IB physics Data booklet review. KINEMATICS. Graphs:. Average velocity : slope of the straight line joining the initial and final position on the position -time graph. (Instantaneous) velocity at a given point: slope of the tangent line at given time on the position -time graph.
Data booklet review
Average velocity: slope of the straight line joining the initial andfinal position on the position -time graph.
(Instantaneous) velocityat a given point: slope of the tangent line at given time on the position -time graph.
Average Acceleration: slope of the straight line joining the initial andfinal position on the velocity - time graph
(Instantaneous) acceleration at a given point: slope of the tangent line at given time on the velocity - time graph
Change in velocity is the area under acceleration– time graph
▪ The drag force increases as the speed of the falling object
increases resulting in decreasing downward acceleration
▪ When the drag force reaches the magnitude of the gravitational force,
the falling object will stop accelerating and fall at a constant velocity.
▪ This is called theterminal velocity/speed.
Mass is numerical measure of the inertia of a body (kg)
Weight is the gravitational force acting on an object . W = mg
Force is an influence on an object that causes the object to accelerate
• 1 N is the force that causes a 1-kg object to accelerate 1 m/s2.
Fnet(resultant force)is the vector sum of all forces acting on an object
Free Body Diagramis a sketch of a body and all forces acting on it.
Newton’s first law:An object continues in motion with constant speed in a straight line (constant velocity) or stays at rest unless acted upon by a net external force.
Object is intranslational equilibrium if no change in velocity
Newton’s second law:
• Δpis the change in momentum produced by the net force F in time Δt.
• Δp= Δ(mv)
1. velocity changes, mass doesn’t change:
Δp= mΔv → F = ma
If a net force is acting on an object of mass m, object will acquire acceleration
Direction of acceleration is direction of the net force.
2. mass changes, velocity doesn’t change: Δp = vΔm → F = v
Δm/Δt in (kg/s)
Newton’s third law: Whenever object A exerts force on object B, object B exerts an equal in magnitude but opposite in direction force on object A
Normal/Reaction force(Fn or R) is the force which is preventing an object from falling through the surface of another body .
That’s why normal force is always perpendicular (normal) to the surfaces in contact.
when you have to draw FREE BODY DIAGRAM (object and all forces acting on it), there is a requirement to draw as many normal/reaction forces as there are points of contacts .
For example if you have a 2-D car (with two wheels) you have to draw two normal /reaction forces. Each on one wheel.
Table with two legs – the same thing.
Emu with two legs – the same thing
Friction forceis the force that opposes slipping (relative motion ) between two surfaces in contact; it acts parallel to surface in direction opposed to slipping. Friction depends on type and roughness of surfaces and normal force.
F sin θ + Fn = mg
F cos θ – Ffr = ma
direction perpendicular tothe incline:
Fnet = ma = 0
Fn= mg cos θ
Along the incline direction:
mg sin θ – Ffr = ma
Linear momentumis defined as the product of an object’s mass and its velocity:
p = mv vector!(kg m/s)
Impulseis defined as the product of the net force acting on an object and time interval of action:
FΔt vector! (Ns)
Impulse F∆t acting on an object will produce the change of its momentum Δp:
F∆t = ∆p Δp = mv - mu Ns = kg m/s
Achieving the same change in momentum over a longer time
requires smaller force, and over a shorter time requires greater force.
WHEN YOU TRY TO FIND CHANGE IN MOMENTUM
REMEMER TO LABEL VELOCITIES AS POSITIVE OR NEGATIVE
The impulse of a time-varying forceis represented
by the area under the force-time graph.
Law of Conservation of Momentum:The total momentum of a system of interacting particles is conserved - remains constant, provided there is no resultant external force. Such a system is called an “isolated system”.
momentum of the system after collision = momentum of the system before
collision for isolated system (p = pi ) vector sum
REMEMBER TO DRAW A SKETCH OF THE MASSES AND VELOCITIES BEFORE AND AFTER COLLISION.
LABEL VELOCITIES AS POSITIVE OR NEGATIVE.
Elastic collision: both momentum and kinetic/mechanical energy are conserved. That means no energy is converted into thermal energy
Inelastic collision: momentum is conserved but KE is not conserved.
Perfectly inelastic collision: the most of KE is converted into other forms of energy when objects after collision stick together.
To find how much of KE is lost in the system, subtract KE of the system after collision from KE of the system before the collision.
If explosion happens in an isolated system momentum is conserved but KE increases (input of energy from a fuel or explosive material.)
Workis the product of the component of the force in the direction of displacement and
the magnitude of the displacement. (scalar)
W = Fdcos Ѳ (Fd = F cos Ѳ) (Joules)
Work done by a varying force F along the whole
distance travelled is the area under the graph FcosѲ
versus distance travelled.
Energyis the ability to do work. Work changes energy.
Potential energyis stored energy.
(Change in) Gravitational potential energy ∆EP = mg ∆h
Elastic potential energy = work is done by external force in stretching/compressing
the spring by extension x.
EPE = W = ½ kx2
Kinetic energyis the energy an object possesses due to motion EK = ½ mv2
Work done by applied/external forceis converted into (changes) potential energy
(when net force is zero, so there is no acceleration).
Work – Kinetic energy relationship: work done by net force changes kinetic energy:
W = ∆KE = final EK – initial EK = ½ mv2 – ½ mu2
the work done by centripetal forceis zero:
Wnet = 0 → Wnet = ∆KE → no change in KE → no change in speed;
centripetal force cannot change the speed, only direction.
Examples: gravitational force on the moon,
magnetic force on the moving charge.
it can only be changed from one form to another.
For the system that has only mechanical energy
(ME = potential energies + kinetic energy)
and there is no frictional force acting on it,
so no mechanical energy is converted into thermal energy,
mechanical energy is conserved
ME1 = ME2 = ME3 = ME4 mgh1 + ½ mv12 = mgh2 + ½ mv22 = • • • • • •
f friction cannot be neglected we have to take into account work done by friction force which doesn’t belong to the object alone but is shared with environment as thermal energy.
