) as

€

ω 2 =k

m.

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€

ET =1

2kA2 sin2 ωt + δ( ) + cos2 ωt + δ( )[ ] =

1

2kA2

4.2.2. Apply the expressions

€

Ex =1

2mω2 A2 − x 2

( ) for the kinetic energy of a particle undergoing SHM,

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ET =1

2mω2x0

2 for the total energy and for the potential energy.

€

ET =1

2kA2 =

1

2mv 2 +

1

2kx 2

€

v = ±k

mA2 − x 2

( ) = ± ω A2 − x 2( )

€

EK =1

2mv 2 =

1

2mω A2 − x 2

( )

€

EP =1

2kx 2 =

1

2mω2x 2

4.2.3. Solve problems, both graphically and by calculation, involving energy changes during SHM.

4.3. Forced oscillations and resonance4.3.1. State what is meant by damping. Damping: the presence of resistance forces on oscillations. 4.3.2. Describe examples of damped oscillations. Under-damping: when the oscillations continue with decreased amplitude until eventually the

amplitude approaches zero and the oscillations stop. Critical damping: when the amount of damping is large enough for the system to return to

equilibrium as fast as possible without performing oscillations. Over-damping: the system returns to equilibrium without oscillations, but much slower than in the

case of critical damping. 4.3.3. State what is meant by natural frequency of vibration and forced oscillations. Forced oscillations: when an external force is applied on a free system with a frequency , the

system may respond by switching to oscillations with a frequency equal to the driving frequency .

4.3.4. Describe graphically the variation with forced frequency of the amplitude of vibration of an object close to its natural frequency of vibration. For a small degree of damping, the peak of the curve occurs at the natural frequency of the system. The lower the degree of damping, the higher and narrower the curve. As the amount of damping increases, the peak shifts to lower frequencies. At very low frequencies, the amplitude is essentially constant. 4.3.5. State what is meant by resonance. The state in which the frequency of the externally applied periodic force equals the natural

frequency of the system. This results in oscillations with large amplitude. 4.3.6. Describe examples of resonance where the effect is useful and where it should be avoided. Useful: microwave oven, radio. Harmful: bridges, aero plane wings.

4.4. Wave characteristics4.4.1. Describe a wave pulse and a continuous progressive (traveling) wave. A wave is a disturbance that propagates through some material medium or space, a means by

which energy is transferred between two points in a medium without any net transfer of the medium itself, or a method of transferring energy through a medium by means of a distortion that travels away from the place where the distortion of the medium is produced.

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A pulse is a single vibratory disturbance that travels away from its source through the medium. A continuous progressive wave is a continued and repeated wave pulse. 4.4.2. State that progressive (traveling) waves transfer energy. Note that there is no net motion of the medium through which the wave travels. Progressive waves transfer energy through a distortion that travels away from the source of

distortion. There is no net transfer of medium. 4.4.3. Describe and give examples of transverse and longitudinal waves. Transverse waves are waves in which the vibrations of the medium are at right angles to the

direction in which the wave is traveling, e.g. light waves. Longitudinal waves are waves in which the particles of the medium vibrate back and forth along

the path that the wave travels, e.g. sound waves. 4.4.4. Describe waves in two dimensions, including the concepts of wavefronts and of rays. (Huygens-Fresnel Principle) A wavefront is the locus of points having the same phase. Huygen-Fresnel Principle: Each point of an advancing wave front is in fact the center of a fresh

disturbance and the source of a new train of waves; the advancing wave as a whole may be regarded as the sum of all the secondary waves arising from points in the medium already traversed.

A ray is an arrow drawn on a diagram to show the direction of propagation of a set of waves. It is always at right angles to the wavefront.

Collimated light is light whose rays are parallel and thus has a planar wavefront—light that does not disperse over an infinite distance.

4.4.5. Describe the terms crest, trough, compression and rarefaction. Crest: the maximum height of a transverse wave. Trough: the lowest point of a transverse wave. Compression: a region of higher pressure in the medium of a longitudinal wave. Rarefaction: a region of reduced pressure in the medium of a longitudinal wave. 4.4.6. Define the terms displacement, amplitude, frequency, period, wavelength, wave speed and intensity. * Displacement: the amount by which a particle is moved from equilibrium position. Amplitude: the maximum displacement of a particle from its equilibrium position. Period: the time that it takes a particle to make one complete oscillation, or the time that it takes

for the wave to travel a complete wavelength. Wavelength: the distance along the medium between two successive particles with the same

displacement. Wave speed: the speed with which energy is carried in the medium by the wave—only dependent

on the nature and properties of the medium. Intensity: ??4.4.7. Draw and explain displacement-time graphs and displacement-position graphs for transverse and for longitudinal waves.

4.4.8. Derive and apply the relationship between wave speed, wavelength and frequency.

4.4.9. State that all electromagnetic waves travel with the same speed in free space and recall the orders of magnitude of the wavelengths of the principal radiations in the electromagnetic spectrum. * Waves that travel through a material medium are called mechanical waves. Waves that carry various forms of light are electromagnetic waves and travel through space at the

speed of light.

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4.5. Wave properties4.5.1. Describe the reflection and transmission of waves at a boundary between two media. This should include the sketching of incident, reflected and transmitted waves, and the case of reflection at free and fixed ends. * The law of reflection: when a wave is reflected, the angle of incidence equals the angle of

reflection and the incident ray, the normal line, and the reflected ray line in one plane. Reflection (fixed end): when a pulse of a string attached to a support hits the wall it is attached to,

it is reflected—inverted with the same shape (undergone a 180 – degree change in phase). Reflection (free end): like above, the pulse comes back but without being inverted. 4.5.2. State and apply Snell’s law (law of refraction). Snell’s law states that the ratio of the sines of the angles of incidence and refraction is equal to the

ratio of velocities in the two media, or equivalently to the inverse ratio of the indices of refraction.

The indices of refraction n, represent the factor by which light is slowed down within a refractive medium compared to its velocity in a vacuum.

4.5.3. Explain and discuss qualitatively the diffraction of waves at apertures and obstacles. Diffraction refers to the phenomena observed when waves are obstructed by obstacles or pass

through apertures. The magnitude of these effects depends on the wavelength of the waves.

4.5.4. Describe examples of diffraction.

4.5.5. State the principle of superposition and explain what is meant by constructive and by destructive interference. The effect of two separate causes is equal to the sum of the separate causes. Constructive interference occurs when two pulses displaced in the direction overlap. The resultant

displacement is the sum of both displacements.

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Destructive interference occurs when two pulses displaced in opposite directions overlap. The resultant displacement is the difference of both displacements.

4.5.6. State and apply the conditions for constructive and for destructive interference in terms of path difference and phase difference. Two waves arriving at a point in phase (points reach maximum at the same time) with each other

will result in constructive interference. Two waves arriving at a point in anti-phase with each other will result in destructive interference. 4.5.7. Apply the principle of superposition to determine the resultant of two waves. *

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Topic 5: Electric Currents

5.1. Electric potential difference, current and resistance

Electric potential differenceCoulomb’s LawThe force between two charges is directly proportional to the product of the two charges and inversely proportional to the square of the distance between them.

, where is the coulomb’s constant. is the permittivity

constant of space.

Electric-Field StrengthThe electric field strength is at a point is the force felt by one (positive) unit test charge. It is equal to the force per positive unit charge at that point.

The electric field charge due to charge Q is given by:

5.1.1. Define electric potential difference To move a charge from point A to point B, a force must be applied equal to . The work

done is equal to . The electric potential difference between two points in an electric field is defined as the work done

in moving a positive charge from the point at lower potential to the point at higher potential. Positive charge is high potential; negative charge is low potential. Electric potential difference is represented by the symbol V. The unit of electric potential difference is Volt (V) and equivalent to J/C.

(Note: stands for electric potential energy).

5.1.2. Determine the change in potential energy when a charge moves between two points at different potentials. 5.1.3. Define the electronvolt. One electron-volt (1 eV) is defined as the energy acquired by an electron as a result of moving

through a potential difference of one volt. The charge on an electron (or a proton) is . One Joule is the work done or energy required to move a charge of one Coulomb through the

potential difference of one volt. 5.1.4. Solve problems involving electric potential difference. In moving a charge from point A to point B, the force applied is in opposite direction to the electric

field strength. Therefore, .

