Higher Physics

Projectiles at different height

- The projectile may not necessarily take off and land at the same height. - If the projectile's flight path is not symmetrical, you will need to fill in the 1/2at*2 + ut - s = 0 equation and from that use the quadratic equation to calculate the time. NB that this will work if the projectile's path is symmetrical - you will get the same answer twice. Or alternatively, it could be tackled in two stages using... - V*2 = U*2 + 2as followed by v = u + at. This way means that you do not have to do the quadratic equation.

Velocity-time graph of a bouncing ball.

- Velocity-time graph: The velocity graph has two main parts. The first is ALWAYS DECREASING due to gravity's negative acceleration. The second part is positive and occurs once the ball has hit the ground and is rebounding. * The gradient of line line provides the acceleration of the ball. * The area idea the graph provides the displacement.

Voltage divider

The voltage diver questions are essentially series circuits on their sides. When you have the supply voltage and both voltages or both resistances, it is possible to find the remainder of the missing values by applying our circuit rules and also using the voltage divider equation: V1/V2 = R1/R2 Which is also written as: V1 = (R1)/(R1 + R2) x Vs

Weight

Unlike mass, this changes depending on where you are in the universe. The mass of an object multiplied by the gravitational field strength gives the weight of an object. Each planet has its own strength of gravity and space itself is 0 (meaning that there is no weight to the object). W = mg

Newton's First Law and friction

"An object will remain at rest or travel in a straight line unless acted upon by an unbalanced force." This has important application in everyday life. For example, this is how seat belts in cars work. This also is important in terms of space travel; once in space, there is little resistance so rockets only need to use their engines to change speed r direction saving fuel and money. Friction is any force that acts against the primary force/direction.

Newton's Second Law

"An unbalanced force will cause an object to accelerate or decelerate". The law states that an objects unbalanced force depends on the mass and the acceleration and can be combined to make the equation: F=ma

Forces at an angle to motion calculations

Any object above the level ground is subject to downward force from gravity. This downward force is the weight which acts straight downwards. As force is a vector, it can be split in to two different 'rectangular' components. - There is a component that is acting perpendicular to the slope. This is the weight (m x g) - There is a component that acts upwards called R or W perpendicular (m x g x cosϴ). - There is a component force that is acting parallel to the slope. (It is this force that acts parallel to the slope that makes the object slide downwards). (m x g x sinϴ) - Friction must also be taken in to consideration. It will oppose the force that is parallel to the slope and will affect the acceleration down the hill or the force required to move something up the hill.

Conductors, Semiconductors and Insulators

Conductors - In a conductor, the electrons are free to move and flow through the material. Examples are: metals, carbon (semi-metals) Semiconductors - In its pure form, it behaves like an insulator however if an impurity is added or a condition is changed (light, heat, voltage) then it behaves as a conductor. Examples are (element form) silicon, Geranium and Selenium and (compound form) Gallium Arsenide and Indium Antimonide. Impurities are mainly arsenic and indium. Insulators - In an insulator, there are very few electrons which are free to move. Examples are: plastic, rubber, glass, wood e.c.t.

Equations of Capacitance

From the graph, the following relationship can be established: Ecapacitor = 1/2 x Q x V where Q is the charge and V is the voltage. By substituting Q=VC, a further two equations: Ecapacitor = 1/2 x C x Vsquared Ecapacitor = 1/2 (Qsquared/C)

Tension and internal forces

Horizontal Tension: the tension in a rope attached to the engine and object being pulled is equal to the supply force. If the tension is known, then the tension can be calculated using Newton's second law: F=ma. The unbalanced force can be found by adding or subtracting forces. Usually, the two forces acting are tension and friction. In that instance, the unbalanced force would be: F = tension - friction. Note that when no force is given use 9.8N.

What happens to an a.c.'s trail when the timebase setting is turned off?

If the timebase setting is switched off, there will be a vertical line on going from the zero line to the peak violate on either side of the zero line. There will be no horizontal trail.

Momentum

Momentum is a measure of an object's motion and is the product of its mass and velocity. The law of conservation of linear momentum states that: "Total momentum before a collision is equal to the total momentum after a collision in the absence of external forces". p = m x v (where 'p' is momentum (kgms*-1), 'm' is mass (kg) and 'v' is velocity (ms*-1)). When two objects combine to form one... m1u1 + m2u2 = (m1 +m2)v When two object collide and stay two objects... m1u1 + m2v2 = m1v1 + m2v2 When one object breaks up to form two separate objects... (m1+m2)u = m1v1 + m2v2 NB: it is useful to draw a picture about what is happening. This will makes sure that you know which direction things are traveling in. When the velocity is positive, the object will move to the right. When the velocity is negative, the object will move to the left.