Friction converts part of kinetic energy of the object into thermal energy.
Frictional force has dissipated energy:
ME1 – Ffr d = ME2 (Wfr = – Ffr d)
Power is the rate at which work is performed or the rate at which energy is transmitted/converted.
scalar (1 W(Watt) = 1 J/ 1s )
Another way to calculate power
Efficiency is the ratio of how much work, energy or power we get out of a system compared to how much is put in.
Centripetal acceleration causes change in direction of velocity, but doesn’t change speed. It is always directed toward the center of the circle.
Period T: time required for one complete revolution/circle
speed around circle of radius r:
Macroscopic level: temperature gives indication of the degree of hotness or coldness of a body, measured by thermometer
Thermal equilibriumoccurs when all parts of the system are at the same temperature. There is noexchange of thermal energy/please do not mention heat.(This is how a thermometer works)
Thermal energyof a system =internal energy—the sum total of the potential energy and kinetic energy of the particles making up the system.
Potential energyof the molecules arises from the forces (bonds/ because of intermolecular forces) between them.
Kinetic energyof the molecules arises from the translational, rotational, ad vibrational motion of the particles.
Microscopic level: (absolute) temperature directly proportional to theaveragekinetic energy of the molecules of a substance: (KE)avg = kT.
k is Boltzmann constant
Heatis thethermal energythat flows/is transferred from one body or system of higher temperature to another of lower temperature.
of a carbon-12 atom.
The moleis the amount of substance that contains the same number
of atoms/molecules as 0.012 kg of carbon-12.
Molar Massis the mass of one mole of a substance (kg/mol).
1 mole of a gas at STP occupies 22.4 l (dm3) and contains
6.02 x 1023 molecules/mol.
Heat/Thermal Capacityis the amount of thermal energy needed to raise the temperature of a substance/object by one degree Kelvin.
C = → Q = C ΔT unit: (C) = J K-1
Specific heat capacityis the quantity of thermal energy required to raise the temperature of one kilogram of a substance by one degree Kelvin.
c = → Q = mc ΔT unit: (c) = J kg-1K-1
amount of thermal energy needed to increase the temperature of m kgof a substancewith specific heat capacity c by ΔT amount of thermal energy released when the temperature of m kgof a substancewith specific heat capacity c decreases by ΔT
homogeneous substance: C = mc
Latent heatis the thermal energy that a substance/body absorbs or releases during a phase change at constant temperature.
L = Qatconst. temp.unit: J
Specific latent heatis the thermal energy required for a unit mass of a substance to undergo a phase change.
L = → Q = mLunit: (L) = J/kg
Ifelectrical energyis converted into increase of internal energy of the system, then:
solid, liquid, gas and plasma; ordinary matter – only three phases
system from one phase to another.
S → L melting or fusion L → S freezing or solidification
S → G sublimation G → S deposition or desublimation
L → G vaporization G → L condensation
includes boiling and evaporation
While melting, vibrational kinetic energy increases and particles gain enough thermal energy to break from fixed positions. Potential energy of system increases.
Melting pointof a solid is the temperature at which it changes state from solid to liquid. Once at the melting point, any additional heat supplied does not increase the temperature. Instead is used to overcome the forces between the solid molecules increasing potential energy.
◌ At the melting point the solid and liquid phase exist in equilibrium.
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
(It is negative!!! = attraction: intermolecular forces become stronger).
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.
The distinguishing characteristic of a phase transition is an abrupt changein one or more physical properties, in particular the heat capacity, and the strength of intermolecular forces.
During a phase change, the thermal energy added or released is used to change (increase/decrease) 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, so temperature will not change.
Evaporationis a change of phase from the liquid state to the gaseous state that occurs ata temperature below the boiling point.
Evaporation causes cooling.
A liquid at a particular temperature has a range of particle energies, so at any instant, a small fraction of the particles will have KE considerably greater than the average value. If these particles are near the surface of the liquid, they will have enough KE to overcome the attractive forces of the neighbouring particles and escape from the liquid as a gas. The escape of the higher-energy particles will lower the average kinetic energy and thus lower the temperature.
The rate of evaporationis the number of molecules escaping the liquid per second. Evaporation can be increased by
• increasingtemperature/more particles have a higher KE
• Increasingsurfacearea/more particles closer to the surface
• Increasing air flow above the surface (gives the particles somewhere
to go to)/ decreasing the pressure of the air above liquid
P – pressure,
V – volume,
k – Boltzmann constant,
T - temperature
Gas pressureis the force gas molecules exert due to
their collisions (with a wall – imaginary or real), per unit area.
Assumptions of the kinetic model of an ideal gas.
• Gases consist of tiny hard spheres/particles called atoms or molecules.
• 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
• 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.
• Collisions of short duration occur between molecules and the walls of the container and the collisions are perfectly elastic
(no loss of kinetic energy).
Temperature is a measure of the average random kinetic energy of the molecules
of an ideal gas.
Macroscopic behavior of an ideal gas in terms of a molecular model.
• Increase intemperatureis equivalent of an increase in average kinetic energy (greater average speed). This leads to more collisions and collisions with greater impulse. Thus resulting in higher pressure.
• Decrease involume 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.
IT IS SIMPLE HARMONIC MOTION
to a pendulum and moving paper beneath it at a constant
velocity, or by shining the light on and oscillating spring.
The shape of this displacement – time graph is cosine curve.