Electric current and resistance5.1.5. Define Electric Current (I) An electric current is a flow of electric charge.

16


We define electric current as the rate at which charge flows past a given cross-section. It can also be defined in terms of force per unit length between parallel current carrying

conductors.

The unit of electric current is ampere (A), which stands for coulomb per second. 5.1.6. Define Resistance (R) Electrical resistance is a measure of how easily charge flows in a material. The electrical resistance of a piece of material is defined by the ratio of the potential difference

across the material to the current that flows through it.

The unit of resistance is volts per ampere (V/A). There is also a standard unit of ohm Ω that represents the same unit.

The variables of resistance: length, cross-sectional area, resistivity, and temperature. Resistance is proportional to length, inversely proportional to cross-section area, and proportional

to the temperature.

5.1.7. Apply the equation for resistance in the form, , where p is the resistivity of the material

of the resistor. represents the resistivity in Ωm. L represents the length of the conductor in m. A represents the cross section area in . R is the resistance of the conductor in Ω. 5.1.8. State Ohm’s Law. Provided the physical conditions such as temperature are kept constant, the resistance is constant

over a wide rage of applied potential differences, and therefore the potential difference is directly proportional to the current flowing.

The direct current flowing in a circuit is directly proportional to the voltage applied to the circuit. 5.1.9. Compare Ohmic and non-Ohmic behavior. Ohmic behavior is when a resistor / conductor obeys Ohm’s law. I.e. the current is linearly

proportional to the voltage. On a graph with current as the dependent variable and voltage as the independent variable, an

ohmic conductor is shown as linear. For a non-ohmic conductor, such as one where heat increases with voltage, there is a non-linear

relationship between the current and the voltage. The current-voltage graph of a filament lamp resembles a logarithmic curve. 5.1.10. Derive and apply expressions for electrical power dissipation in resistors. Electric power (P) is the rate at which energy is supplied to or used by a device, measured in J/s or

Watts. The energy dissipated is equal to the potential energy lost by the charge as it moves through the

potential difference that exists between the terminals of the load.

5.2. Electric Circuits5.2.1. Define electromotive force (emf).

17


Electromotive force is the work per unit charge made available by an electrical source (i.e. Joules per Coulomb, Volts).

Because of internal resistance in batteries, the voltage dropped across the circuit is often less than the prescribed voltage.

Thus, with r representing the internal resistance of the battery and R representing the total resistance in the circuit (excluding battery internal resistance), .

5.2.2. Describe the concept of internal resistance. Internal resistance is the output impedance, or the resistance of a voltage source itself. 5.2.3. Apply the equations for resistors in series and in parallel. Serieso All components share one current pathway. o All components of the circuit have the same current through them. o The sum of the potential drop across each component is equal to the emf of the cell.

Parallelo There is more than one current pathway. o All components have the same potential difference across them. o The sum of the currents flowing into any poin is equal to the sum of the currents flowing out at

that point. 5.2.4. Draw circuit diagrams.

5.2.5. Describe the use of ideal ammeters and ideal voltmeters. Ammetero Always connected in series with a circuit. o Has a very low resistance so not to alter the current within the circuit. o Has a low resistor connected in parallel with a galvanometer.

Voltmetero Always connected across a device in parallel. o Has a very high resistance so it does not take current from the device measured. o Consists of a high resistor connected in series with a galvanometer.

5.2.6. Describe a potential divider. A potential divider is an electric circuit containing a cell and two resistors in series. 5.2.7. Solve problems involving ohm’s law.

Topic 6: Forces and Fields

6.1. Gravitational Force and Field1) Newton’s Law of Universal GravitationEvery body attracts every other body with a force, which is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers of mass.

,where is the gravitational constant.

This is applicable to point masses, or spherical masses, which act as if all their mass is concentrated at their centers.

2) Gravitational Field StrengthGravitational Field Strength (at a point): the force exerted per unit mass on a particle of small mass placed at that point.

18


(I representing gravitational field strength)

3) Gravitational Potential Assumption: the gravitational potential energy is zero when the distance between two masses is infinity. Gravitational Potential Energy: the work done to move a small mass from the surface of a body to

infinity.

€

W = −GMm

r2

⎛

⎝ ⎜

⎞

⎠ ⎟

R

∞

∫ dr = −GMm1

r2R

∞

∫ d = −GMm −1

r

⎡ ⎣ ⎢

⎤ ⎦ ⎥R

∞

= −GMm 0 − −1

R

⎛

⎝ ⎜

⎞

⎠ ⎟

⎡

⎣ ⎢

⎤

⎦ ⎥= −

GMm

R (unit: J)

Gravitational Potential: the gravitational potential energy per unit mass.

€

V =V

m= −

Gm

R (unit: J/kg)

6.2. Electric Force and Field1) Static Electric Charge

Electron excess = negative charge Electron deficiency = positive charge Unit: Coulomb Charging by friction: rubbing two different insulators together. Charging by induction: charge of charged object opposite to that of charging object. Charging by contact: net charge conserved.

2) The Law of Conservation of Electric ChargeIn a closed system, the amount of charge is constant. Charge is conserved.

3) Coulomb’s LawThe force between two charges is directly proportional to the product of the two charges and inversely proportional to the square of the distance between them.

, where is the coulomb’s constant. is the permittivity

constant of space.

4) Electric-Field StrengthThe electric field strength is at a point is the force felt by one (positive) unit test charge. It is equal to the force per positive unit charge at that point.

The electric field charge due to charge Q is given by:

5) Electronic Potential DifferenceDefinition: the work done moving a positive unit charge from the point of lower potential to the point of higher potential. Note: positive charge is high potential; negative charge is low potential.

19


Where work is the force required to move the charge (equal and opposite to the

force from the electronic field).

Unit: Volt (V) also Joules per Coulomb (J/C).

6) Electrostatic PotentialThe electric potential at a point in an electric field is defined as being numerically equal to the work done in bringing a unit positive charge from infinity to the point.

*Scalar quantity; unit: volt.

€

V =kQ

r2r

∞

∫ dr = kQ r−2

r

∞

∫ dr = kQ −1

r

⎡ ⎣ ⎢

⎤ ⎦ ⎥r

∞

= kQ 0 − −1

r

⎛

⎝ ⎜

⎞

⎠ ⎟

⎡

⎣ ⎢

⎤

⎦ ⎥=

kQ

r

6.3. Magnetic Force and FieldMagnetic Field Strength (B) A magnetic field is a vector field that permeates space and which can exert a magnetic force on

moving electric charges and on magnetic dipoles. Magnetic Field Strength = Magnetic Flux Density = magnetic flux per area Its magnitude is defined in terms of the magnetic force exerted on a moving electrically charged

test particle as

€

B =FBr

q ⋅v .

6.3.1. State that moving charges give rise to magnetic fields. Moving charges give rise to magnetic fields. Magnetic field strength (B): Also magnetic flux density, the magnetic flux per area. Magnetic field

strength is a vector quantity whose magnitude is the strength of a magnetic field at a point in the direction of the magnetic field at that point.

6.3.2. Draw magnetic field patterns due to currents.

Right-hand Rule for electric wire loops. Grip the wire with the fingers of the right hand so that the thumb points in the current’s direction, then direction in which the fingers curl is the direction of the magnetic field.

6.3.3. Determine the direction of the force on a current-carrying conductor in a magnetic field.

20


Vector Cross Product:

€

rF = I ⋅

r B ×

r L ( )

6.3.4. Determine the direction of the force on a charge moving in a magnetic field.

6.3.5. Define the magnitude and direction of a magnetic field. The magnitude of the magnetic field B created by the current varies linearly with the current in the

wire and inversely with the perpendicular distance from the wire: , where I is current, r is

perpendicular distance,

€

μ0 = 4π ×10−7 NA−2 is the magnetic permeability of vacuum. Direction is given by the right-hand rule, in which the fingers grip towards the direction of the

current and the thumb points in the direction of the magnetic field. 6.3.6. Solve problems involving magnetic forces, fields, currents.