Circuit Rules of series and parallel circuits

Series circuits Current: in a series circuit, the current is the same at all points. This means that the total current is equal to the current at any point of the circuit. Voltage: in a series circuit, the total voltage is the total sum of all the voltage of all the single components. Resistance: the total resistance is equal to all the resistance in a circuit added up. Parallel circuits Current: in a parallel circuit, the current is not the same at all points. It is the sum of all the readings added up. Voltage: voltage is the same at all points of a parallel circuit. The total voltage is the same as the voltage of any component of the circuit. Resistance: the total resistance of a parallel circuit is the most complicated rule. The total resistance will be less than the smallest resistor of the circuit. It is calculated by: 1/Rt = 1/R1 + 1/R2 + 1/R3...

What is the terminal potential voltage? (t.p.d.)

The terminal potential difference is the effective output of a source. It is the amount of energy that is converted in t another form of energy by a component in a circuit.

Wheatstone bridges

These are circuits that can measure resistances that are unknown to a greater deal of accuracy and precision. They can either be written as a rectangular shape with a line down the middle or as a diamond-like structure; both are the same. It works by putting two resistors on one line and two resistors on the second line. The reading between the two lines can either be taken by an ammeter, voltmeter or by a more sensitive ammeter/voltmeter called a 'galvanometer'. The symbol for this is the same as the ammeter or voltmeter but has a 'G' in the middle instead of a 'V' or 'A'. One of the resistors, say R4, is varied until the value on the meter reaches 0V. This is known to be the balance point. The balance point of a Wheatstone bridge can be calculated by the equations: R1/R2 = R3/R4 or R1/R3 = R2/R4 * It is either the two resistors that are side by side or above and below that are equal to each other* **NEVER THOSE DIAGONAL FROM EACH OTHER!** Also, the resistance value may not be necessarily given in the question. They might give you the power and voltage in which case you will need to do the P = Vsquared/R to find the value! The Wheatstone brides are said to be 'balanced' when the mete reads 0V. This is a common question. You will be asked to find a resistance value for a resistor which will cause it to be balanced. To do this, you will need to make the numbers on each side of the equation equal to each other (then when it is taken over, it is cancelled out thus, the value is 0V). For example, - if line one had resistors: R1 (60 ohms) R2 ... and line two had resistors R3 (3.6 ohms) R4 (18 ohms) Then, using the equation R1/R3 = R2/R4 it can be found that R2 = (R1/R3) x (R4)

Valence band and conduction bands

- Electrons move from the valence band to the conduction band. - In an insulator, the band gap is too large for the electrons to jump across (they do not have enough energy). It therefore does not conduct. - In a semi-conductor, the band gap is smaller and therefore the electrons can move across it (From the valence band to the conduction band; it will therefore conduct.). - In a conductor, there is no band gap so the electrons can freely move between the two bands and thus, they are able to conduct.

Components of force

Similarly to velocity, forces can be split in to horizontal and vertical and can then be used to find the resultant force. Vertical : Fv = F x sinϴ Horizontal : Fh = F x cosϴ Because they form rectangles, Pythagorus' theorem and SoH CaH ToA can be used to find the angle. Force vectors that are not at right angles must be calculated upon by the other rules of trigonometry (the sine and cosine rules which are also used to find resultant velocities). If there are two forces acting in different directions but cause the object to move in a straight line then the force must be doubled.

Linking the three graphs together.

Since the three measurements are all linked, the graphs are therefore also linked. - The gradient of a displacement-time graph provides the velocity. - The gradient of a velocity-time graph provides acceleration. - The area under the acceleration-time graph provides the velocity. - The area under the velocity-time graph provides the displacement. NB: if it the trail goes in to the '+' and '-', the displacement is the difference between the two. (If it comes out to be a negative answer is not wrong, it just means that the object travelled further in once it had changed direction, than its original direction).

How do you calculate resultant velocity?

To calculate the size and direction (which is an angle) you should use trigonometry or (less preferred) scale diagram. The angle should be given as 'due x° from North' or as a three figure bearing.

What is 'free fall'?

When falling, an object will accelerate due to gravity. When the weight of the object is equal to the air resistance opposing it, the object is said to be travelling at 'terminal velocity'.

Why do satellites stay in orbit?

- "Gravity continually accelerates the object to the surface of the Earth, but the horizontal speed is great enough that it keeps missing the Earth and stays in orbit".