The amplitude is x0 is initial displacement
displacement x = x0 cos ωt
where angular frequency is: ω = 2πf= 2π/T
Simple Harmonic Motionis periodic motion in which the acceleration/ restoring force is proportional to and in opposite direction of the displacement.
a = − ω2x.
spring: a = F/m = – kx/ m = – (k/m)x = = − ω2xω2 = k/m
General equation for the position of a particle undergoing simple
harmonic motion: x = x0cosωt.
x0 – amplitude, f – frequency f = 1/T T – period for full oscillation
angular frequency = 2 f (how many full circles 2 per second) = 2/T
x = x0cosωt.
v = dx/dt = – x0 sin ωt = – v0 sin ωt
a = dv/dt = – 2x0cosωt = – a0cost
a = – 2x
x0, v0, a0 positive maximumvalues
v = = – x0 sin ωt = =
EK = ½ m v2 = ½ m2 ( )
EK for x = 0 → EK(max) = ½ m2
EK(max) = EP(max) = ETotal
potential energy at any moment = total energy – KE EP = ½ m2 x2
Energy (total) of SHM is proportional to amplitude2 (
Perioddoes not depend on amplitude!!!!!!
Damping: Due to the presence of resistance/friction forces on oscillations in the opposite direction to the direction of motion of the oscillating particle
Amplitude of oscillations decreases
Friction force is a dissipative force.
"to damp" is to decrease the amplitude of an oscillation.
Decreasing the amplitude doesn’t change period.
Light/under damping: The decay in amplitude is relatively slow and the oscillator will make quite a few oscillations before finally coming to rest.
Critical/heavy damping: occurs if the resistive force is so big that the system returns to its equilibrium position without passing through it. The mass comes to rest at its equilibrium position without oscillating. The friction forces acting are such that they prevent oscillations.
Over-damping: the system returns to equilibrium without oscillations, but much slower than in the case of critical damping.
Natural frequencyis the frequency an object will vibrate with after an external disturbance.
Forced oscillations: when an external periodic force with frequency fD is applied on a free system with a natural frequency f0 , the system may respond by switching to oscillations with a frequency equal to the driving frequency fD.
Variation of the amplitude of vibrations of an object subjected to the forced frequency close to its natural frequency of vibration.
Qualitative description of the factors that affect the frequency response and sharpness of the curve.
▪ 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.
▪ At very heavy damping, the amplitude is essentially constant.
Resonanceis increase in amplitude of oscillation of a system exposed to a periodic driving force with a frequency equal to the natural frequency of the system.
▪ Useful: microwave oven, radio. .
▪ Harmful: bridges, aero plane wings, internal organs in the case of heavy machinery .
When a wave (energy)propagatesthrough a medium, oscillations of the particles of the medium aresimple harmonic.
Progressive waves transfer energy through a distortion that travels away from the source of distortion. There isnonet transfer of medium.
▪ Transverse wavesare waves in which the particles of the medium oscillate perpendicular to the direction in which the wave is traveling.
◌ EM waves: light, radio waves, microwaves:
need no medium, electric and magnetic field oscillate perpendicular
to each other and to the direction of wave propagation.
◌ Earthquake secondary waves, waves on a stringed musical instrument,
waves on the rope.
◌ Transverse wave can not propagate in a gas ( and actually pure transverse
can not propagate in liquid either)
▪ Longitudinal wavesare waves in which the particles of the medium vibrate parallel to the direction in which the wave is traveling.
◌ Sound waves in any medium, shock waves in an earthquake,
compression waves along aspring
A wavefrontis set of points having the same phase/displacement.
Arayis an arrow drawn on a diagram to show the direction of propagation of waves. It is always at right angles to the wavefront.
Energy of a wave of amplitude A is proportional to the amplitude2
: E ∞ A2
Although the speed of a wave depends only on the medium, there is a relationship between wavelngth 𝜆 , frequency f (period T) and the speed
Waves that need medium to travel through are calledmechanical waves.
Electromagnetic waveis made up of changing electric and magnetic fields perpendicular to each other and to the propagation of the wave.
They travel through vacuum with the SAME SPEED!speed of light c ≈ 3 x 108 m/s
Index of refraction nof a medium is the ratio of the speed of light in a vacuum, c, and the speed of light, v, in that medium:
As the speed of light in air is almost equal to c, nair ≈ 1
Refraction: When a wave passes from one medium to another, its speed changes resulting in a change in direction of the refracted wave
Snell’s lawstates that for a given pair of media, the ratio of the sines of the angles of incidence and refraction is equal to the ratio of velocities in the two media
The refracted ray is refracted more in the medium with greater n, slower speed of light
= = = =
v = 𝜆 f ; frequency doesn’t change in refraction, so in the medium with smaller wave speed, wavelength will be smaller.
Chromatic dispersionis phenomenon in which the index of refraction depends on wavelength/frequency, so the speed of light through a material varies slightly with the frequency of the light and each λ is refracted at a slightly different angle.
The longer λ, the smaller index of refraction.
nred < nblue , red light is refracted less than blue light
Dispersion is the phenomenon which gives separation of colours in prism/rainbow and undesirable chromatic aberration in lenses.
Diffractionis the spreading of a wave into a region behind an obstruction (into a region of geometrical shadow).
Diffraction effects are more obvious when wavelength of the wave is similar in size to aperture/obstacle or bigger.
remember: big λ (compared to aperture or obstacle), big diffraction effects
Interference is the addition (superposition) of two or more waves overlapping that results in a new wave pattern.
Principle of superposition: When two or more waves overlap, the resultant displacement at any point and at any instant is the vector sum of the displacements of the individual waves at that point: y = y1 + y2
PD = path difference is the difference in distances traveled by waves
from two sources to a point P: PD = d2 – d1
Two coherent waves traveling along two
different paths to the same point will:
interfere constructively if the difference in distance traveled
is equal to a whole number of wavelengths:
PD = n λ n = 0, ± 1, ± 2, ± 3, …
interfere destructivelyif the difference in distance traveled
is equal to a half number of wavelengths:
PD = (n + ½ ) λ n = 0, ± 1, ± 2, ± 3, …
▪ Coulomb’s law: Force betweenTWO POINT charges q1 and q2 at distance r :
(E) = NC-1
▪ Electric field is the force per unit positive charge .