21


Topic 7: Atomic and Nuclear Physics

7.1. The Atom

Atomic Structure7.1.1. Describe a model of the atom that features a small nucleus surrounded by electrons. Rutherford Model: the atom consists of a small dense positive nucleus, surrounded by electrons

that orbit the nucleus (as planets orbit the sun) as result of electrostatic attraction between the electrons and the nucleus.

7.1.2. Outline the evidence that supports the nuclear model of an atom. Geiger and Marsden’s experiment: o Alpha particles bombarded at a sheet of gold foil mostly passed through—atoms mostly consist of

empty space. o Particles that were deflected bounced straight back from the foil—the huge deflection of the

alpha particles must have been caused by electrostatic repulsions between the positive alpha particles and a dense, positive nucleus.

7.1.3. Outline one limitation of the simple model of the nuclear atom. Did not explain why electrons surrounding the nucleus were not drawn into the nucleus by strong

electrostatic attractions to the protons of the nucleus. Did not specify composition of nucleus. How did protons in the nucleus stay closely bound when electrostatic forces should have forced

them apart? 7.1.4. Outline evidence for the existence of atomic energy levels. All elements will emit light in characteristic colors when heated. The patterns of light from heated gases differ from those of sunlight, consisting of a series of bright

lights separated by dark gaps—line spectrum. Emission spectrum: a spectrum of light emitted by an element; a series of bright lines, with dark

gaps between the lines where no light is emitted. Absorption spectrum: a bright continuous spectrum covering the full range of visible colors, with

dark lines where the element absorbs light. Spectroscopy: the study of emission and absorption spectra. When an electron falls between two energy levels it will emit a photon equal in energy to the

difference in energy levels. The energy of a photon is dependent on its frequency. Thus, the existence of discrete wavelengths in the spectrum is evidence that energy levels are discrete.

Nuclear Structure7.1.5. Explain the terms nuclide, isotope, and nucleon. Nuclide: a species of atom characterized by the constitution of its nucleus and hence by the

number of protons, the number of neutrons, and the energy content. Nucleon: a proton or neutron. Isotopes: different forms of the same element that contains the same amount of protons but

different amount of neutrons. 7.1.6. Define nucleon number A, proton number Z and neutron number N. Nuclide: a nuclear isotope, , where X is the chemical symbol of the element, A is the mass

number of the isotope, and Z is the atomic number of the element. Nucleon: mass number of a nuclear isotope, is the total number of nucleons (protons and

neutrons) found in the nucleus. 7.1.7. Describe the interactions in a nucleus.

22


Gravitational forces are proportional to the mass of the objects and inversely proportional to the distance between them; thus they are negligible within the nucleus.

Repulsive electromagnetic forces between the protons would cause the nucleus to disintegrate if it were the only force.

The strong nuclear force is an attractive force, which exists between all nucleons to hold them together. It is effective only over a very short range.

The weak nuclear force exists only in the nucleus and is responsible for the disintegration of a neutron into a proton and an electron in beta decay.

7.2. Radioactive Decay

Radioactivity7.2.1. Describe the phenomenon of natural radioactive decay. Radioactive decay: process in which unstable atomic nucleus loses energy by emitting radiation

in form of particles or EM waves, resulting transformation of parent nuclide into daughter nuclide.

Unit: becquerel (Bq), transformation per second. Alpha decay: atomic nucleus emits alpha particle, equivalent to Helium nucleus . E.g. .

Governed by strong nuclear force. Beta decay: atomic nucleus emits beta particle (electron or positron).

o In β-− decay, the weak interaction converts a neutron (n0) into a proton (p+) while emitting an

electron (e-) and an anti-neutrino ( ): . o In β+ decay, energy is used to convert a proton into a neutron, a positron (e+) and a neutrino

( ): energy + p+ →n0 + e+ + . Requires energy thus cannot occur in isolation. Gamma radiation: electromagnetic waves (high-energy photons, ) are emitted during

radioactive decay. E.g. . *Decay Rate Constants half life — symbol t1 / 2 — the time for half of a substance to decay. mean lifetime — symbol τ — the average lifetime of any given particle. decay constant — symbol λ — the inverse of the mean lifetime.

7.2.2. Describe the properties of alpha and beta particles and gamma radiation. 7.2.3. Describe the ionizing properties of alpha and beta particles and gamma radiation. Particle Alpha ( ) Beta ( ) Gamma ( )Nature Helium nucleus Electron PhotonCharge +2e -e 0Mass 4u 1/1850 u 0Penetrative power A few cm of air A few mm of metal Many cm of leadIons per mm of air for 2 MeV particles

10000 100 1

Magnetic fields Is affected Is affected Not affected

7.2.4. Outline the biological effects of ionizing radiation. Prompt effects: effects, including radiation sickness and radiation burns, seen immediately after

large doses of radiation delivered over short periods of time. Delayed effects: effects such as cataract formation and cancer induction that may appear months

or years after a radiation exposure

23


7.2.5. Explain why some nuclei are stable while others are unstable. Some nuclei have a larger neutron-proton ratio and thus a relatively larger strong nuclear

force as opposed to its repelling electromagnetic force. Those nuclei are more stable.

Half-life7.2.6. State that radioactive decay is a random and spontaneous process and that the rate of decay decreases exponentially with time. 7.2.7. Define the term radioactive half-life.

The interval of time required for one-half of the atomic nuclei of a radioactive sample to decay. 7.2.8. Determine the half-life of a nuclide from a decay curve.

QuickTime™ and a decompressor

are needed to see this picture.



7.2.9. Solve radioactive decay problems involving integral numbers of half-lives.

€

A = A0 ⋅1

2

⎛

⎝ ⎜

⎞

⎠ ⎟

t

thalf −life

7.3. Nuclear Reactions, Fission and Fusion

Nuclear Reactions7.3.1. Describe and give an example of an artificial transmutation.

Artificial transmutation is causing particles to decay by bombardment of particles. E.g. Uranium atoms bombarded with neutrons to start fission reaction.

7.3.2. Construct and complete nuclear equations.

24


7.3.3. Define the term unified atomic mass unit. One twelfth of a carbon-12 atom. 1u = 1.6605402 × 10-27 kg

7.3.4. Apply the Einstein mass-energy equivalence relationship.

Calculate the mass defect; multiply by the squared speed of light or by 931.5 MeV to convert to energy. 7.3.5. Define the concepts of mass defect, binding energy and binding energy per nucleon.

Binding energy: the work required to completely separate the nucleons of a nucleus. Mass defect: the difference between the total mass of all nucleons in the atom and the mass of

the atom itself. Equivalent to and lost due to binding energy. Binding energy per nucleon: the work required to remove one nucleon from the nucleus;

roughly the binding energy divided by number of nucleons in nucleus. 7.3.6. Draw and annotate a graph showing the variation with nucleon number of the binding energy per nucleon.

Y: Average binding energy per nucleon (MeV) X: Nucleon number A Note: nickel at 62 is has highest y-value. Rises sharply and gradually falls, concave down

throughout.

7.3.7. Solve problems involving mass defect and binding energy.

ii) The binding energy required to assemble two atoms of H is larger than that required to assemble one atom of He. Therefore when two atoms of H combine to form one atom of He, energy must be released.

Fission and Fusion7.3.8. Describe the processes of nuclear fission and nuclear fusion.

Nuclear fission: process in which a heavy nucleus splits up into lighter nuclei. 25


Large amounts of energy produced, can be self-sustaining due to chain reactions. Nuclear fusion: joining of two light nuclei into a heavier one. High temperatures required to provide sufficient kinetic energy to approach each other,

overcoming electrostatic repulsion. 7.3.9. Apply the graph in 7.3.6. to account for the energy release in the processes of fission and fusion.

7.3.10. State that nuclear fusion is the main source of the Sun’s energy. Nuclear fusion is the main source of the Sun’s energy.

7.3.11. Solve problems involving fission and fusion reactions.

26


Topic 8. Energy, Power, and Climate Change

8.1. Energy Degradation and Power Generation8.1.1. State that thermal energy may be completely converted to work in a single process, but that continuous conversion of this energy into work requires a cyclical process and the transfer of some energy from the system. 8.1.2. Explain what is meant by degraded energy. Degraded energy: energy that has become less useful, i.e. cannot perform mechanical work due to

being transformed into other forms of energy, e.g. thermal energy. 8.1.3. Construct and analyze energy flow (Sankey) diagrams and identify where the energy is degraded.