Acceleration-time graph of a bouncing ball.

- Acceleration-time graph: The ball is subject to constant acceleration downwards giving rise to the horizontal line. When it hits the ground and rebounds, it changes direction and this is shown by the peaks of the graph.

Significant Figures

- As a general rule, your answer should include the same number of significant figures as the numbers that are given in the question. It should be either one less or two more than the least accurate reading. - When doing further calculations (follow through calculations) it is important not to use any rounded numbers. You should only round numbers at the final stage (your final answer).

Calculations involving maximum height

- At the maximum height, a projectile's vertical velocity will be 0 ms*-1. - To calculate the height, we need to get the time first from the equation v = u + at - Then, the v*2 = u*2 + 2as can be used to gain the maximum height.

Displacement-time graph of a bouncing ball.

- Displacement-time graph: The downward direction is taken to be negative. Note that the original dropping height will not be reached in absence of unbalanced force due to a loss in energy meaning its rebound height gets lesser after each bounce.

Evidence supporting the expansion of the universe.

- Hubble's Law - Dark Matter and Dark Energy - Stars only showing 'Redshift' rather than 'Blueshift'

Unbalanced Wheatstone bridges

- If the reading on the meter is greater than zero, then the Wheatstone Bridge is said to be unbalanced. - Rv is there to protect the voltmeter when the bridge is out of balance. - R4 is varied until the reading on the voltmeter decreases close to 0 (the balance point). - The switch is then closed and short circuits allowing more accurate readings to be taken by the meters.

Motion in special cases. (the bouncing-ball)

- The ball is dropped and accelerates until it hits the ground at the bottom peak of the graph. - The ball decelerates and compresses until it reaches 0 ms*-1 where it regains its shape and rebounds upwards. - The ball leaves the ground and decelerates upwards until it reaches it maximum height where its v = 0. - This will continue until it has no energy left and comes to rest. (Ep goes to Ek, Es and Eh).

Charge scored in a capacitor

- The charge stored in a capacitor is measured using a coulomb meter. - As the change in the capacitor increases, so too does the voltage across the capacitor. - When the capacitor is fully charged, the voltage stored in it will be the same as the supply voltage. - The relationship between the two can be obtained from a graph of voltage versus charge. * The area under a graph is equal to the charge stored in the capacitor. (On the graph it is important to have a 0 where the two graphs meet)

Calculations involving range of a projectile

- The range of a projectile is dependent on the initial horizontal velocity and the time in which the object is in flight. - The theoretical range is always greater than the range in real life because it does not take n to account external unbalanced forces. - Note that you may need to perform a calculation involving the vertical components in order to gain the time even if you are not directly instructed to do so.

emf, short circuit current and the internal resistance.

- Where the line crosses the y-axis is the emf. - Where the line crosses the x-axis is the short circuit. - The gradient of the line is the negative internal resistance value.

What is a projectile?

A Projectile is any object that when projected continues by its own inertia. It will travel with constant horizontal velocity and constant downwards acceleration in absence of air resistance. The combination of the horizontal and vertical motion gives rise to the curved path.

Cells and Batteries

A battery is made of two or more connected cells. The current flows out of the negative terminal and in to the positive terminal. If a cell is connected in the opposite direct to the other cell then the quoted voltage becomes negative; e.g. if you had three cells, each of 2 volts, and two were connected with the negative terminal to the right and the third was connected with the negative to the left than the total voltage would not be 6 volts but instead it would be 2v (4 volts - 2 volts).

Graphs of motion: Displacement-time graphs

A displacement-time graph is used to show how an object's displacement varies over time. It can show an object's velocity at any given point of its journey. Because displacement is a vector quantity, the graph can go in to both the '+' and '-' axises. - Curves show that the displacement is NOT changing constantly (acceleration or deceleration). - Straight lines show that the displacement is changing constantly (constant velocity).

What is the difference between a vector and a scalar quantity?

A scalar quantity has only size - like speed, time, distance, energy and mass. A vector quantity has both size and magnitude - like velocity, displacement and all forces.

P-N junctions

A semiconductor is grown so one half is 'p-type' and the other is 'n-type'. The product of this is the formation of a diode. The symbol for the diode is the picture attached.

Graphs of motion: Velocity-time graphs

A velocity-time graph is used to show how an object's velocity changes over time. The velocity is plotted don the 'y-axis' while time is on the 'x-axis'. Again, because it is a vector quantity, there is both size and direction to it; '+' and '-' are acceptable. - A positive gradient shows an increasing velocity. - A horizontal line shows a constant velocity. - A negative gradient shows a decreasing velocity. If the trail stays in the '+' axis, it has not changed direction. If it goes in both the '+' and the '-', it has changed direction.