Direction of the field is the direction of the force on a positive test charge placed at that point.
▪ Electric field lines show direction of the force on positive charge
▪ always point away from + charges, towards – charges…
▪ positive charge placed in the field would move along field line,
negative charge would move opposite
Essentially, potential energy is capacity for doing work which arises from position or configuration.
In the electrical case, a charge placed in electric field will have electric potential energy. If left on its own it will start accelerating due to electric force acting on it. We say it has electric potential energy which will be converted into kinetic energy. On the other hand if external force pushes the charge against electric field, the work done by that force will be stored as potential energy in the charge.
Potential energy difference between two points (is equal to the work done on a charge in order to move it from one point to the other.
Potential difference between two points (is equal to the work done per unit positive charge in order to move it from one point to the other.
Capacitor: uniform electric field (the one that has constant magnitude and direction) is generated between two oppositely charged parallel plates. Edge effect is minimized when the length is long compared to their separation.
▪ ①Work done by external force on charge against an electric field between two points is stored in the charge as the change in electrical potential energy, U.
W = ∆U
Fext d = q ∆V
qEd= q ∆V ⇒ ⇒ (E) = NC-1 = Vm-1
▪ ② Work done by electric force
If a charge, q, is moved on its own through a potential difference, ∆V,
the work done on it by electric force is equal to the decrease in its electric potential energy which is converted into kinetic energy:
W=∆U = Fd = q Ed = q ∆V = ½ mv2
▪ Positive charge accelerates from higher to lower potential (from positive to negative).
▪ Negative charge accelerates from lower to higher potential. (from negative to positive)
▪1 electron-Volt (eV) is the amount of energy/work it takes to move an electron through a
potential difference of 1volt.
1 eV = W = ∆U = q ∆V = (1.6x10-19 C) (1V) 1 eV = 1.6x10-19 J
▪ Current is the rate at which charge flows past a given cross-section
▪ Electrical resistance , R is the ratio of the potential difference across the resistor/conductor
to the current that flows through it.
1 (ohm) = 1V/1A
▪ The resistance of a conducting wire depends on four main factors:
• length, L
• cross-sectional area, A
• material/resistivity, ρ
• temperature, T:
• if temperature is kept constant:
▪ OHM’S LAW: Current through resistor is proportional to potential difference across the resistor
if the temperature of a resistor is constant (the resistance of a conductor is constant).
I – current through resistor,
V – potential difference across R
Ohmic and Non-Ohmic conductors
How does the current varies with potential difference for some typical devices?
metal at const. temp. filament lamp diode
devices are non-ohmic if
Devices for which current through them is directly proportional to the potential difference across device are said to be ‘ohmic devices’ or ‘ohmic conductors’ or simply resistors. There are very few devices that are trullyohmic. However, many useful devices obey the law at least over a reasonable range.
▪ When a current is flowing through a load such as a resistor, it dissipates energy in it. In collision with
lattice ions electrons’ kinetic energy is transferred to the ions, and as a result the amplitude of
vibrations of the ions increases and therefore the temperature of the device increases.
KE is transferred to thermal energy.
▪ Electric power is the rate at which energy is supplied to or used by a device.
▪ Electric power is the rate at which electric energy is converted into another form such as
mechanical energy, thermal energy, or light.
Power dissipated in a resistor/circuit: P = I V
W = qV → P = qV/t and I= q/t, so P = IV
▪ Electromotive force (V), (E or EMF or ε) is the work done per unit charge in moving charge
completely around the circuit.
∆V = ∆U/Q
▪ Electromotive force, (E or EMF or ε) is the power supplied to the circuit per unit current
electric potential =
P = IV ⟹ V = P/I
▪ Energy supplied by the source = ε Q (coming from U = Q ∆V)
Total energy supplied by the source = energy used in the resistors: ε Q = V1 Q+ V2Q + …..
divide it by time ⟹ ε I = V1 I+ V2 I+ …..
ex: the cell supplies 8.0 kJ of energy when 4 kC of charge moves completely across the circuit with
constant current. Find ε: ε = energy/charge = 2 V
▪ Power supplied by the source will be dissipated in the circuit:
Power of the source = sum of the powers across the resistors: Pout = Σ Pi ⟹ ε I = V1I + V2 I + …..
Resistors in Series: connected in such a way that all components have the same current through them.
Burning out of one of the lamp filaments in series or simply opening the switch causes a break.
Equivalent resistance is greater that the greatest resistance in series.
Resistors in Parallel: are connected to the same two points of an electric circuit, so all resistors in parallel have the same potential difference across them.
The current flowing into the point of splitting is equal to the sum of the currents flowing out at that point: I = I1 + I2 + …
A break in any one path does not interrupt the flow of charge in the other paths. Each device operates independently of the other devices.
The greater resistance, the smaller current. Equivalent resistance is smaller than the smallest resistance in series.
Internal resistance, r: some of the power/energy delivered by a cell is used/dissipated
in driving the current though the cell itself
Terminal voltage (the actual voltage delivered to the circuit): V = ε – Ir
• Ammeter is in SERIES with resistor R in order that whatever current passes through the resistor also passes
through the ammeter. Ram<< R, so it doesn’t change the current being measured.
• would ideally have no resistance with no potential difference across it so no energy would be dissipated in it.
To measure the potential difference across resistor, we use a VOLTMETER.
• Voltmeter is in PARALLEL with the resistor we are measuring. Rvm >> R so that it takes very little current
from the device whose potential difference is being measured.
• an ideal voltmeter would have infinite resistance with no current passing through it and no energy
would be dissipated in it.