Energy is degraded wherever there is an outwards arrow.

8.1.4. Outline the principal mechanisms involved in the production of electrical power. Electrical energy may be produced by rotating coils in a magnetic field.

8.2. World Energy SourcesFuel: a substance that can release energy by changing its chemical or nuclear structure. 8.2.1. Identify different world energy sources. Fossil Fuels emitting CO2

o Coalo Oil and gaso Wood and biomass

Nuclear fuel Energy derived from the Sun

o Solar energyo Hydroelectric powero Wind powero Wave power

Energy sources not derived from the Suno Tidal power: o Geothermal energy

The Sun is the prime energy source for the world’s energy. 8.2.2. Outline and distinguish between renewable and non-renewable energy sources. 8.2.3. Define the energy density of a fuel. Energy density: the amount of energy that can be extracted per kilogram of fuel. Unit: 8.2.4. Discuss how choice of fuel is influenced by its energy density.

27




8.2.5. State the relative proportions of world use of the different energy sources that are available. Oil: 38%; Coal: 26%; Gas: 23%; Hydroelectric: 6%; Nuclear: 6%; Renewables: 1%. Renewable energy: Solar: 44%; Wind: 27%; Geothermal: 17%; Biofuels: 12%. 8.2.6. Discuss the relative advantages and disadvantages of various energy sources.

8.3. Fossil Fuel Power Production8.3.1. Outline the historical and geographical reasons for the widespread use of fossil fuels. Industrialization led to a higher rate of energy usage, leading to industry being developed near

large deposits of fossil fuels. 8.3.2. Discuss the energy density of fossil fuels with respect to the demands of power stations. Estimate the rate of fuel consumption by power stations .8.3.3. Discuss the relative advantages and disadvantages associated with the transportation and storage of fossil fuels. 8.3.4. State the overall efficiency of power stations fuelled by different fossil fuels. Coal: 40% Gas: 59%, up to 80% if waste heat is used to heat houses. 8.3.5. Describe the environmental problems associated with the recovery of fossil fuels and their use in power stations.

8.4. Non-Fossil Fuel Power Production

Nuclear Power8.4.1. Describe how neutrons produced in a fission reaction may be used to initiate further fission reactions (chain reaction). Energy is required to split a U-236 nucleus. This can be supplied by adding a neutron to the U-236

nuclei, which increases the binding energy and causes the nucleus to split in two. Extra neutrons are produced, which can go on to react with other U-236 nuclei in a self-sustaining

chain reaction. However they must be first slowed down to less than 1 eV. Critical mass: the minimum mass required for a chain reaction. 8.4.2. Distinguish between controlled nuclear fission (power production) and uncontrolled nuclear fission (nuclear weapons).

8.4.3. Describe what is meant by fuel enrichment. Uranium comes naturally as 99.3% U-238. However only U-235 is used in the reaction process. The process of increasing the percentage of U-235 in the material is called enrichment. 3% U-235 must be reached in order to be power a nuclear reactor. 8.4.4. Describe the main energy transformations that take place in a nuclear power station. 8.4.5. Discuss the role of the moderator and the control rods in the production of controlled fission in a thermal fission reactor. Moderator: material whose atoms slow down neutrons to make them suitable for reaction. Control rod: material that absorbs excess neutrons to prevent an uncontrollably large release of

energy. 8.4.6. Discuss the role of the heat exchanger in a fission reactor. To transfer heat from the reactor to the turbine, the medium through which nuclear energy

converts to heat and then to motion and electricity. 8.4.7. Describe how neutron capture by a nucleus of uranium-238 results in the production of a nucleus of plutonium-239. 8.4.8. Describe the importance of plutonium-239 as a nuclear fuel. Plutonium-239 is used as a fuel in other types of reactors.

28


8.4.9. Discuss safety issues and risks associated with the production of nuclear power. Thermal meltdown: Nuclear waste: Mining of uranium: environmental damage, workers safety hazards. Possibility that a nuclear power program may also be used to produce nuclear weapons. 8.4.10. Outline the problems associated with producing nuclear power using nuclear fusion.

8.4.11. Solve problems on the production of nuclear power.

Solar Power8.4.12. Distinguish between a photovoltaic cell and a solar heating panel in terms of energy transfers and utility. Solar panel is used for central heating or for making

hot water for household use, placed on roofs of houses, consisting of metal absorber, water pipes, and glass. Energy is merely converted from solar power, electromagnetic waves of light, to heat.

A photovoltaic cell converts solar radiation into electrical energy.

8.4.13. Outline reasons for seasonal and regional variation sin the solar power. The power per unit area received at a distance r from

the sun is called the intensity I:

€

I =P

4πr2 .

On Earth, this amounts to roughly 1400 W/m2, the solar constant, the power received by one square meter placed normally to the path of the incoming rays at a distance of

€

1.50 ×1011m from the sun. Due to the time of the day, this may vary

€

±1.5% daily; due to Earth’s elliptical orbit, this may vary an additional

€

±4.0% seasonally. 8.4.14. Solve problems involving specific applications of photovoltaic cells and solar heating panels.

Hydroelectric Power8.4.15. Distinguish between different hydroelectric schemes. Pumped storage schemes: when energy from nearby coal plants are used to pump water up a

reservoir by night. Run-of-the-river power stations: stations that use water diverted from a fast-flowing river without

damming the river. Harnessing tidal power: 8.4.16. Describe the main energy transformations that take place in hydroelectric schemes.

The rate of change of the potential energy converted into kinetic

energy is

€

P =mgh

Δt=

ρΔVgh

Δt= ρ

ΔV

Δtgh = ρQgh , where Q is known

as the volume flow rate (volume per second).

8.4.17. Solve problems involving hydroelectric schemes.

29


Wind Power1. Basic wind: Sun heats the air, which rises.

Cool air moves into low-pressure area. Movement is wind.

2. Coastal wind: water has larger specific heat capacity than land and therefore does not rise in temperature as much as land. Hot air from land rises, cool air from sea moves in.

3. Katabatic wind: high pressure from cold air presses down at the top of a mountain, resulting in airflow downhill.

8.4.18. Outline the basic features of a wind generator. Consists of a horizontal axis with two blades.

8.4.19. Determine the power that may be delivered by a wind generator, assuming that the wind kinetic energy is completely converted into mechanical kinetic energy, and explain why this is impossible.

Consider the above tube of air with density

€

ρ , velocity

€

v , cross-sectional area

€

A . The kinetic

energy of this air tube is given by:

€

Ek =1

2mv 2 =

1

2ρAvΔt( ) ⋅v 2 =

1

2ρAΔtv 3 .

Kinetic energy per unit time gives power:

€

P =Ek

Δt=

1

2ρAv 3 .

The underlying assumption of this calculation is that the wind is stopped by the wind turbine, which is not the case.

8.4.20. Solve problems involving wind power.

Wave Power8.4.21. Describe the principle of operation of an oscillating water column (OWC) ocean-wave energy converter. The waves make the water alternately rise and fall, causing the air within the column to move out

and in, turning the turbine.

30


8.4.22. Determine the power per unit length of a wavefront, assuming a rectangular profile for the wave.

€

P

L=

pvgA2

28.4.23. Solve problems involving wave power.

8.5. The Greenhouse Effect

Solar Radiation

The Greenhouse Effect

8.6. Global Warming

31


Topic 9. Motion in Fields

9.1. Projectile Motion9.1.1. State the independence of the vertical and the horizontal components of velocity for a projectile in a uniform field.

9.1.2. Describe (prove) and sketch the trajectory of projectile motion as parabolic in the absence of air resistance.

9.1.3. Describe qualitatively the effect of air resistance on the trajectory of a projectile. The path is no longer parabolic The maximum height and range decreases The angle at which the projectile impacts the ground steepens. 9.1.4. Solve problems on projectile motion.

32


9.2. Gravitational Field, Potential and Energy9.2.1. Define gravitational potential and gravitational potential energy.

Gravitational potential energy: vector quantity

€

EP = −GMm

r; the energy stored in the gravitational

field of the two masses when they are separated by a distance r—the total work done in moving the mass from infinity to r.