What is acceleration?

Acceleration is the rate of change of the velocity of something. In physics '∆' is used to represent the change in something; be it velocity or temperature e.c.t.. Because acceleration is a vector quantity, it is necessary to quote both size and direction. For Higher, it is only necessary to have a '+' or a '-' sign to show this. This is why we use -9.8ms*-2 to show the acceleration due to gravity. (Note that acceleration may also be calculated using F=ma)

Graphs of motion: Acceleartion-time graphs

An acceleration-time graph is used to show how an object's acceleration varies over time. Only straight box-like lines are used at higher level. - Lines in the '+' section of the graph are considered to be acceleration. - Lines in the '-' section of the graph are considered to be deceleration.

Charging and Discharging Capacitors (the graphs)

Charging Current When charging, the current will start high and decrease until it reaches 0 when it is fully charged. Voltage When charging, the voltage starts low and increases quickly and then eases until it reaches the total voltage. Discharging Current When discharging, the current will start high and will decrease quickly and ease off as it reaches 0. NB that the current will be negative because it is flowing in the opposite direction meaning that even though it may seem to be increasing (say -0.6A to -0.1A) it is actually decreasing. Voltage When discharging, the voltage will start high and will decrease at a slowing rate until it reaches 0V.

What is Dark matter and Dark energy?

Dark matter: this is everything we cannot see. All the known mass of the universe added up does not equal the total mass of the universe. It has been named 'Dark Matter' until we discover what it is! Dark energy: this is the force that opposes gravitational force (again, we do not know what this is so it has been named 'Dark energy' until we discover what it actually is!)

a.c. and d.c. current

Direct current only flows in one direction. It is therefore a straight line above the zero line. Alternating current changes direction meaning that the electrons flow in one direction and then the other direction. It changes direction every half cycle resulting in a sine graph like trace on the oscilloscope.

Impulse

During a collision, for a period of time, the forces change the momentum. Here, the mechanics of the forces during a collision are considered with the concept of impulse. Ft = mv - mu where Ft is impulse (Ns), mv is the final momentum (kgms*-1) and mu is the initial momentum (kgms*-1). Thus, impulse is equal to the change in momentum. The factors that affect the change in momentum are: 1. Contact time 2. The size of the force Force-time graphs The area under the graph is equal to the impulse. If a hard ball is hit at speed x, the contact time will be less than if a softer ball was kicked at the same speed. The force however, would be greater each second meaning that the areas under graphs is equal. If you are asked to draw a second path of an impulse graph change the peak force and contact time in proportion to each other so that the areas are still the same.

What is e.m.f.?

E.m.f. stands for the electromotive force and is energy transferred from an external source to the circuit. It is the amount of energy that a source has to start with before internal resistance is considered. Sources of e.m.f. include: - Chemical Cell - Thermocouple - Solar Cell

Moving source

For a moving source, the wavelength and frequency are NOT constant. - When the object is moving towards the observer, the WAVELENGTH IS SHORTER and the FREQUENCY IS HIGHER. - When the object is moving away from the observer, the WAVELENGTH IS LONGER and the FREQUENCY IS LOWER. This is why when a siren approaches and passes you the sound changes.

Stationary source

For a stationary source, the wavelength and frequency are constant.

Elastic and inelastic collisions

For an ELASTIC collision, ALL OF THE ENEGY IS CONSERVED. (only occurs in atoms) For an INELASTIC collision, NOT ALL OF THE ENERGY IS CONSERVED. (more common) To prove whether a collision is 'elastic' or 'inelastic', use the kinetic energy calculation: Ek = 1/2mv*2.

Hubble's Law

Hubble's Law shows the relationship that exists between the velocity of a galaxy , v, and the distance which it recedes from us, d. Hubble's constant is 2.3x10*-18 Ho = v/d and... 1/Ho = age of universe. ** Note that the units in the diagram are incorrect in terms of SQA. They should be s*-1 for time and ms*-1 for the speed. **

Theoretical Questions on emf circuits

If you had a simple emf circuit and added another resistor in parallel what would happen to the tpd voltage when the switch is closed. - The total resistance would decrease. - As the resistance goes down, the current will increase. - The lost volts will increase. - So the tpd will decrease as E = Ir + V (E is constant meaning that when Ir goes up the V goes down).