A photoresistor or light dependent resistor (LDR) is a resistor whose resistance decreases with
increasing incident light intensity; in other words, it exhibits photoconductivity
• Potentiometer – variable resistor
Electric (Coulomb’s law)/gravitational force (Newton’s law of gravitation) between two POINT charges/masses is proportional to the product of two charges/masses and
inversely proportional to the distance between them squared.
Both laws can be applied to the objects that are spherically symmetrical (do not look like potatoes).
In that case we consider that the charge/mass is concentrated at the center.
Electric /gravitational force is a vector. If two or more point charges/masses act on some charge/mass, the net force on that charge/mass is a vector sum of all individual forces acting on that charge/mass.
The electric/gravitational fieldat point P is defined as the force per unit charge/mass placed at that point.
g = G
M – mass of the planet
R – radius of the planet
gEarth = G = 9.80 m s-2
Direction of electric field due to charge Q at some point Pis equal to the direction of the force on a positive charge placed at that point.
Direction of gravitational field due to mass M
at some point P is toward mass M.
Gravitational force acting on a mass m placed there is:
Electric force acting on a charge q placed there is:
commonly called “weight of mass m”
▪ Uniform gravitational field, g
▪ Uniform electric field, E
If a positive charge q is released at point A, force F = qE will accelerate it in the direction of the field toward point B.
Work done on charge by force F along displacement d is converted into kinetic energy.
W = Fd = qEd = ½ mv2 (remember: const E, const. F so W = Fd)
If a mass q is released at point A, force F = mg will accelerate it in the direction of the field toward point B.
Work done on mass by force F along displacement d is converted into kinetic energy.
W = Fd = mgd = ½ mv2
(remember: const E, const. F so W = Fd)
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.
We define the magnitude of the magnetic field by measuring the magnetic force on a moving charge q:
1 T(Tesla) =
Direction at any location is the direction in which the north pole of the compass needle points at that location.
Outside magnet: N → S Inside magnet: S → N (always closed loops)
① An electric charge experiences a magnetic force when moving in a magnetic field.
Magnetic force on a wire carrying current Iin a magnetic field B: F = I LB sinq
Magnetic force acting on a charge q
in a magnetic Field B:F = qvBsinq
q = charge [C]
v = velocity [m/s]
B = magnetic field [T]
= angle between v and B
I = current [A]
L = length [m]
B = magnetic field [T]
= angle between Iand B
Outstretch fingers in the direction of v (or current I).
Curl fingers as if rotating vector v (I ) into vector B.
Magnetic force on a positive charge (orI) is in
the direction of the thumb.
Magnetic force on a negative charge
points in opposite direction.
The magnetic force: Fmag = qvB sin
● is always perpendicular to the direction
of the magnetic field
● acts on a charged particle only when the particle
is in motion and only if v and B do not point in
the same or opposite direction
(sin 00 = sin 1800 = 0).
● Force is perpendicular to the direction
of the motion, so the work done by
magnetic force is zero.
W = Fmagd cos θ1 = 0 (cos 900 = 0).
W = ΔKE = 0
Hence change in kinetic energy of the charge is 0,
and that means that mag. force cannot change
the speed of the charge. Magnetic force can only
change direction of the velocity – therefore it acts
as centripetal force.
The electric force: Felec = Eq
● is always parallel to the direction of the
● acts on a charged particle independent of the
particle’s velocity (even at rest).
● does the work when moving charge.
The work, W = Feld cos θ1, is converted into kinetic energy which is, in the case of conductors, transferred to thermal energy through collisions with the lattice ions causing increased amplitude of vibrations seen as temperature rise
θ1 is angle between F and direction of motion
2) the force on a current-carrying conductor.
1) The trajectory of a charge q in a uniform magnetic field B
● Force is perpendicular to B,v
● Magnetic force does no work! (W = F d cos θ1 = 0 )
● Speed is constant (W = Δ KE = 0 )
● Circular motion
Charged particle in a magnetic field when v B:
In the case the charge q is subject to the uniform field B, centripetal force Fc
is magnetic force forcing the charge to move in a circle:
Positive charge q in magnetic field B
B = magnetic field [T]
R=is the radius of the path
Fmais magnetic force on the charge directed toward
the centre of the circular path
m= mass [kg]
v= velocity [m/s]
q= charge [C]
● massive or fast charges – large circles
● large charges and/or large B – small circles
R-H-R 2: The direction of the magnetic field produced by electric current is given
by the right-hand rule 2:
If a wire is grasped in the right hand with the thumb in the direction of current flow,
the fingers will curl in the direction of the magnetic field.
Magnetic field B around a wire with current I
Magnetic Field B Inside of a Solenoid
B = 0 n I
0 = the permeability of free space 4p×10-7T·m/A
I = current [A]
r = distance from the center of the conductor
n = N/L number of turns of wire per unit length
The magnetic field is concentrated into a nearly uniform field in the centre of a long solenoid. The field outside is weak and diverging
Currents in opposite direction repel!
One Ampere is defined as that current flowing in each of two infinitely‑long parallel wires of negligible cross‑sectional area separated by a distance of one metre in a vacuum that results in a force of exactly 2 x 10‑7 N per metre of length of each wire.
What is the direction of the force on the top wire, due to the two below?
1) Left 2) Right3) Up4) Down5) Zero
What is the direction of the force on the midlle wire, due to the two others?
What is the direction of the force on the left, due to the two others?
1) Left 2) Right3) Up
4) Down5) zero5) Zero
1) Left 2) Right3) Up
4) Down5) Zero
Other way: 1. find magnetic field due the other two and then use RHR1
What is the direction of the force on the midlle wire, due to the two others?
What is the direction of the force on the midlle wire, due to the two others?
