Physics January Revision.
Topic 2, Further Mechanics.
Linear Momentum.
Momentum is equal to mass times velocity and therefore the units are kilogram seconds to the minus one or
Newton seconds.
Momentum is a vector because velocity is a vector.
The principle of conservation of linear momentum states that in any interaction between bodies, linear
momentum is conserved provided no external force acts on the bodies.
The rate of change of momentum of an object is directly proportional to the resultant force which acts on the
object. Force is equal to change in momentum divided by time. Although if mass is constant force is equal to
mass times acceleration.
Impulse is equal to change in momentum. Impulse is equal to force times change in time.
In momentum collisions in 2 dimensions the component of the momentum in the x direction is conserved and
the component in the y direction is conserved.
Momentum and energy.
Energy cannot be created or destroyed. Energy can be transferred from one form to another but the total
amount of energy in a closed system will not change.
Kinetic energy is equal to half times the mass times the velocity squared. Kinetic energy is also equal to
momentum squared divided by 2 times mass.
Elastic potential energy is equal to half times k times the change in x squared.
Gravitational potential energy is equal to mass times gravity times the change in height.
In elastic collisions kinetic energy is conserved and momentum is always conserved. In inelastic collisions
kinetic energy is not conserved but momentum is always conserved.
Motion in a circle.
One radian is equal to 57.3 degrees.
To convert degrees to radians you times by pie over 180.
To convert radians to degrees you divide by pie over 180.
Angular velocity is the same as angular frequency and angular speed.
Angular speed is equal to angle turned divided by time.
Angular speed is also equal to 2 pie over time for one rotation.
Angular speed is also equal to 2 pie times frequency.
Linear speed is equal to angular speeds times the radius of the circle.
Centripetal acceleration is equal to linear speed squared divided by the radius of the circle.
Centripetal acceleration is also equal to radius times the angular speed squared.
Centripetal acceleration is produced by the centripetal force and there are 2 equations for centripetal force.
Centripetal force is equal mass times velocity squared divided by radius.
Centripetal Force is also equal to mass times angular speed squared times radius.
If you remove the centripetal force the object would fly off at a tangent.
Electric and magnetic fields.
Electric Fields.
If a charged object is placed in an electric field it will experience a force.
Coulomb’s law states that the force of attraction or repulsion between two point charges is equal to k times
charge 1 times charge 2 divided by radius squared. It is an inverse square law, the further apart the charges,
the weaker the force between them.
A point charge has a radial field and a uniform field is produced by two parallel plates. In a uniform field the
filed lines go from positive plate to the negative plate.
Electric field strength is force per unit charge. It is calculated by force divided by charge. The unit for electric
field strength it the Newton per coulomb.
You can think of field strength by how tightly packed the field lines are.
In a radial field electric field is equal to k times charge divided by radius squared.
In a uniform field the size of the electric field strength can be represented by voltage divided by distance
between the plates. In a uniform field the field lines are parallel so are always the same distance apart. This
means the field strength is the same at all points within the field.
Capacitance.
Capacitance is equal to charge divided by voltage. Capacitance is measured in Farads. Capacitance is usually
measured in micro Farads, nano Farads or pico Farads.
Energy stored by the capacitor is equal to a half times charge times voltage. Energy stored in a capacitor is also
equal to half times capacitance times voltage squared. The third equation for energy stored by a capacitor is
charge squared divided by 2 times the capacitance.
The time taken to charge or discharge depends on two factors. The capacitance of the capacitor, this affects
the amount of charge that can be transferred at a given voltage. The second factor is the resistance of the
circuit which affects the current in the circuit.
Exponential growth is when something gets larges by the same fraction or proportion in each time interval.
Exponential decay is when something gets smaller by the same fraction or proportion in each time interval.
Time constant is equal to resistance times capacitance.
Magnetic Fields.
A magnetic field is a region where a force is exerted on magnetic materials. Magnetic field lines go from north
to south. The closer together the lines the stronger the field,
There’s a magnetic field around a wire carrying electric current. The direction of the magnetic field can be
worked out using the right hand rule.