Conservation of energy continued

In a frictionless scenario: When an object of mass, m, is at a height, h, then it has gravitational potential energy given by Ep = m x g h In absence of frictional forces like air resistance none of the energy is converted in to heat or sound meaning that all of it is transformed in to the new form. When this object is released, the energy changes in to kinetic energy so Ep = Ek mgh=1/2mv*2 2gh = v*2 v = Square root of 2gh This has an important application: the speed of an object when it hits the ground is not dependent on its mass. This is why on the moon, where there is no atmosphere or resistance, if you dropped a hammer and a feather from the same height, they would land at the same time. However, in reality, friction does act and causes some of the energy to be 'lost' (converted in to less obvious forms). Total energy is still conserved however meaning that an object falling towards the earth may have its Ep changed in to many form but the sum of all of these will equal the original amount of Ep. i.e. if it was converted in to kinetic and heat then, mgh = 1/2 mv*2 + mc∆T An application of this is in vehicle breaking. A disk makes contact with a moving part (wheel) and converts the energy into heat to reduce the speed. This means that: 1/2mv*2 = mc∆T

What is Displacement?

It is a vector quantity that describes the path of something from the start to finish in a straight line. It is given a size and direction because it is a vector quantity. Note that this is NOT the same as distance. Distance is the total amount of meters travelled so is aways equal to or greater than displacement.

Gravitation

Newton's Law of Gravitation involves combining masses, the distance between objects' centres and the gravitational constant (6.67x10*-11 Nm*2kg*-1) in the formula attached.

Acceleration down an incline plane

Newton's second law states that an object will accelerate in the direction of the unbalanced force. The greater the angle of inclination, the greater the acceleration. F=ma If friction is neglected, you can calculate the acceleration of the object using: ma = F ma = mgsinϴ (divide both sides by m) a = gsinϴ Friction on an inclined slope If friction is included in the question, it will affect the acceleration. If an object is moving downhill, the friction will be acting uphill. If an object is moving uphill, the friction will be acting downhill. The unbalanced force is therefore equal to the difference between force acting down on the place end the force of friction. Fun = Fslope - Friction Fun = mgsinϴ - Friction Once this unbalanced force has been established, the acceleration can be calculated by F = ma. Alternatively, if an object is being pushed up the slope, friction would be acting in the same direction of the weight so would mean that: Fun = Fslope + Friction Fun = mgsinϴ + Friction *Good advice for tackling these questions is to draw out a diagram to make sure that you know which forces are which and in which direction they are action upon*

Doppler Effect

Note that the same rules that are used for sound can also be applied to light. Usually, light is considered in terms of wavelength rather than frequency. This means that the Doppler Equation can also be written as: λo = (c±vs)/fs

Cosine Rule

Note that these are not giving in the exam.

Sine Rule

Note that these are not giving in the exam.

Further evidence supporting 'The Big Bang'

Olber's Paradox: this explains why the sky is dark at night. If our universe followed the 'steady state' model, there would be an even distribution of stars in all directions. This would mean that the light from the stars should reach the Earth and make the sky bright. This does not happen. Instead, the Big Bang gives the universe a finite age and therefore only the stars in the observable universe can be seen. This means that only stars within 15,000 light years will be observed. Not all the stars of the universe are within this distance meaning lots of the light does not reach the Earth. Thus, the sky is dark at night.

What is the random uncertainty?

Random fluctuations occur from reading to reading. The best estimate is given by repeating the readings and calculating their mean fluctuation by taking the lowest value away from the greatest reading and then dividing it by the number of readings. This number that is given is the random uncertainty.

For a stationary observer the frequency is calculated by...

Source moving towards from them: fo = fs (v/(v-vs)) NB that it is v '-' vs * higher observed frequency than the source's actual frequency. Source moving away from them: fo = fs (v/(v+vs)) NB that it is v '+' vs * lower observed frequency than the source's actual frequency. To remember this, think about the distance that the object is from the observer. > If it is moving towards the observer, the distance is decreasing so '-'. > If it is moving away from the observer, the distance is increasing so '+'.

How to remember which letters go with which observers

T' goes with L (these are the bigger values and are the STATIONARY OBSERVER'S MEASUREMENTS) L' goes with T (these are the smaller values and are the MOVING OBSERVER'S MEASUREMENTS)

What is the 'Doppler Effect'?

