a2 Physics (Updated)

8/10/2019 a2 Physics (Updated)

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Momentum is the product of mass and velocity.

Its represented by the symbol P.P = mv

Its a vector quantity since velocity is vector.

If we look at the equation representing Newtons 2ndlaw:

F = ma

Since a = v/t

F = mv/t

F = P/t

So Newtons 2nd law can also by defined as: the resultant force is

directly proportional to rate of change of momentum and the

momentum is in the direction of the resultant force.

One more equation can be derived which is:

P = F x t

Impulse = F x t

A change in momentum will cause an impulse.

PRINCIPLE OF CONSERVATION OF MOMENTUM


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The momentum before collision is equal to the momentum after

collision provided that there is no external resultant force acting on

the system.

HOW TO INVESTIGATE THE PRINCIPLE?

Two trolleys A and B are kept on a friction compensated slope.

A is kept at the start of the slope with a card. It has a cork at

the front with a pin.

B is kept in between the two light gates (connected to a

computer) without a card. It has a cork on its front.

A is given a push and the first light gate will record the time for

it to cut it. Velocity = length of card/time

When A attaches to B, they will both start moving in the same

direction with a common final velocity.

This velocity is recorded by the second light gate.

The principle can be verified by:

Mau = v(ma + mb)


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The recorded and the calculated velocity will be same.

When the masses are added to the end of the pulley, the trolley

will accelerate.

The motion sensor will record the displacement of the trolley at

regular intervals.

The different velocities will be calculated by the computer.

The mass is kept constant.

Calculate P = mv for all the velocities.

Graph will be:


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Gradient is F since P/t = F

F is constant because mass is constant.

Ek = mv2 P = mv

To remove v:

V2 = 2Ek/m P2= m2 v2

Therefore:

P2= m2 x 2Ek/m

P2= m22Ek/m

P2 = m2Ek


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Ek = P2/2m

This equation works for problems in everyday life.

This equation can only be used to fast moving particles when they

are non-relativistic (particles that have a speed less than 10 % of

the speed of light.)

CONSERVATION OF MOMENTUM IN 2D

When a particles of mass m collide with another particle of same

mass at rest, in an off-centered collision they move away from

each other at 90o

When a particle of mass m collides with another particle of same

mass at rest in a centered collision, the one moving comes to rest

and the other starts moving.


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When a bigger particle collides with a smaller particle at rest,

the smaller particle will move at an acute angle and bigger

particle will move in the same direction as it was moving.

When a smaller particle collides with a bigger particle at rest,

the smaller particle will move at an obtuse angle and the biggerparticle moves forward.

All of these only apply if the collision is elastic.


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ELASTIC COLLISION

Kinetic energy before collision is equal to kinetic energy after

collision.

Kinetic energy is conserved.

This type of collision is called elastic collision.

INELASTIC COLLISION Kinetic energy before collision is not equal to kinetic energy after

collision.

Kinetic energy not conserved.

This type of collision is called inelastic collision.

When a body is moving in a circular motion, the speed remains

constant.

But since the direction is continuously changing, the velocity

changes.Hence there is an acceleration.

According to Newtons 1st law if there is a motion there must be a

resultant force.


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This resultant force needed for circular motion is called

centripetal force.(Fc)

Centripetal force is directed towards the center.

According to Newtons 2nd

law if there is a resultant force theremust be an acceleration.

This acceleration is called centripetal acceleration (ac)

If the resultant force is not there, there wont be an

acceleration. Hence there wont be a change in velocity so no

circular motion.

Angular displacement is the vector measurement of angle in

radians.

1 degree = 180/pi

For a body travelling from A to B:

Angle = s/r

For a body completing a whole circle:

Angle in radian = 2pir/r


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= 2pi

To calculate velocity for a body moving in a circle, we need to

know the time it takes to complete one revolution.

The quantity is called angular velocity (w), unit: rads-1

Angular velocity = angular displacement/ timeFor a body completing a whole circle:

W = 2/T

T= 2/

Since f = 1/T

W = 2f

And since instantaneous v = s/t

And s = rtheta/t

Theta/t = W

Therefore v = rw


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A = v2/r

Therefore:

F = ma

= mv2/r

And since: v = rw= m(rw)2/r

= mr2w2/r

= m rw2

F = m a

a= rw2


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The mass m can be a rubber bung.Rotate the rubber bung making sure that the radius r remains

constant.