The total magnetic flux passing through an area perpendicular to a magnetic field is equal to magnetic field
times area. When you move a coil in a magnetic field, the size of the e.m.f induced depends on the magnetic
flux and the number of turn s on the coil. The product of these is called the flux linkage.
Flux linkage is equal to number of coils times magnetic flux.
Flux linkage is also therefore given by magnetic field strength times area times number of coils.
The unit for magnetic flux and flux linkage is the weber.
A wire carrying a current in a magnetic field will experience a force which is calculated by magnetic flux density
times current times length. The direction of the force is given by Flemings Left hand rule.
When the current carrying wire is at right angles to the magnetic field, the force is equal to magnetic field
strength times current times length of the wire. At an angle the force is equal to magnetic field strength times
current time length sin angle.
The force is greatest when the wire and field are perpendicular.
Charged Particles in Magnetic Fields.
Forces act on charged particles in magnetic fields.
Force is equal to magnetic field times current times length,
Force is also equal to magnetic field times charge on the particle times velocity.
Force is also equal to magnetic field times charge times velocity sin angle. The angle is the angle between the
direction of motion and the magnetic field.
Charged particles in a magnetic field are deflected in a circular path.
If a conductor moves through a magnetic field its electrons will experience a force so they will accumulate at
one end of the rod. This induces an e.m.f as a battery would. If the rod completes the circuit then a induced
current will flow through it – this is electromagnetic induction. An e.m.f is induced whenever there is a relative
motion between a conductor and a magnet. The conductor can move and the magnetic field stay still or the
other way round. An e.m.f is produced whenever line of force (flux) is cut. Flux cutting always induces e.m.f
but will only induce a current if the circuit is complete.
Faradays law states the induced e.m.f is directly proportional to the rate of change of flux linkage.
Induced e.m.f is equal flux change over time taken.
The size of the e.m.f is show by the gradient of a graph of flux linkage against time.
The area under the graph of e.m.f against time gives the flux change.
Electromagnetic Induction.
Lenz’s law states the induced e.m.f is always in such a direction as to oppose the change that caused it.
You can change the voltage induced in the coil by changing the following factors.
1.
The angle between the coil and the field.
2.
Number of turns of the coil.
3.
Area of the coil.
4.
Magnetic field strength (flux density).
5.
Angular speed off the coil.
An alternator is a generator of alternating current. Generators also know as dynamos convert kinetic energy
into electrical energy- as they induce an electric current by rotating a coil in a magnetic field.
Transformers work by electromagnetic induction. An alternating current flowing in the primary coil produces a
magnetic flux. The magnetic field is passed through the iron core to the secondary coil, where it induces an
alternating voltage of the same frequency.
Step up transformers increase voltage by having more secondary coils.
Step down transformers reduce the voltage by having fewer coils in the secondary coil.
Particle Physics.
Rutherfords Model of the Atom.
The conclusions from Rutherford’s alpha particle scattering experiment were:
1.
Most of the fast, charged alpha particles went straight through so therefore the atom is mostly empty
space.
2.
Some of the alpha particles are deflected back through significant angles, so the centre of the atom
must be tiny but contain a lot of mass.
3.
The alpha particles were repelled, so the nucleus must have a positive charge.
4.
Atoms are neutral overall so the electrons must be on the outside if the atom separating one atom
from the next.
Electrons and nuclei.
Proton number or atomic number is the number of protons in an atomic nucleus. Neutron number is the
number of neutrons in the nucleus of an atom. The nucleon number is the total number of protons and
neutrons.
Particle accelerators.
Electron guns produce electrons by thermionic emission. When you heat a metal, its free electrons gain a load
of thermal energy. If they gain enough energy they break free from the surface of the metal. Once they have
been emitted, the electrons can be accelerated by an electric field in an electron gun.
De Broglie Wavelength is equal to Planck’s constant divided by mass times velocity, where mass times velocity
equals momentum.