Gravitational potential: a scalar quantity, the work done per unit mass in bringing a small point mass from infinity to a point. If work done is W, the gravitational potential is the ratio of work

done to the mass m:

€

V =W

m=

EP

m=

−GMm

rm

= −GM

r; units:

€

JKg−1.

9.2.2. State and apply the expression for gravitational potential due to a point mass. (See 9.2.1.) 9.2.3. State and apply the formula relating gravitational field strength to gravitational potential gradient. (See 9.2.1.)

€

EP = mV9.2.4. Determine the potential due to one or more point masses. The gravitational potential is a field but it is a scalar not a vector. One way of thinking of the gravitational potential is that it is the gravitational potential energy per unit mass. The gravitational potential due to a point mass (or uniform sphere) can be described mathematically as:

Where V is the gravitational potential. The gravitational potential gives us a way to describe “gravity” due to one mass. We are able to attain some information about gravity with out having to use or know about a second mass. 9.2.5. Describe and sketch the pattern of equipotential surfaces due to one and two point masses. An equipotential surface consists of all points with the same potential.

9.2.6. State the relation between equipotential surfaces and gravitational field lines. Consider two equipotential surfaces distance

€

Δr apart, with gravitational potential difference

€

ΔV . The work done moving a point mass from one surface to another is given by

€

W = mΔV . It can also be given by force times distance:

€

W = Fd = mgΔr

€

mΔV = mgΔr ⇒ g =ΔV

Δr The gravitational field strength is therefore given by the rate of change of gravitational potential

difference with respect to distance. Equipotential surfaces and gravitational field lines are at right angles to each other. WHY???9.2.7. Explain the concept of escape speed from a planet.

Total energy of mass m moving near large stationary mass M:

€

E =1

2mv 2 −

GMm

r; v is the speed of

m when at distance r from M. o If

€

E > 0: mass escapes and never returns. o If

€

E = 0: mass just barely escapes.

33


o If

€

E < 0: mass moves out a certain distance and returns.

Therefore the smallest value of v such that m will be able to escape must fit

€

E =1

2mv 2 −

GMm

r= 0 .

Escape velocity,

€

v =2GM

r, is the minimum velocity needed by a mass launched from the surface

of the Earth to reach infinity and stop there. 9.2.8. Derive an expression for the escape speed of an object from the surface of a planet. (See 9.2.7.)9.2.9. Solve problems involving gravitational potential energy and gravitational potential.

9.3. Electric Field, Potential and EnergyPrelims (See Topic 6) Electric field - the force per unit charge experienced by a small positive test charge

o

€

E =F

q

o Unit:

€

NC−1

By Coulomb’s Law (

€

F = kQ1 ⋅Q2

r2 ), the force experienced by a test charge placed a distance r from a

point charge Q is given by

€

F = kQq

r2 .

The electric field from a single point charge Q at a point a distance r away is therefore

€

E =F

q= k

Q

r2 .

9.3.1. Define electric potential and electric potential energy. The electric potential at a point in an electric field is defined as being numerically equal to the

work done in bringing a unit positive charge from infinity to that point.

o *Scalar quantity; unit: volt.

€

V =kQ

r

o

€

V =kQ

r2r

∞

∫ dr = kQ r−2

r

∞

∫ dr = kQ −1

r

⎡ ⎣ ⎢

⎤ ⎦ ⎥r

∞

= kQ 0 − −1

r

⎛

⎝ ⎜

⎞

⎠ ⎟

⎡

⎣ ⎢

⎤

⎦ ⎥=

kQ

r Electric Potential Energy : the work done moving a positive unit charge from the point of lower

potential to the point of higher potential. o Note: positive charge is high potential; negative charge is low potential.

o

€

ΔV =ΔEp

q=

ΔW

q Where work is the force required to move the charge (equal and

opposite to the force from the electronic field).

o Unit: Volt (V) also Joules per Coulomb (J/C). 9.3.2. State and apply the expression for electric potential due to a point charge.

Electric potential due to a point charge is given by

€

V = kQ

r.

34


The red circles represent equipotential lines, and the black lines

9.3.3. State and apply the formula relating electric field strength to electric potential gradient.

€

E = −dV

dr=

ΔV

Δr9.3.4. Determine the potential due to one or more point charges. The electric potential (voltage) at any point in space produced by any number of point charges can be calculated from the point charge expression by simple addition since voltage is a scalar quantity. The potential from a continuous charge distribution can be obtained by summing the contributions from each point in the source charge.

9.3.5. Describe and sketch the pattern of equipotential surfaces due to one and two point charges. Equipotential surfaces are always perpendicular to electric field lines. No work is required to move a charge along an equipotential. Equipotential surfaces connect points of the same potential. 9.3.6. State the relation between equipotential surfaces and electric field lines.

Equipotential surfaces are always perpendicular to electric field lines.

Here, in a constant field (parallel conducting plates like a capacitators), the field lines (dashed) are perpendicular to the plates.

The equipotential surfaces are parallel to the plates.

9.3.7. Solve problems involving electric potential energy and electric potential.

9.4. Orbital motion 9.4.1. State that gravitation provides the centripetal force for circular orbital motion.

€

F =GMm

r2 provides a centripetal force for circular motion.

Let

€

F =GMm

r2 = m ⋅v 2

r (centripetal force of circular motion).

€

v 2 =GM

r will give the square of the

orbital velocity of m. 9.4.2. Derive Kepler’s third law.

35


Let T represent the time taken for an orbiting satellite or planet to make one revolution around a

large mass. Therefore,

€

v =2πr

T. Substituting formula for orbital velocity,

€

2πr

T

⎛

⎝ ⎜

⎞

⎠ ⎟2

=GM

r⇒ T =

4π 2

GMr3 .

Kepler’s Third Law: the period of a planet around the sun is proportional to the 3/2 power of the orbit radius.

9.4.3. Derive expressions for the kinetic energy, potential energy and total energy of an orbiting satellite. 9.4.4. Sketch graphs showing the variation with orbital radius of the kinetic energy, gravitational potential energy and total energy of a satellite. 9.4.5. Discuss the concept of “weightlessness” in orbital motion, in free fall and in deep space. In orbit, the net force on an astronaut is given by the difference between his weight and the

reaction force from the floor. This is also the centripetal force acting on him.

Therefore:

€

GMm

r2− N = m

v 2

r⇒ N = G

Mm

r2− m

v 2

r=

m

r

GM

r− v 2 ⎛

⎝ ⎜

⎞

⎠ ⎟.

However, orbital velocity is given by:

€

v 2 =GM

r.

Thus, the reaction force N = 0. The astronaut feels weightless because he experiences no reaction force from the floor.

In free fall, the astronaut is falling at the same speed as the spacecraft. There is therefore no reaction force from the floor and the astronaut feels weightless.

9.4.6. Solve problems involving orbital motion.

36


Topic 10. Thermal Physics

10.1. Thermodynamics

Gas Laws10.1.1. State the equation of state for an ideal gas.

The Pressure Law: At constant V,

€

p

T= k

Charle’s Law: At constant p,

€

V

T= k .

Boyle’s Law: At constant T,

€

pV = k .

€

PV = nRT R is the molar gas constant:

€

R = 8.314mol−1K−1 . 10.1.2. Describe the difference between an ideal gas and a real gas. An ideal gas is one that follows the gas laws for all values of p, V, and T. For an ideal gas: o Newton’s laws apply to molecular behavior. o There are no intermolecular forces. The molecules are treated as points. o The molecules are in random motion. o The collisions between the molecules are elastic (no energy is lost). o There is no time spent in these collisions.

The pressure of a gas is a result of collisions between the molecules and the walls of the container. Real gases can approximate to ideal behavior if intermolecular forces are small enough to be

ignored. The density / pressure must be low and the temperature must be high. 10.1.3. Describe the concept of the absolute zero of temperature and the Kelvin scale of temperature. Absolute zero is 0 on the Kelvin scale and -273 on the Celsius scale. It is characterized by the

complete absence of heat – the point at which all atomic and molecular energy ceases. There is no kinetic energy between the molecules.