Start a stopwatch as soon as you start rotating.

Use the stopwatch to record the time taken to make 10

revolutions.

Repeat with different masses added to the weight hanger.

Each time measure the radius r and record it too.Draw a graph of F against rw2where F= mrw2

The graph will be a straight line through origin and its gradient

will be mass m.

Assumptions:

The bung rotates in a horizontal circle.

There is no friction between glass tubing and string.

Safety precautions:

Wear goggles to protect the eyes.

Carry out investigation in a wide space.


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UNIFORM:


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Electric field is an area where an electric force can be

experienced.

Q q1 q2

Force from Q experienced by q1 is greater than the force

experienced by q2.

Electric Field Strength

Its a vector quantity.

Magnitude is E.

E = F/Q

Unit is NC-1


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Move the probe across the paper and mark a position with some

voltage for example 6V.

Mark another position with the voltage 6V.

Repeat this to get 5-8 dots. Join all these points and you will getequipotential lines.

Those lines are perpendicular to electric field lines.

There is no p.d on equipotential lines.

Hence the work done to move a charge along an equipotential line

is zero

W = VQ

V = 0 W=0

Applying a potential difference to two parallel plates produces a

uniform electric field between them.

We can investigate this using the following procedure.

Attach an aluminum foil to a ruler.

Keep the ruler at different positions between the plates.

The foil will deflect.

The angle between the ruler and the foil will be constant.By this we know that F is constant.

Since q is also constant, we conclude that E is constant.

There is another equation which is specific for uniform electric fields

which is:


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E = V/s

E = 12000/2

= 6000 Vm-1

Vm-1is actually the same as NC-1since:

Vm-1

V= J/C

= NmC-1

NmC-1x m-1

= NC-1


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Coulumbs Law states that the force acting on two masses is

directly proportional to the product of their charges divided by

the square of their separation.

F directly proportional to Q1Q2/r2

F = kQ1Q2/r2

K = 1/0

And for a point charge:

E = kQ1/r2

E0is epsilon zero and this gives an idea of how easily an electric

field can pass through space.

When r decreases by 2x reading increases by 4x.

We can measure r using a ruler kept between the 2 spheres.

The balance reading will give an idea of the magnitude of the

force of attraction between the spheres.

It can be seen that F is inversely proportional to r.


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When a capacitor is connected to a power supply, electrons move

from the negative terminal towards the capacitor but they cantpass to the next plate due to the insulating medium between the

plates.

The other plate gets positively charged by induction.

Electrons accumulate in the capacitor and charge builds up.

Charge build up is directly proportional to potential difference

Q directly proportional to V

Q = CVWhere C is capacitance

C = Q/V

= CV-1

SI unit: Farad (F)

Capacitance is the capacity of the capacitor to store charge.

Experiment to measure capacitance


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Record current and voltage at regular intervals using a stopwatch

so that we can find Q = It and hence C = Q/V

Instead of a stopwatch and ammeter we can use coulometer but

that is used for very small charge.

Charge is directly proportional to voltage

Q = CV

V = W/Q

W = VQ

W = V x CV

W = CV2

Or

W = VQ


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W = Q/C x Q

W= Q2/C

Note: because of the energy is used to charge the capacitor and is stored.

You can investigate how the energy stored in a capacitor can bealtered in order to make it suitable for a particular combination

of bulbs.

For the circuit above, the total resistance is 5 ohm.

The 100 F capacitor was charged with 6V and then connected to

this circuit.

The bulb lighted up with the highest brightness.

Now use a different combination of bulbs.


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Each individual bulb has a resistance of 5 ohm.

Calculating the total resistance will give 5 ohms.

This is the same total resistance as the previous circuit.

Now with the capacitor charged to 6V, connect it to this circuit.

This time all bulbs wont light up with the same brightness as

before since the voltage is split between bulbs in series.