The Doppler Effect is the change in observed frequency of a wave when the source or observer is moving. fo = fs (v/(v±vs))

Applications of the Doppler Effect

The Doppler Effect is used in Radar systems. It relies on this to measure the velocity of an object. This is also used in weather forecasting, speed guns and air traffic control. Doppler Radar systems rely on the equation above: The object (plane) is considered to be the source and reflects the original signal. The movement of the object relative to the radar results in a shift that is given by: fo = fs (v/(v-vs)) * moving towards the radar fo = fs (v/(v+vs)) * moving away from the radar

Forces at an angle to motion explanation

The Inclined Plane: this is the uneven slope that the object is moving on. It has its own angle 'ϴ' which shows how steep it is. This angle can be used by ToA from trigonometry. An object will slide down when the angle of inclination is big enough. This means that as the slope steepness increases so too does the force acting down. When the force acting down on the place exceed that of friction, the object will being in move down the slope. This explains why it is more difficult to go uphill in comparison to flat and downhill land.

The Lorentz Factor

The Lorentz Factor is a scaling factor that is used to calculate how much the measured time has been affected by the speed. It can be concluded that: t' = t x γ (where γ is the Lorentz factor)

Gravitational Field strength

The attraction that objects have for other objects can be explained using gravitational filed strength. It is though that anything with a mass attracts and is attracted to other things with masses. As the mass of the object increases so does the gravitational strength. It is generally accepted that this is one of the ways in which the Big Bang started to form masses. This combining of mass from the gravitational strength gets so great that it can cause fusion to occur and thus, stars are formed. This theory can be proven from the rings of dust particles that are found around may stars. A further application of gravitational attracting explains why we get low tides and high tides (due to the moon's gravitational pull). The moon exerts a force on the Earth and the Earth exerts an equal but opposite force in the moon. This explains why the planets and moons stay in orbit.

Capacitors

The circuit symbol for a capacitor is two parallel plates that are equal in length. A capacitor is used to store electrical charge and electrical energy. C = Q/V from this equation it can be stated that 1 farad is equal to 1 coulomb per volt.

What is length contraction?

The distance between two events depends on the frame that they are measured in. The length of the object measured in the stationary frame is called the proper length and is bigger than the length measured by a moving observer. The Lorentz factor can also be used here to indicate the amount which the speed has changed the length. L = L'/γ

Tension applications (train)

The engine of a train must pull all of the carriages. The tension however, is not constant between each carriage. The carriage closest to the engine will have a greater tension that the one at the end because it is pulling more rather than the end one which is in fact just being pulled. In calculations, you use the TOTAL mass to find the acceleration as that is constant. You should only use of the mass that is being pulled to calculate the tension. Also, if friction is acting on the objects being pulled, this must be added to the tension calculated from T=ma.

Calculations from the readings

The frequency can be calculated from the period. This is achieved by calculating the horizontal distance for one wave to complete its cycle. (from peak to peak or trough to trough). f = 1/T where f is the frequency and T is the period. The peak voltage can also be found from the oscilloscope. It is the number of boxes from the zero line to the highest point times by the volts per division. It is important to watch out for prefixes in this type of question.

The Big Bang (Evidence)

The main evidence supporting the Big Bang is to do with the temperature of distant stars. - Cosmic Microwave Background Radiation (CMBR) existing everywhere in the universe. - The abundance of hydrogen and helium atoms. By examining the spectrum of a distant star, its temperature ca be calculated. p = σT*4 where: p is power (W), σ is Stefan's constant (5.67x10*-8 Wm*-2k*-4) and T is temperature (K).

Semiconductor

The most common semiconductor is silicon. It has four outer electrons which it shares with the other atoms. This means no electrons are free to conduct so it has high resistance. n-type semiconductor - The semiconductor is 'doped' with a Arsenic (As) nucleus (or anything with atoms with 5 outer electrons). As there is one 'extra' electron the conductivity is increased. Because there are more electrons than holes, it is overall negative hence the name 'n-type'. p-type semiconductor - The semiconductor is 'doped' with an Indium (In) nucleus. This has three outer electrons meaning that there is one more hole than electron. This causes the material to have an overall positive charge (the holes are not positive by are not negative meaning that they cause it to seem that way) giving rise to the 'p-tpe' name.

Factors affecting the rate of charge and discharge

The time taken for a capacitor to charge is controlled by: - The resistance of the resistance. - The capacitor of the capacitor. The factors do not affect the total voltage store meaning that the areas under the two graphs are the same.

Equations of motion

There are 5 possible variables which must be considered as horizontal and vertical components. Vertical component must be considered in terms of: s - displacement (if this is negative, acceleration must also be negative.). (+ or - m) u - initial velocity (ms*-1) v - final velocity (ms*-1) a - acceleration (+ or - ms*-2) (If this is negative, displacement must also be negative. Also, if no acceleration is give, used -9.8ms-1.). t - *time (s) Horizontal component must be considered in terms of: d - distance (m) v - velocity (ms*-1) t - *time (s) *time is the only variable that can be constant in both vertical and horizontal

The Oscilloscope

There are two main readings on the oscilloscope: 1. Timebase setting: this is the time taken for one wave to move along the oscilloscope measured in seconds per division or seconds per cm. 2. Y-gain setting: this controls the voltage. It is measured in volts per division or volts per cm.