10.1.4. Solve problems using the equation of state of an ideal gas.

10.2. Processes

The first law of thermodynamics10.2.1. Deduce an expression for the work involved in a volume change of a gas at constant pressure.

€

ΔW = F ⋅Δs = PA ⋅Δs (s represents the distance shrunk, P the pressure, A the area) 10.2.2. State the first law of thermodynamics. The change in the internal energy of a closed thermodynamic system is equal to the sum of the

amount of heat energy supplied to the system and the work done on the system.

€

ΔU = Q −W Note that for an ideal gas, it assumed that there are no intermolecular forces. Thus the internal

energy of the gas (defined as the total kinetic energy of the molecules of the gas plus the potential energy associated with the intermolecular forces) is reduced to the total kinetic energy of the

molecules. This is given by:

€

U = Ek =3

2nRT .

10.2.3. Identify the first law of thermodynamics as a statement of the principle of energy conservation. Energy can be transformed (changed from one form to another), but it can neither be created nor

destroyed. The increase in the internal energy of a system is equal to the amount of energy added by heating

the system, minus the amount lost as a result of the work done by the system on its surroundings.

37


10.2.4. Describe the isochoric (isovolumetric), isobaric, isothermal and adiabatic changes of a state of an ideal gas. Isochoric: constant volume.

Isobaric: constant pressure.

Isothermal: constant temperature.

Adiabatic: no heat transferred.

A rapid compression or expansion is approximately adiabatic.

10.2.5. Draw and annotate thermodynamic processes and cycles on P-V diagrams.







38








10.2.6. Calculate from a P-V diagram the work done in a thermodynamic cycle.

Work done equals the net area within the quadrilateral (the cycle).

10.2.7. Solve problems involving state changes of a gas.

10.3. Second law of thermodynamics and entropy10.3.1. State that the second law of thermodynamics implies that thermal energy cannot spontaneously transfer from a region of low temperature to a region of high temperature. i. Heat Engine (Kelvin-Planck) Statement : It is impossible to extract an amount of heat QH from a hot

reservoir and use it all to do work W. Some amount of heat QC must be exhausted to a cold reservoir. This precludes a perfect heat engine.

ii. Refrigerator (Clausius) Statement : It is not possible for heat to flow from a colder body to a warmer body without any work having been done to accomplish this flow. This precludes a perfect refrigerator.

iii. Entropy Statement : In any cyclic process the entropy will either increase or remain the same. 10.3.2. State that entropy is a system property that expresses the degree of disorder in the system.

A change in entropy is defined as

€

dS =dQ

T, which can be integrated to give entropy as

€

ΔS =ΔQ

T.

The change in entropy can be described as the heat added per unit temperature and has the units of Joules/Kelvin

€

JK−1.

39


10.3.3. State the second law of thermodynamics in terms of entropy changes. The entropy of the universe can never decrease. Whenever thermal energy flows from a hot object to a colder object, overall the total entropy has

increased. 10.3.4. Discuss examples of natural processes in terms of entropy changes. A refrigerator taking thermal energy from the ice box and ejecting it into the surroundings.

40


Topic 11. Wave Phenomena

11.1. Standing Waves11.1. Describe the nature of standing waves. * No energy or momentum is transferred. The distance between two successive nodes or two successive antinodes is half a wavelength. Students should consider energy transfer, amplitude and phase. *11.2. Explain the formation of one-dimensional standing waves. When two waves of the same speed and wavelength and equal or almost equal amplitudes traveling

in opposite directions meet, a standing wave is formed. It is the result of the superposition of the two waves traveling in opposite directions.

A standing wave has nodes, points at which the displacement is always zero, and antinodes, points at which displacement is at maximum.

11.3. Discuss the modes of vibration of strings and air in open and in closed pipes.

String fixed at both ends: for the nth harmonic the wave has n antinodes.

String fixed at one end (closed pipe):

String free at both ends (open pipe):

The lowest-frequency mode is known as the first harmonic or fundamental frequency. 11.4. Compare standing waves and traveling waves. 11.5. Solve problems involving standing waves.

11.2. Doppler Effect11.2.1. Describe what is meant by the Doppler effect. The change in frequency received by an observer compared with the frequency at which it was

emitted, due to motion between the emitter and receiver.

The frequency observed is given by: . The positive or negative signs are

such that if the movement between the receiver and transmitter is towards each other, a larger frequency will be observed and vice versa.

11.2.2. Explain the Doppler effect by reference to wavefront diagrams for moving detector and moving source situations. 1. Moving Source; Stationary Observer

Towards the observer: because the stationary

observer has a velocity of zero; the distance between the transmitter and receiver is decreasing (thus denominator must decrease).

Away from the observer: because the stationary

observer has a velocity of zero; the distance between the transmitter and receiver is increasing (thus denominator must increase).

2. Moving Observer; Stationary Source

Towards the source: because the stationary

transmitter has a velocity of zero; the distance between the transmitter and receiver is decreasing (thus numerator must increase).

41


Away from the source: because the stationary

transmitter has velocity of zero; the distance between the transmitter and receiver is increasing (numerator must decrease).

11.2.3. Apply the Doppler effect equations for sound. A sound wave of frequency 500 Hz is emitted by a stationary source toward a receding observer. The signal is reflected by the observer and received by the source, where the frequency is measured and found to be 480 Hz. What is the speed of the observer? Answer: let represent the speed of the observer.

The frequency received by the observer should be:

The frequency received back at the transmitter should be: ,

where represents the frequency reflected by the observer.

Rearranging algebraic terms from the equation above, .

The frequency reflected by the observer should be the same as the frequency it receives.

Therefore: .

11.2.4. Solve problems on the Doppler effect for sound. 11.2.5. Solve problems on the Doppler effect for electromagnetic waves using the approximation,

.

11.2.6. Outline an example in which the Doppler effect is used to measure speed. Blood-flow measurements Measurement of vehicle speeds

11.3. Diffraction11.3.1. Sketch the variation with the angle of diffraction of the relative intensity of light diffracted at a single slit.

If wavelength is larger than aperture , then diffraction occurs. Intensity is 1 at 0 degrees and 0 at each minimum. Bell-shaped curve.

42


11.3.2. Derive the formula for the position of the first

minimum of the diffraction pattern produced at a single slit.

If the distance between opening and screen is much larger than the opening, the paths of light can be thought of as parallel and eventually reaching the same point. The distances bc, de, fg, will therefore be the respective path differences. This needs to equal a multiple of in order for the two waves to cancel out.

In general, we get destructive interference at points P if

, n = 1, 2, 3... If the angle is sufficiently small, . For a circular slit, the formula

becomes: .

11.3.3. Solve problems involving single-slit diffraction.

11.4. Resolution11.4.1. Sketch the variation with the angle of diffraction of the relative intensity of light emitted by two point sources that has been diffracted at a single slit.

11.4.2. State the Rayleigh criterion for images of two sources to be just resolved. The Rayleigh criterion states that two sources are just resolved if the central maximum of the

diffraction pattern of one source falls on the first minimum of the other. 11.4.3. Describe the significance of resolution in the development of devices such as CD’s and DVD’s, the electron microscope and radio telescopes.

11.5. Polarization11.5.1. Describe what is meant by polarized light. Polarized light is light whose waves only oscillate along one plane. 11.5.2. Describe polarization by reflection.

43


11.5.3. State and apply Brewster’s law:

€

tanθB =n1

n2

.

Brewster's angle (also known as the polarization angle) is an angle of incidence at which light with a particular polarization is perfectly transmitted through a surface, with no reflection.

11.5.4. Explain the terms polarizer and analyzer. Polarizer: a sheet of material with molecular structure that only allows a specific orientation of the

electric field to go through. Analyzer: a polarizer used for the purpose of determining whether light is polarized. 11.5.5. Calculate the intensity of a transmitted beam of polarized light using Malus’ law. The resultant electric field of an electromagnetic wave whose original electric field

€

E0 makes an angle

€

θ with the transmission axis is given by

€

E = E0 cosθ .

The transmitted intensity I is proportional to the square of the electric field.

€

I = I0 cos2 θ11.5.6. Describe what is meant by an optically active substance. The rotation of the plane of polarization is called optical activity. Materials showing this

phenomenon are said to be optically active. The angle by which the plane of polarization rotates depends on the distance traveled within the

material and the wavelength of the light used. 11.5.7. Describe the use of polarization in the determination of the concentration of certain solutions.