Therefore we can remove the capacitor and charge it to a highervoltage say 8V.

Connect the capacitor back to the circuit above and see whether

the bulbs light up with the highest brightness.

Keep increasing the voltage of the capacitor until all bulbs light

up to the highest brightness.

And then calculate E = CV2with that final voltage used and the

capacitance on the capacitor.

Note: in this investigation we must make combinations of bulbs such

that for all the combinations, the total resistance is constant.


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Discharging graphs

Q decreases with time since the capacitor is discharging.

V decreases with time since there is nothing else in the circuit

besides the capacitor, and the potential difference across the

capacitor is decreases.


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Current with which the capacitor is discharged decreases since

the voltage across it decreases.

Charging Curves

Charge on capacitor increases since the capacitor is beingcharged.

Voltage across capacitor increases since it is gaining the voltage

from the cell.


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Current decreases since the potential difference across the cell

and capacitor decreases.

Time Constant

It is the time required to decrease the charge/voltage/current

on the capacitor by 37% of its initial charge/voltage/current.

It is the time required to increase the charge/voltage/current on

the capacitor by 63% of its final charge/voltage/current

Time constant = RC

Q = Q0e-t/RC

Since Q = CV

And Q0= CV0

CV = CV0e-t/RC

C is cancelled

Therefore: V = V0e-t/RC

since V = IR

and V0= I0R

IR = I0Re-t/RC


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I is cancelled.

Therefore: I = I0e-t/RC

magnetic flux density:the strength of a magnetic field

symbol: B

unit: Tesla (T)

flux: the strength of magnetic field in a whole area

symbol:

formula: phi = BA

unit: Weber (Wb)

flux linkage:strength of magnetic field in whole area through a coil

symbol: N

formula: Nphi = BAN N= number of turns

unit: Weber turns (Wb turns)


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It will be a straight line with gradient Bl.

Electron beams would follow a circular path when passing througha magnetic field.

This is force F = BeV

Force F is perpendicular to both magnetic field and the direction

the electron is moving

The electron tries to move in a straight line but that forcecontinuously pulls the electron to the center of the curvature.

Hence the force is known as the centripetal force.

Mv2/r = BeV

Since BeV is perpendicular to the path of the electrons, it does

no work on them.

Therefore the speed and KE of electrons remain constant.


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A relative motion between a coil and permanent magnet will

produce an emf.

This is because a change in magnetic flux will produce a voltage.

dN/dt

BAN/s

NA-1m-1m2/s

NmA-1/s

J/AsE/It

V = E/Q

When there is a change of current in the coil linked with the

magnet, then also an emf will be induced.

Factors that increase induced emf:

Increasing number of turns on coil.

Increasing magnetic field strength.

Investigating Induced EMF

Prepare a circuit with a coil of wire and a resistor.

Connect the circuit to a data logger and the data logger to a

computer.

Set the computer so that it draws a graph of V against t

Drop a short bar magnet through the coil.

The graph will be:


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At first the emf is increasing as the magnet first enters the coil

and there is a change in magnetic flux.

Emf starts decreasing since there is less and less of change inmagnetic flux as the bar moves into the coil.

Emf becomes zero since there is no morechange in magnetic

fluxas the bar is fully in the coil

There is a magnetic flux but not a change in magnetic flux.

Beyond zero, graph goes below the x axis since an emf is again

produced as the bar moves out of the coil.

Its negative since this time the emf is in opposite direction.

Nucleon number: total number of protons and neutron in the nucleus

of an atom.

Proton number: the number of protons in the nucleus of an atom.


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Observations and Conclusions Drawn from Rutherfords Alpha

Scattering Experiment

It was seen that most of the alpha particles pass the gold foil

without any deflection. This means that most of the atom is

empty space.

Some alpha particles get deflected. This means that the atom has

a nucleus with a positive charge.

Only a few alpha particles bounce back. This means there is a

small nucleus concentrated at the center.

The escape of electrons from a metal surface when it is heated

to a very high temperature is called thermionic emission.

How are electrons accelerated by:

1.

Electric Field

Force on an electron in an electric field is parallelto the field.

Electrons are negative therefore there is a force of attraction

on them towards the positive plate.