1) Left 2) Right3) Up
4) Down5) Zero
1) Left 2) Right3) Up
4) Down5) Zero
Source: Charges Moving Charges
Act on: Charges Moving Charges
Magnitude: F = q E F = q v B sin θ
Direction: Parallel to E Perpendicular to v,B
Opposites ChargesAttract Currents Repel
Rutherford/Planetary/Nuclear Model of atom: the atom consists of a very tiny but very massive positive nucleus, surrounded by electrons that orbit the nucleus as result of electrostatic attraction between the electrons and the nucleus
evidence: Geiger and Marsden’sexperiment:
• Alpha particles bombarded at a sheet of gold foil mostly passed through—atoms mostly
consist of empty space.
• 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.
• According to Maxwell, any accelerating charge will generate an EM wave
• This EM wave would be a release of energy and give off light at all sorts of
• electron releasing energy should slow down and eventually spiral into the nucleus .
• Electrons orbit at specific energy levels (“discrete states”), called “stationary states.”
– we say energy of is quantized
• Electrons in these stationary states do not emit EM waves as they orbit.
• Photon must be first absorbed in order to be emitted. Absorbed photon has the energy equal
to the difference between excited and ground state.
• Photon is emitted when an electron jumps from excited state to a lower energy state.
Energy of that photon is equal to the energy difference between two states. Ephoton = ΔE,
and frequency is given by Einstein’s relationship between energy and frequency of a photon:
E = hf h = Planck's constant = 6.627x10-34Js
Modern approach - Schrodinger wave function:
• energy level model - give possible energies of electrons and probability to find
electrons somewhere is given by wave function.
(without prism white light)
• a spectrum having all wavelengths over a comparatively wide range
• All possible frequencies of EM waves are present.
• Generally, solids, liquids, or high pressured (dense) gases emit a continuous spectrum when heated.
• Generally, strong interaction between molecules (spreading energy band)
Discrete/ Line spectrum - Evidence of electron energy levels
Pattern of distinct lines of color, corresponding to particular wavelengths.
Generally, weak or no interaction between molecules (no spreading of energy band)
• Emission Spectrum
• Set of frequencies of the electromagnetic waves emitted by atoms of a particular element.
• A hot, low-density / low pressure gas (gas in the atomic state) produces
an emission-line spectrum – energy only at specific λ.
• Absorption Spectrum
• Pattern of dark lines against a continuous spectrum background that results from
the absorption of selected frequencies by an atom or molecule.
• An absorption spectrum occurs when light passes through a cold, dilute gas and atoms in the
gas absorb at characteristic frequencies; since the re-emitted light is unlikely to be emitted
in the same direction as the absorbed photon, this gives rise to dark lines (absence of light)
in the spectrum.
Nuclide: A particular combination of protons and neutrons that form a nucleus.
Itisused to distinguishisotopesamongnuclei.
• X is chemical symbol of the element
• Z is the atomic number = number of electrons or protons
• A is the nucleon (mass) number = number of neutrons + protons
• A – Z = number of neutrons
Isotopes: Nuclides contains the same number of protons but different number of neutrons.
Isotopes are evidence for the existence of neutrons
Repulsive electromagnetic forcesbetween the protons would cause the nucleus to disintegrate
if it were the only force.
Strong nuclear forceis an attractive force, which exists between all nucleons to hold them
together. It is effective only over a very short range.
Weak nuclear forceexists only in the nucleus and is responsible for the disintegration of
a neutron into a proton and an electron in beta decay.
Nuclear Stability: depends on the neutron-proton ratio
Nuclei are held together by a strong nuclear force, which counteracts the repulsive force among protons contained within it. As long as the attractive nuclear forces between all nucleons win over the repulsive Coulomb forces between the protons the nucleus is stable. It happens as long as the number of protons is not too high. Atomic nuclei are stable subject to the condition that they contain an adequate number of neutrons, in order to "dilute" the concentration of positive charges
♦ Small nuclei- tend to have equal number of neutrons and protons
♦ Large nuclei- tend to have more neutrons to counterbalance repulsive Coulomb force.
The most massive isotope found in nature is uranium isotope
For more massive nuclei strong nuclear force can’t overcome electric repulsion.
Spontaneous decay of unstable nuclei.
• process in which unstablenucleus loses energy by emitting “radiation” in form of particles or EM waves,
resulting in transformation of parent nuclide into daughter nuclide.
• three common radiations - alpha, beta, gamma
• they differ in charge, ionization and penetration power.
• nucleus ejects an α particle, the atomic number is decreased by two and the atomic mass is decreased by four
• charge is + 2e
• the most ionizing and therefore the least penetrating(a few cm of air)
•Governed by strong nuclear force =α decay occurs primarily among heavy elements because the nucleus has too
many protons which cause excessive repulsion. In an attempt to reduce the repulsion, a helium nucleus is
emitted. Mass of parent > mass of daughter + mass of alpha
• difference = kinetic energy
• nucleus spontaneously emits beta particle and an antineutrino
• the most common decay occurs when the neutron to proton ratio is too great in the nucleus and
• In β− decay, the weak interaction converts a neutron into a proton while emitting an electron and
• charge is – e
• medium ionizing and therefore medium penetrating(a few mm of metal)
• EM waves (high-energy photons) are emitted from a nucleus in an excited state dropping to a
lower energy state (more stable)
• charge is 0
• no ionizing and therefore highly penetrating(a few cm of lead)
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
Radioactive Decay is a random processon the atomic level, in that it is impossible to predict when a particular atom will decay, but given a large number of similar atoms, the decay rate, on average, is predictable. The rate of decay decreases exponentially with time.
Half – life T 1 /2is the interval of time required for one-half of the atomic nuclei of a radioactive sample to decay.
Activity(becquerel - Bq) of a radioactive sample is the average number of disintegrations per second.
Nuclear Reactions– A reaction that occurs whenever the number of protons or neutrons changes.
Nuclear reactions include natural and artificial transmutation, fission, and fusion.