44


The amount of rotation of the plane of polarization in a sugar solution depends on the concentration of the solution. Therefore measurement of the plane of polarization can help determine the angle of rotation of the polarization plane.

11.5.8. Outline qualitatively how polarization may be used in stress analysis. For certain materials, the degree to which the substance becomes optically active is proportional

to the stress. Therefore examination of the polarization pattern occurring through this material will give information as to its level / state of stress.

11.5.9. Outline qualitatively the action of liquid-crystal displays (LCD). To create an LCD, you take two pieces of polarized glass. A special polymer that creates

microscopic grooves in the surface is rubbed on the side of the glass that does not have the polarizing film on it. The grooves must be in the same direction as the polarizing film. The grooves will cause the first layer of molecules to align with the filter's orientation. Then add the second piece of glass with the polarizing film at a right angle to the first piece. Each successive layer of TN molecules will gradually twist until the uppermost layer is at a 90-degree angle to the bottom, matching the polarized glass filters.

As light strikes the first filter, it is polarized. The molecules in each layer then guide the light they receive to the next layer. As the light passes through the liquid crystal layers, the molecules also change the light's plane of vibration to match their own angle. When the light reaches the far side of the liquid crystal substance, it vibrates at the same angle as the final layer of molecules. If the final layer is matched up with the second polarized glass filter, then the light will pass through.

If we apply an electric charge to liquid crystal molecules, they untwist. When they straighten out, they change the angle of the light passing through them so that it no longer matches the angle of the top polarizing filter. Consequently, no light can pass through that area of the LCD, which makes that area darker than the surrounding areas.



11.5. 10. Solve problems involving the polarization of light.

45


Topic 12: Electromagnetic Induction

12.1 Induced Electromotive Force

12.1.1. Describe the inducing of an e.m.f by relative motion between a conductor and a magnetic field.

Wire of length L is shifted downwards with velocity v perpendicular to magnetic field of flux density B.

According to right hand rule (consider negative electron charge), there will exist a force due to the magnetic field acting on the electrons in the wire, pushing them towards the right.

Thus, electrons will flow to the right, forming an electric potential

across the wire equal to

€

V , the value of the electric field will be

€

E =V

L.

The flow of electrons will only stop when the magnetic force pushing the electrons towards the end of the wire equals the electrostatic repulsive force between the electrons flowing towards the ends and the electrons already there. I.e.

€

FE = eE = FM = evB ⇒ V = vBL .

Note:

€

E =F

q=

kQ

r2 ;

€

EEPE = W = F ⋅d = E ⋅q ⋅d =kQq

r;

€

ΔV =ΔEEPE

q=

ΔW

q=

kQ

r12.1.2. Derive the formula for the emf induced in a straight conductor moving in a magnetic field. See above. 12.1.3. Define magnetic flux and magnetic flux linkage. Magnetic flux:

€

Δφ=BΔA or

€

φ=BAcosθ . Flux linkage:

€

φ=NBAcosθ , where N represents the number of loops in the wire. Unit:

€

1Wb =1Tm2

12.1.4. Describe the production of an induced emf by a time-changing magnetic flux. A stationary magnet near a loop will have no effect, but a moving magnet towards and from a loop

will induce an emf:

€

ε =−NΔΦ

Δt.

12.1.5. State Faraday’s law and Lenz’s law. Faraday’s Law: the induced emf is equal to the negative rate of change of magnetic flux:

€

ε =−NΔφ

Δt.

Lenz’s Law: the induced current will be in such a direction as to oppose the change in magnetic flux that created the current.

12.1.6. Solve electromagnetic induction problems.

12.2 Alternating current

12.2.1. Describe the emf induce in a coil rotating within a uniform magnetic field.

12.2.3. Describe the effect on the induced emf of changing the generator frequency.

12.2.4. Discuss what is meant by the root mean squared (rms) vale of an alternating current or voltage.

12.2.5. State the relation between peak and rms values for sinusoidal currents and voltages.

12.2.6. Solve problems using peak and rms values.

46


12.2.7. Solve AC circuit problems for ohmic resistors.

12.2.8. Describe the operation of an ideal transformer.

12.2.9. Solve problems on the operation of ideal transformers.

12.3. Transmission of electrical power

12.3.1. Outline the reasons for power losses in transmission lines and real transformers.

12.3.2. Explain the use of high-voltage step-up and step-down transformers in the transmission of electrical power.

12.3.3. Solve problems on the operation of real transformers and power transmission.

12.3.4. Suggest how extra-low-frequency electromagnetic fields, such as those created by electrical appliances and power lines, induce currents within a human body.

12.3.5. Discuss some of the possible risks involved in living and working near high-voltage power lines.

47


Topic 13: Quantum Physics and Nuclear Physics

13.1. Quantum Physics

The Quantum Nature of Radiation13.1.1. Describe the photoelectric effect. Emission of electrons resulting from light falling on a metallic surface. Electromagnetic Explanation: the energy of electromagnetic radiation is carried within the wave

itself. As the electromagnetic wave (of intensity I) collides with the surface, the electron absorbs the energy from the wave until it exceeds the binding energy, releasing the electron from the metal.

Predictions: 1. The maximum kinetic energy of the electrons should be directly proportional to the intensity of

radiation. 2. The photoelectric effect should occur regardless of frequency or wavelength. 3. There should be a time delay between the light coming into contact with the metal and the

initial release of photoelectrons. Laws of Photoelectric Emission (actual results):

1. The number of electrons emitted per second is directly proportional to the intensity of the incident light.

2. The maximum kinetic energy (measured by stopping voltage) of the electrons increases with the frequency of the radiation.

3. There is a minimum frequency (critical frequency) below which no electrons are emitted. o There is no time delay.

Stopping voltage: the voltage required to stop the outward movement of electrons emitted by photoelectric effect; is dependent on the frequency of the light source.

Critical frequency: frequency threshold at which no electrons are emitted at frequency less than it, regardless of intensity.

Work function: the minimum amount of energy (in eV) required to remove an electron from the surface of a metal.

13.1.2. Describe the concept of the photon, and use it to explain the photoelectric effect. Einstein suggested that the energy carried by light is quantized by small light particles called

photons that carry electromagnetic energy proportional to their frequencies. There is a minimum energy required for an electron to break free. An electron gains energy from a colliding photon. Therefore the energy gained by each electron is

determined by the frequency. Thus light intensity will impact the number of electrons emitted, but not affect their maximum kinetic energy.

The energy of a photon is equal to the work function of the electron and its kinetic energy:

A photon is an elementary particle of light that carries electromagnetic energy proportional to its frequency. A photon has zero mass, zero electric charge and indefinite lifetime. It travels at the speed of light.

13.1.3. Describe and explain an experiment to test the Einstein model (Millikan).

48


A metal surface is connected to a circuit as shown and subjected to electromagnetic radiation. To observe the photoelectric effect, the power supply is turned to zero, and a current will be

detected through an ammeter. To observe the stopping voltage, the power supply is changed until there is no current in the

circuit. This voltage, as measured by the voltmeter, is the stopping voltage. 13.1.4. Solve problems involving the photoelectric effect.

The Wave Nature of Matter13.1.5. Describe the de Broglie hypothesis and the concept of matter waves. De Broglie Hypothesis: all matter has a wave-like nature (particle-wave duality).

The wavelength of a particle is given by .

13.1.6. Outline an experiment to verify the de Broglie hypothesis. Proof of the particle-wave duality of matter lies in the diffraction of matter particles (provided that

the opening d is sufficiently small—i.e. smaller than or equal to the particle’s de Broglie’s wavelength. The distance between atoms in crystals provide exactly the opening required.)

The Davison-Germer experiment involves firing electrons from an electron gun through a known potential difference at a crystal. A detector records the positions of scattered electrons.

It was found that the intensity of the electrons has no impact on experiment results—electrons will still diffract even if there is only one electron going through the slit at a time.