If there is a force there must be acceleration.

F = ma

E = F/QF = EQ

EQ = ma

a= EQ/m


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2.

Magnetic Field

Force on an electron in a magnetic field is perpendicular to the

field.

When an electron is in a magnetic field, it moves in a circularpath.

This is because the magnetic force on the electron is

perpendicular to both magnetic field and electron path.

Applying the Flemings left hand rule, we would find that the

force F is always towards the center.

This resultant force F is the centripetal force.

Centripetal force produces a centripetal acceleration. Momentum can be found from radius.

r= P/BQ

Particles need to be accelerated so that they can collide with one

another, break into pieces thereby allowing us to study them.

If particles collide with slow speeds they would just bounce back.

There are 2 types of particle accelerators.

1. Linear accelerators

2.

Cyclotron

Linear Accelerators (Linac)


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Linear accelerators are a series of metal tubes connected to an

ac power supply.

The proton is fired when the left of tube one is negatively

charged.

When the proton is midway along tube 1, the ac changes so thatnow the right of that tube is negative.

Proton is accelerated towards the end of tubes 1

As it is just about to leave, ac changes so that now the start of

tube 2 is negative.

So the proton is further accelerated towards tube 2 and the

process repeats.

Every successive tube is made longer since at each succession theparticle is moving with a higher speed.

And also because the frequency at which the ac changes is

constant.

If all tubes in the diagram above were of the same size, the

proton might reach the end of tube 2 while its still positive.

This will cause the proton to repel and decelerate.

Disadvantage of the linear accelerator would be that it takes alot of space since it needs to be made longer for greater

accelerations.

Cyclotron


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Cyclotron makes the particles move in a circle.

When a charged particle, for instance an electron, moves in the

first hollow chamber (dee A) it will move in a circular path since

there is a magnetic field.

Magnetic field will provide the centripetal force to maintain

circular motion.

In dee A, the electron will complete a semicircle and just as it

does, ac changes so that there is a positive charge on dee B.

So the electron gets accelerated towards dee B.

Electron will make another semicircle in dee B and just as it does,

ac changes making dee A positive.

Electron gets accelerated towards dee A and moves in asemicircle with a greater radius.

It moves in a greater radius since it has gained kinetic energy.


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In a GM tube, the particle to be detected passes through it

ionizing the argon gas present in it.

The electron released while ionizing together with the ions are

accelerated by an electric field. The electrons are discharged when they reach the electrodes

that produce the electric field.

This produces a pulse of electricity which is counted by counter

connected to a tube.

In a mass spectrometer, the sample is vaporized then ionized by

bombardment of electrons.

The ions are accelerated by an electric field. The ions are deflected by a magnetic field.

The amount of deflection will be proportional to m/e ratio.

Hence ion can be identified by the amount of deflection.

Force acting on a charged particle moving in a magnetic field is

given by:

F = Bqv

The charged particle moves in a circle in a magnetic field.

For any object moving in a circle the force acting on it is given by:

F = mv2/r

Therefore: mv2/r = Bqv

Mv2/v = Bqr

Mv = Bqr

P = Bqr

R = p/Bq


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Hence for a given magnetic field, the radius of the path of the

particle is proportional to momentum.

For a particle interaction to occur, the charge, energy and

momentum should be conserved.

Consider the following collision

e+ + e-------- +

When a positron and an electron collided, massless particles of

gamma are produced.

How is energy conserved?

The energy is conserved since massless particles with high

velocity are produced from particles that have a greater mass

and lower velocity.

E = mv2

How is charge conserved?

Charge is conserved since the charge is zero even at the start

and the end.

How is momentum conserved?

Conserved since massless particles with high velocity are

produced from particles that have a greater mass and lower

velocity.


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Initial momentum = final momentum

P = high mass x low velocity = p = low mass x high velocity

The length of the tracks depends on the energy of the particles.

Magnetic fields deflect the charged particles and hence the

tracks are bent.

The curvature depends on momentum, charge and strength of

magnetic field.

We can tell whether the particle is positive or negative usingFlemings left hand rule. The direction of current will be the

direction of positive charge and for negative charge, the

direction is just opposite.