Electron volt is defined using accelerated charges. 1 electron volt is the kinetic energy carried by an electron
after it has been accelerated through a potential difference of 1 volt.
Energy gained by an electron in electron volts is equal to accelerating voltage.
The two linear accelerators are linear accelerator and the cyclotron.
A linac is a long straight tube containing a series of electrodes. A high frequency alternating current is applied
to the electrodes. The high energy particles leaving the linac collide with a fixed target at the end of the tube.
A cyclotron uses two semicircular electrodes to accelerate charged particles across a gap. An alternating
potential difference is applied between the electrodes. A magnetic field is used to keep the particles moving in
a circular motion.
The mass of particles increases with speed.
Classification of particles.
Hadrons are particles that feel a force called the strong interaction. There are two types of hadrons. They are
baryons and mesons.
Particles made up of three quarks are called baryons. Protons and neutrons are examples of baryons. A
protons quark structure is up, up down. A neutrons quark structure is up, down, down. The proton is the only
stable baryon.
Mesons are made up of a quark and an anti-quark. All mesons are unstable. Pions are the lightest mesons and
there are three versions with different electric charges: plus, minus and neutral. Kaons are heaver and more
unstable and you get different ones like plus, minus and neutral kaons. Mesons interact with baryons via the
strong interaction.
Leptons are fundamental particles and they do not feel the strong interaction force. The only way they can
interact with other particles is via the weak interaction, gravity and the electromagnetic force if they are
charged.
Electrons are stable and there are two other leptons. The two other leptons are muons and taus and they are
unstable and are just like heavier electrons. Muons and taus eventually decay into ordinary electrons. The 3
leptons have their own neutrino and have zero mass or electric charge.
Neutrons decay into protons.
Anti particles .
Antiparticles were predicted before they were discovered by Paul Dirac. Every particle has an antiparticle with
the same mass but an opposite charge. Even neutrinos have antiparticles called anti neutrinos.
When energy is converted into mass you have to make equal amounts of matter and antimatter.
If an extra proton is created, there has to be an antiproton. This is called pair production.
The opposite of pair production is annihilation. This is when a particle meets its antiparticle and all the mass in
the reaction turns to energy.
Mesons are their own antiparticles.
Quarks.
Quarks are fundamental particles. There are three types of quarks.
Up quarks have a plus two thirds charge.
Down quarks have a charge of minus a third.
A strange quark has a charge of minus a third.
There are three other types of quarks.
A top quark has a charge of plus two thirds.
A bottom quark has a charge of minus a third.
A charm quark has a charge of plus two thirds.
Pions are made up of up, down, anti up and anti down, whereas Kaons have strangeness as well.
It is not possible to get a quark by itself – this is called quark confinement.
There are five properties conserved in particle reactions. Total charge, baryon number, mass energy,
momentums and lepton number are conserved. In lepton number each of the three types of lepton have to be
conserved separately.
Detecting Particles.
When a charged particle passes through a substance it causes ionisation, leaving a trail of ions.
There are two types of particle detectors which only show up charged particles.
Cloud chambers work using a super cooled vapour. The ions left by particles make the vapour condense and
you get vapour trails.
Heavy, short tracks mean lots of ionisation so those will be alpha particles. Fainter long tracks are beta
particles.
Bubble chambers work by hydrogen being kept as a liquid above its normal boiling point by putting it under
pressure. If the pressure is suddenly reduced, bubbles of gas will form in the places where there is a trail of
ions.
A charged particle in a magnetic field will experience a force making the particle follow a curved track. The
radius of the curved track is equal to momentum divided by magnetic field strength times the charge on the
particle.
Positive and negative particles curve in other ways which can be worked out using Fleming’s left hand rule.
You see spirals because interactions with the detector decrease the energy and therefore momentum.
Neutral particles only show up when they decay.
Cloud and bubble chambers are no longer used. Detectors used give out electrical signals that are sent straight
to a computer.
Key equations.
Density is equal to mass divided by volume.