Transmutation– Change of one element into another.
In natural transmutationsthe nucleus decays spontaneously. There is only one nucleus that undergoes the transformation.
Artificial transmutationis induced by the bombardment of the nucleus by high-energy particles (Uranium atoms bombarded with neutrons to start fission reaction.)
Unified Atomic Mass Unit (u) is 1/12 of the mass of one atom of carbon-12 atom (6p+6n+6e)
• 1 u = 1.66056655 x 10-27kg
• 1 u = 931.5 MeV c-2 due to relationship E = mc2
• 1 u of mass converts into 931.5 MeV
Mass Defect(∆m) is the difference between the total mass of all nucleons in the nucleus
and the mass of the nucleus itself
∆m= Zmp + Nmn - Mnucleus (can be calculated in kg or u) . Equivalent to binding energy.
Binding Energyis the work/energy required to completely separate the nucleons of a nucleus
/ energy released when nucleons form a nucleus.
nuclear binding energy is actually energy that corresponds to mass defect
1. BE in MeV:
• find mass defect in u and multiply it by 931.5 MeV
2. ME in J:
• BE = ∆m c2(c = 3x108 m/s, ∆m= mass defect in kg)
In order to balance nuclear reaction the total mass/energy and total charge number of the reactants has to equal the total mass/energy and total charge number of the products.
Nuclear reactions A + B → C + D can either release energy or requires energy input.
• release energy: Energy will be released in nuclear reaction if Δm = LHS – RHS > 0
The total amount of energy released will be in the form of kinetic energy of products.
If there was initial kinetic energy, that will be added up to released energy.
energy released in nuclear reaction is found the same way as binding energy:
first find mass difference and then equivalent energy
Δm in u, E = (Δm) x 931.5 (MeV) or Δm in kg, E = (Δm) c2 (J)
• energy input: if Δm = LHS – RHS < 0, reaction cannot be spontaneous.
For example, some nuclei will decay only if energy is supplied to it - collision with fast
moving α particle:
α particle must have enough KE to make up for imbalance in masses, and to provide
for kinetic energy of products.
Energy released in a decay- conservation of total energy (energy + mass). as always
M > m1 + m2 , but
total energy on the left = total energy on the right
Mc2= m1 c2+ m2 c2+ KE1 + KE2
• spontaneous decay: M > m1 + m2 →binding energy of the decaying nucleus < binding energies
of the product nuclei.
This is why radioactive decay happens with heavy elements lying to the right of maximum
in the binding energy curve.
Energy released is in the form of kinetic energy of the products.
Binding energy per nucleon: the work required to remove one nucleon from the nucleus;
roughlythe binding energy divided by the total number of nucleons in nucleus.
The binding energy of a nucleus is a measure of how stable nucleus is.
Greater mass defect – higher binding energy – greater stability.
Most nuclei have a binding energy per nucleon of approximately 8 MeV.
Nuclear fission: process in which a large nucleus (A>200) splits up into two smaller nuclei, generally accompanied by the release of one or more neutrons and energy (as gamma rays and as kinetic energy of the fragments).
Large amounts of energy produced, can be self-sustaining due to chain reactions. The total BE would increase which means that the daughters are more stable than parent. Spontaneous fission is very rare.
Nuclear fusion: joining of two small nuclei into a bigger one, releasing great amounts of energy in the process.
High temperatures are required to provide sufficient kinetic energy to approach each other, overcoming electrostatic repulsion.
When two small nuclei the product of fusion would have more BE per nucleon.
The increases in binding energy per nucleon are much larger for fusion than for fission reactions, because the graph increases more steeply for small nuclei, so fusion gives out more energy per nucleon than fission.
assumption: wind is stopped by the wind turbine,
which is not the case, so not all of KE of the wind is
turned into electricity.
To calculate how much energy there is in the wind, we consider a cylinder of air with a radius the same as the radius of the turbine as shown.
If the velocity of air is v then in it will move a distance v. The volume of air passing by the turbine per second is vπ r2where ris the length of one of the turbine blades.
(K-1 or oC-1)
The mass of this cylinder of air, m = ρ vπ r2where ρ is the density of air.
increase in temp.
The KE of this air = ½ mv2 = ½ ρ vπ r2v2
= ½ ρ π r2v3
Since this is the KE of air moving past the turbine per second, the power in the wind is KE/.
P = ½ ρ π r2v3
consists of a column that is half full of water, such that when a wave approaches it pushes water up the column. This compresses the air that occupies the top half,
oscillating water column (OWC)
ocean-wave energy converter
The energy in a wave alternates between PE as the water is lifted tip, and KE as it falls.
pushing it through a turbine which drives an electric generator. The turbine is specially designed so that it also turns when the water drops back down the column, pulling air into the chamber. The main components of an oscillating water column generator.
The form of a wave can be approximated to a rectangle (length λ, height A and width L travelling at velocity v).
The PE of this mass of water is given by PE = mgh, where h = the average height of the wave = A/2
PE = mg A/2
density of water = ρ m = ρ x volume = ρλ A L
PE = ρ λ A L g A/2 = ρ λLgA2/2
Power = energy per unit time, so if the waves arrive every T seconds then
Power = ρ λLgA2/2T , but λ/T = wave velocity, v, so power = ρ vLgA2/2
The power per unit length of wavefront is
gravitational PE of water → KE of water → KE of turbines → electrical energy
The energy stored in a lake is gravitational PE = mgh. h is the height difference between the outlet from the lake and the turbine. Since not all of the water in the lake is the same height, the average height is used (this is assuming the lake is rectangular in cross section).