If the radius is decreasing, it means the particles are slowing

down as they are releasing energy.

If the particles collide with a low energy, they would just bounce

back and we wont be able to observe the smaller particles within

them.

When particles collide with a higher energy, they split into the

particles they are made up of. So we can study the fine

structure.


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E = energy

M = mass

C = speed of light (3 x 108)

Light is the fastest moving particle.

If any other object tries to move faster than light, its energy

gets interchanged to mass.

This is called Einsteins Special Relativity.

o

According to the equation, matter can appear out of nowhere.

o It is converted from energy.

Equation applied to Annihilation

o Annihilation is the process by which matter and antimatter

collide to form a high energy, massless particle. (usually

electromagnetic radiation)

o

Just as energy can be interchanged to mass, mass can be

interchanged to energy.

o The matter and antimatter vanish from existence to produce

equivalent energy in the form of electromagnetic radiation.


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To convert MeV to joule:

Energy value x 1.6 x 10-19x 106

To convert GeV to joule:

Energy value x 1.6 x 10-19x 109

To convert MeV/c

2

to kg:Mass value x 1.6 x 10-19x 106/ (3 x 108)2

To convert GeV/c2to kg:

Mass value x 1.6 x 10-19x 109/ (3 x 108)2

To convert kg to eV

Mass value / (1.6x10-19)/(3x108)

When an object tries to move faster than light, some of its energy is

converted to mass so that it does not reach that speed.

This fact needs to be taken into account when dealing with speeds near

to that of light. (for particles that have a speed of 10% less than that

of the speed of light.)


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There are 12 fundamental particles.

The fundamental particles are divided into 2 families which are:

1. Quarks (6 members)

2.

Leptons (6 members)Each quark and each lepton has their antiparticle of the same

mass and opposite charge.

QUARKS

QUARK CHARGE ANTIQUARK CHARGE

Up (u) +2/3 e Anti- up quark -2/3 e

Down (d) -1/3 e Anti-down quark +1/3 eCharm (c) +2/3 e Anti-charm

quark-2/3 e

Strange (s) -1/3 e Anti-strangequark

+1/3 e

Top (t) +2/3 e Anti-top quark -2/3 e

Bottom (b) -1/3 e Anti-bottomquark

+1/3 e


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First generation: up and down quarks

Second generation: charm and strange quarks

Third generation: top and bottom quarks.

Strong bonds form between the quarks.

LEPTONS

LEPTON CHARGE ANTILEPTON CHARGE

Electron (e-) -e Antielectron +eElectron

neutrino (Ve-)

0 Antielectron

neutrino

0

Muon (-) -e Antimuon +eMuon neutrino

(V-)0 Antimuon

neutrino0

Tau (-) -e Antitau +e

Tau neutrino(V-)

0 Antitau neutrino 0

All antileptons have the same symbol as their lepton except that

they have +instead of

When a proton was bombarded with high electrons, the proton

splits into three particles

The particles are 2 up quarks and 1 down quark. (uud)

Therefore the charge would be:

2/3e + 2/3e 1/3e = +e

A neutron has 0 charge.


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Therefore it must have 2 down quarks and 1 up quark.

-1/3e + -1/3e + 2/3e = 0

Particles like neutrons and protons are called baryons.

Baryons are particles having 3 quarks.Mesons are particles having a quark and an antiquark.

It was previously known that there are 6 leptons before all the

quarks were discovered.

Then when up, down, strange and charm quarks were discovered,

the quarks were still lagging behind leptons.

The scientists like to believe that the universe is balanced.

Therefore they came to the conclusion that there must be 6quarks with the 6 leptons.

Hence the top and bottom quarks were predicted.

Later they were even discovered for real.

Write and interpret equations for the following reaction

Neutral pion decay in which the pion becomes an electron, a positron

and a gamma photon.

0----e- + e+ +


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This reaction will occur since the charge is conserved.

The momentum, energy/mass should also be conserved for this reaction

to occur.

- Wavelength

h- Planks constant 6.63 x 10-34

p = momentum

p can also be written as mv when asked to find mass or velocity.

a2 Physics (Updated)

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