The Big Bang

There are two theories to how the universe started. It is generally accepted that it started with a sudden appearance of energy which consequently became mass. 1. The steady state universe: this theory states that universe has always been the way it is and alway will be. 2. The Created Universe: this theory tells of a past event that started our universe.

What are uncertainties and why are they important?

There is a degree of uncertainty when any physical quantity is measured. Systematic effect occurs when all measurements are affected in the same way. For example if a meter stick shrinks and is used to measure every thing or if someone measuring something makes the same mistakes every time. Scale Reading indicated how accurate a device can measure something; it is usually given a value of ±x. - For an analogue scale, it is ±half the least division of the scale. - For digital scales, it is ±the least significant digit displayed.

Blackbody Radiation

Things can absorb radiation and release it at a later stage. This is what some of the stars have done with the radiation from the Big Bang. It follows two main rules: 1. The greater the temperature, the shorter the peak wavelength emitted. 2. The greater the temperature, the greater the power emitted.

What is relative velocity?

This concept deals with the idea of relativity. If you are moving and measure another moving object, the velocity you measure will be different to that of what a stationary observer would measure. It can be calculated by adding 'vectors' tip-to-toe'.

Red Shift and Blue Shift

This is another example of the doppler effect. Light from stars, when observed on Earth, is always reduced in frequency and is moved to the red end of the spectrum (hence the name!) which has a longer wavelength. This gives rise to the idea that the stars are moving away from us. The greater the redshift value, the faster the galaxy is moving. Blue shift is the total opposite of this. This is when the light source is moving towards the Earth. The frequency is increased and towards the Blue end where the wavelength is shorter. This would imply that the galaxies are moving towards us and that would mean the universe is contracting - fortunately this has never been found! z = λobserved - λrest / λ rest, where 'z' is red (or blue) shift, λobserved is the wavelength of light form the star or galaxy, λrest is the wavelength of light from the continuous spectrum given from the sun. - If λo > λr, z will be positive and will therefore show redshift. - If λr is > λo, z will be negative and will therefore show blueshift.

Percentage uncertainty

This is found by first of all doing the random uncertainty. From here, use the ± value to gain a percentage of the mean value and thus gain the percentage of accuracy of the measurement.

What is voltage?

This is the amount of energy that is transferred per unit of charge. It is defined by the equation E = QV which, when re-arraged, states that 'one volt is equal to one joule per coulomb'.

Electric Power

This is the amount of energy transferred each second as per the definition from the equation P = E/t. There are four other equations for power which can be found on the relationships sheet.

What is the r.m.s. value of current and voltage?

This is the average value that a source produces. Mains voltage has an r.m.s. value of 230 volts but the peak voltage is actually 325 volts. It is the r.m.s. value that is quoted on appliances as that is the values that the products will be operating under.

What is time dilation?

This is the concept that time does not pass at a constant rate but instead is dependent on the frame in which it is observed. It is said that time passes slower as you get closer to the speed of light. Thus, giving rise to ideas such as the twin paradox. It can be difficult to work out what is what in a question. - The longer time is t' and this is the one that is observed by the stationary observer. - The shorted time is t and this is the one that is observed by a moving observer.

What is current?

This is the flow of charge per second in a circuit. It is defined from the Q = I x t equation which when re-arranged states that 'one ampere is equal to one joule per second'.

What is the peak voltage and peak current?

This is the maximum value that can be reached. It can be calculated by multiplying the r.m.s. value by the square root of two. NB that the formula is pretty much the same for current and voltage.

Absolute Uncertainty

This is the most developed type of uncertainty. To calculate this uncertainty, you will first of all need to do the random uncertainty followed by the percentage uncertainty. To gain the absolute uncertainty, you times the mean value by the percentage to see what the ± value is in terms of the units. For example if the mean reading was 20V and the percentage uncertainty was ±10%, then the absolute uncertainty would be 20±2 V. NB: this is the only type of uncertainty which the units are included in.

What is recessional velocity?

This is the speed at which stars and galaxies are moving away or towards us. z = V galaxy / c (where 'z' is the red (or blue) shift, 'V galaxy' is the speed at which the galaxy is travelling at and 'c' is the speed of light.).