13.1.7. Solve problems involving matter waves.

€

E =p2

m

€

λ =h

p

Atomic Spectra and Atomic Energy States13.1.8. Outline a laboratory procedure for producing and observing atomic spectra. Matter emits light when heated to high temperatures or exposed to high electric fields. This light

can be split into its component wavelengths if put through a spectrometer. Emission spectrum: the spectrum of light that has been emitted by a gas. Absorption spectrum: the spectrum of light transmitted through a gas. 13.1.9. Explain how atomic spectra provide evidence for the quantization of energy in atoms.

49


The energy emitted or absorbed by the matter is assumed to be equal to the difference between the total energy of the atom before and after the emission or absorption. It follows from the observation of atomic spectra that the energy of an atom is discrete.

13.1.10. Calculate wavelengths of spectral lines from energy level differences and vice versa. 13.1.11. Explain the origin of atomic energy levels in terms of the “electron in a box” model. If an electron is confined to move in one dimension by a box, the de Broglie waves associated with

the electron will be standing waves of wavelength where L is the length of the box and n is a

positive integer.

represents the kinetic energy of the electron inside the box.

Electron being confined to a box, will move as a standing wave of wavelength . Momentum of

the electron is given by .

Thus, .

13.1.12. Outline the Schrödinger model of the hydrogen atom. Electrons in the atom may be described by wave functions, which are functions of position and

time. The electron has an undefined position, but the square of the amplitude of the wave function gives

the probability of finding the electron at a particular point—the probability that an electron will be near position x at time t.

Predicts that the total energy of an electron can be given by an integer function, and therefore that energy levels are discrete.

Further predictions: if electron is at a high energy level, it will transition into a lower level, emitting a photon in the process. It is possible to predict the probability of such a transition.

13.1.13. Outline the Heisenberg uncertainty principle with regard to position-momentum and time-energy. Conjugate quantities position-momentum, time-energy, cannot be known precisely at the same

time.

If a particle has a uniquely defined de Broglie wavelength, its momentum is known precisely but all knowledge of its position is lost.

13.2. Nuclear physics13.2.1. Explain how the radii of nuclei may be estimated from charged particle scattering experiments. Energy considerations can be used to calculate the distance of closest approach of the incoming

particle to the target. If an alpha particle of charge , is shot head-on towards a stationary nucleus of charge

, the system initially has total energy . At distance d, the alpha particle turns back, repelled by the electrostatic repulsion from the stationary nucleus. The distance at which the alpha

particle stops, .

50


By shooting charged particles with ever-higher kinetic energy, it is possible to decrease the distance of closest approach d to the radius of the stationary nucleus.

13.2.2. Describe how the masses of nuclei may be determined using a Bainbridge mass spectrometer.

Singly ionized ions (with net positive charge of e) pass through the region AB, with electric and magnetic fields at right angles to each other.

Only ions of given velocity pass AB to go through S2.

Another magnetic field deflects the ions into circular paths according to their mass.

The radius of the circular path is given by:

. Heavier atoms will have a longer

radius. Thus, measurement of the radius will allow for

determination of the atoms mass.

13.2.3. Describe one piece of evidence for the existence of nuclear energy levels.

Radioactive Decay13.2.4. Describe ß+ decay, including the existence of the neutrino. In β+ decay, energy is used to convert a proton into a neutron, a positron and a neutrino. Beta plus decay cannot occur in isolation, because it requires energy, the mass of the neutron

being greater than the mass of the proton. Beta plus decay can only happen inside nuclei when the absolute value of the binding energy of the

daughter nucleus is higher than that of the mother nucleus. The difference between these energies goes into the reaction of converting a proton into a neutron, a positron and a neutrino and into the kinetic energy of these particles.

13.2.5. State the radioactive decay laws as an exponential function and define the decay constant. Decay constant: the probability of decay of a nucleus per unit time. The law of radioactive decay states that the number of nuclei that will decay per second is

proportional to the number of atoms present that have not yet decayed.

€

dN

dt= −λN ⇒ N = N0e

−λ t

13.2.6. Derive the relationship between decay constant and half-life. After one half life, half of the nuclei will have decayed.

Therefore:

Activity: the number of decays per second;

13.2.7. Outline methods for measuring the half-life of an isotope. 13.2.8. Solve problems involving radioactive half-life.

51


€

A = A0

1

2

⎛

⎝ ⎜

⎞

⎠ ⎟

t

t1/2

Topic 14: Digital Technology

14.1. Analogue and digital signals14.1.1. Solve problems involving the conversion between binary numbers and decimal numbers.

€

10101= 24 ⋅1+ 23 ⋅0 + 22 ⋅1+ 21 ⋅0 + 20 ⋅1 =16 + 4 +1= 2114.1.2. Describe different means of storage of information in both analogue and digital forms. Analogue signals: continuous signals varying between two extreme values in a way that is

proportional to the physical mechanism that created the signal. Fast movement is associated with large voltage and slow movement with small voltage. Sound creates the voltage.

Digital signals: coded form of signal that takes the discrete values 0 or 1 only. To convert from analogue to digital, we take samples determined by sampling frequency. Quantization: the process of dividing the age of the analogue signal into a set of levels—

quantization levels.

Quantization error is given by

€

q =M − m

2n .

14.1.3. Explain how interference of light is used to recover information stored on a CD. 14.1.4. Calculate an appropriate depth for a pit from the wavelength of the laser light. 14.1.5. Solve problems on CDs and DVDs related to data storage capacity. 14.1.6. Discuss the advantage of the storage of information in digital rather than analogue form. Larger capacity for data storage. Fast retrieval and easy access to data. Storage is reliable and can be easily reproduced or erased. Can be encrypted. Can be processed and manipulated by computer, can be easily transported. Physically,

electronically. 14.1.7. Discuss the implications for society of ever-increasing capability of data storage.

14.2. Data Capture; digital imaging using charge-coupled devices (CCDs) 14.2.1. Define capacitance. Capacitator is an electronic device used for storing charge. It consists of two conductors separated

and insulated by a vacuum or a dielectric. Capacitance is the ratio of the amount of charge that can accumulate on the plates between the

potential difference between the plates. The “charge per unit potential difference that can accumulate on a conductor”.

; unit: Farad (1F = 1 C/V)14.2.2. Describe the structure of a charge-coupled device (CCD). A CCD is used to obtain images of high resolution in digital imaging.

52


Consists of a silicon chip (2-6 centimeters squared) covered with pixels (light sensitive elements around 5-25 micrometers). Pixels release electrons when encountering incident light in the photoelectric effect process.

Pixels can be thought of as small capacitators, which release electrons to constitute charge Q. Voltage V develops across the ends of pixel: V=Q/C, where C is the pixel’s capacitance.

The number of electrons released when light is incident on a pixel is proportional to the intensity of light. This means that the charge and the potential difference across a pixel are also proportional to the intensity of light on that pixel.

14.2.3. Explain how incident light causes charge to build up within a pixel.

53


The photoelectric effect: incident light causes pixel to release electrons, carrying charge. Voltage difference is created between the two ends of a pixel.

14.2.4. Outline how the image on a CCD is digitized.

14.2.5. Define quantum efficiency of a pixel. The ratio of number of emitted electrons to the number of incident photons. CCD’s have 70% -

80% quantum efficiency. Increased density of pixels enhances clarity of image. 14.2.6. Define magnification. The number of electrons released when light is incident on a pixel is proportional to the light

intensity. Intensity: power per area in Watts / Meters Squared14.2.7. State that two points on an object may be just resolved on a CCD if the images of the points are at least two pixels apart. Two points on an object may be just resolved (seen as two separate points) on a CCD if the images

of the points are at least two pixels apart. 14.2.8. Discuss the effects of quantum efficiency, magnification and resolution on the processed image. 14.2.9. Describe a range of practical uses of a CCD, and list some advantages compared with the use of film. 14.2.10. Outline how the image stored in a CCD is retrieved.

14.2.11. Solve problems involving the use of CCDs.

GlossaryFidelity: similarity between the original signal and the reproduced signal. Perfect reproduction: the recording sounds the same no matter how many times you play it. ADC: analog-to-digital converter. DAC: digital-to-analog converter. Sampling rate: controls how many samples are taken per second. Sampling precision: controls how many different gradations are possible when taking the sample.

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IB Physics Core 2009 Draft2

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Transcript of IB Physics Core 2009 Draft2