The rate of change of the potential energy converted into kinetic energy is
P = = = ρgh = ρ Q g h
Q is known as the volume flow rate (m3/s )
ρ – density of the water V – volume of the lake
distance r from the Sun is the power radiated received at
distance r per unit area
Astrophysics: apparent brightness b
The power from the star received (incident) per m2 of the Earth’s surface. If the energy radiated by a star is emitted uniformly in all directions, then apparent brightness is
where L is luminosity (power radiated) of the star and d its distance from the Earth.
Albedo: Some of the radiation received by a planet is reflected straight back into space. The fraction that is reflected back is called the albedo,
Earth’s albedo varies daily and is dependent on season (cloud formations) and latitude. Oceans have a low value but snow has a high value. The global annual mean albedo is 0.3 (30%) on Earth.
If the temperature of a planet is constant, then the power being absorbed by the planet must equal the rate at which energy is being radiated into space. The planet is in thermal equilibrium.
Surface heat capacity is the energy required to raise the temperature of unit area of a planet’s surface by one degree, and is measured in J m-2 K-1
If the incoming radiation power and outgoing radiation power are not equal, then the change of the planet’s temperature in a given period of time is:
A black body is a theoretical object that absorbs all incident electromagnetic radiation. Therefore it reflects no radiation and appears perfectly black. It is also a perfect emitter of radiation.
It would emit at every wavelength of light, and the “black body radiation” distribution as a function of wavelength, known as Planck’s law, depends upon its temperature.
Although stars and planets are not perfect emitters, their radiation spectrum is approximately the same as black-body radiation.
wavelength at which the intensity of the radiation is a maximum, λmax, is inversely to the temperature of the black body
STEFAN - BOLTZMANN LAW
The total power ((total energy per unit time) radiated by a black body is proportional to 4th power of surface temperature
= Stephan - Boltzmann constant
A – surface area of the emitter
T – absolute temperature of the emitter (in Kelvin)
The Earth and its atmosphere are not a perfect black body.
Emissivity, e, is defined as the ratio of power radiated by an
object to the power radiated by a black body at the same temperature.
There are only two ways to transfer energy from one body to another — either by doing work or by transferring thermal energy.
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 (use of machines that are continuously repeating their actions in a fixed cycle) and the transfer of some energy from the system (to the surroundings and therefore no longer available to perform useful work).
Degraded energyis energy that has become less useful (unavailable), i.e. cannot perform mechanical work due to being transformed
into other forms of energy, e.g. thermal energy (in accordance with the second law of thermodynamics)
Sankey diagramsare used to represent different ways of producing useful energy.
Fuelis a substance that can release energy by changing its chemical or nuclear structure.
All possible sources of energy:
▪ The Sun’s radiated energy
▪ Gravitational energy of the Sun and the Moon
▪ Nuclear energy stored within atoms
▪ The Earth’s internal heat energy
○ The Sun is the prime energy source for the world’s energy.
Energy density is the amount of energy that can be extracted per kilogram of fuel. Unit: J kg-1
Chain reaction: ▪Energy is required to split a U – 236 nucleus. This can be supplied by adding a
neutron to the U –235 nuclei, which destabilizes the nucleus U – 236
(formed after a neutron is caught by U – 235) and causes it to split in two.
▪ Extra neutrons are produced, which can go on to react with other U – 235 nuclei
in a self-sustaining chain reaction.
However neutrons must be first slowed down to less than 1 eV.
Too fast neutrons are not likely to make reaction.
Critical mass: the minimum mass required for a chain reaction. (atomic bomb: mass > critical mass)
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 to make
nuclear fission more likely is called enrichment.
▪ 3% U-235 must be reached in order to power a nuclear reactor.
Controlled nuclear fission (power production) and uncontrolled nuclear fission (nuclear weapons)
nuclear energy → thermal energy → mechanical energy → electrical energy
Three important components in the design of all nuclear reactors are
moderator, control rods and heat exchanger.
▪ Moderator is a medium that slows down fast neutrons to make them suitable for reaction
(water, graphite, heavy water).
▪ Control rodsare movable rods that readily absorb neutrons. They can be introduced or
removed from reaction chamber in order to control the rate of fission of
uranium and plutonium. Made of chemical elements capable of absorbing
many neutrons without fissioningthemselves (cadmium, hafnium, boron, etc)
▪ Heat exchanger is used to seal off the place where nuclear reactions take place from the rest
of the environment. In some nuclear power plants, the steam from the
reactor goes through a heat exchanger to convert another loop of water
to steam, which drives the turbine.
The advantage to this design is that the radioactive water/steam never
contacts the turbine.
Neutron captureby a nucleus of uranium-238 results in the production of a nucleus of
In addition to uranium – 235, plutonium – 239 is also capable of sustaining fission reactions. This nuclide is formed as a by - product of a conventional nuclear reactor. A uranium – 238 nucleus can capture fast moving neutrons to form uranium – 239. This undergoes β – decay to neptunium – 239 which undergoes further undergoes further β – decay to plutonium – 239
Plutonium-239 is used as a fuel in other types of reactors.
Problems associated with producing nuclear power using nuclear fusion: the reaction requires creating temperatures high enough to ionize atomic hydrogen into a plasma state. Currently the principal design challenges are associated with maintain and confining the plasma at sufficiently high temperature and density for fusion to take place.
▪ Solar panel (active solar heater) 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. It converts solar energy into thermal energy of water.
▪ A photovoltaic cell converts solar radiation into electrical energy. Produces very small voltage
The greenhouse effect is the warming of a planet due its atmosphere allowing in ultraviolet radiation from the Sun, but trapping the infrared radiation emitted by the warm Earth.
Temperature of the Earth’s surface will be constant if the rate at which it radiates energy equals the rate at which it absorbs energy.
Short wavelength radiation is received from the sun and causes the surface of the Earth to warm up. The Earth will emit infra-red radiation (longer wavelengths than the radiation coming from the sun because the Earth is cooler than the sun). Some of this infra-red radiation is absorbed by gases in the atmosphere and re-radiated in all directions.