What is velocity?

This is the vector quantity that is used to describe the rate of change. The formula used to find it is similar to average speed but instead of using distance, the displacement is used.

What is Special Relativity?

Time is not measured to be constant for everyone. It will move slower for moving observers in comparison to stationary observers. It can be said that people have their own frames of reference which are relative to the speed that they are travelling at. The postulates of Special Relativity are: 1. That the speed of light is the same for all observers in a vacuum. This means that no matter how fast you travel, you will never catch up with light. (Light always travels towards or away from observers are 3x10*8ms*-1) e.g. if a spacecraft travelling at 2/3 of the speed of light was to put its headlights on, the light would be observed to be traveling at the speed of light by both the stationary observer and anyone on board. 2. When two observers are moving at constant speeds relative to each other, they will observe the same laws of Physics. So basically, the laws of physics are the same in any frame of reference but the value of quantities measured will depend on the frame in which they are measured in. It also brings in the ultimate speed at which no object can travel faster than (the speed of light c, 3x10*8ms*-1).

Horizontal and Vertical components of velocity.

To calculate the horizontal component: (Initial horizontal velocity): uh = u x cosϴ To calculate the vertical component: (Initial vertical velocity): uv = u x sinϴ Where 'ϴ' is the launch angle and 'u' is the velocity at the projected angle.

Further Calculations with Wheatstone bridges

To find the voltage of an unbalanced Wheatstone you should find the voltage on each side of the meter and take the smaller value away from the greater value. The difference between the two is the reading on the meter.

Holes

When an electron leaves a crystalline lattice, there is a space left behind called a hole. The original hole may be filled by another electron but this would cause a different hole to appear- either way there will still be an imbalance in electrons to holes. - In intrinsic (undated) semiconductors, the number of electrons is equal to the number of holes. - In extrinsic (doped) semiconductors, the number of electrons is greater than the number of holes. Doping is the addition of a very small amount of impurity e.g. Arsenic to a pure semi-conductor. This action dramatically changes the electrical properties of a material i.e. it allows the semiconductor to conduct as there are electrons able to move through the band gap. Once doped, the semi-conductors are called 'extrinsic conductors'.

Emf and Internal resistance

When drawn, a battery will have the cells connected with three dashed lines. However, when the inside the battery is revealed through a dashed rectangle, then only one cell is shown (it can represent any number of individual cells) and is connected with solid lines to an internal resistor to the right. The value 'E' of this 'cell' is the emf. The value 'r' of the internal resistor is the internal resistance of the battery. When combined with the rest of the rest of the circuit, 'R' refers to the external resistor and 'I' to the current in the circuit. This gives rise to the equation: (all three parts are voltages) E = Ir + V or E = I(r+R) both are the same. -> 'E' is the e.m.f. -> 'Ir' is the lost volts -> 'V' is the tpd NB: EMF IS ALWAYS GREATER THAN TPD If a voltmeter was placed across the battery and an ammeter was in the circuit then: - When the switch is open, A=0 and V=emf - When the switch is closed, A= >0 and V=tpd

Resultant forces

When more than one force is acting on an object, they can be combined like vectors to form a resultant force, similar to that of velocity. If the resultant forces is 0 then the forces are balanced. The unbalanced force (size and direction) can be calculated in one dimension by adding or subtracting the forces. Fun = Forces acting one way - Forces acting in the opposing direction.

When referring to capacitance or resistance... And also capacitance...

When referring to capacitance or resistance, NEVER talk about the size or volume. i.e. Increase or decrease the capacitance or resistance. When talking about capacitance, you should change your answer in terms of decimal places to get it in to the form of a prefix; mF or pF.

Tension applications (elevator)

When you are going down, you are working with gravity and therefore T, tension, is less than weight. When you are going up, you are working against gravity and therefore T, tension, is more than weight. When T is greater than W, you feel heavier. When W is greater than T, you feel lighter. When you are stationary, the tension is equal to the weight so the unbalanced force is 0N.

Energy

Work is done when a force is applied over a distance. Ew = Fd Gravitational Potential Energy of a mass, m, being lifted to a height, h, is given by Ep = mgh. Kinetic Energy depends on the mass and velocity of an object. It can be calculated by Ek = 1/2 mv*2. Conservation of Energy: Energy cannot be destroyed or created, it can only be changed in to different forms. - work is done when converting one type of energy to another type. - power is the measure of the rate at which the energy is converted/changed. 1 Watt = 1 joule per second. P = E/t

Intrinsic Semiconductors

e.g. Silicon and Geranium - In their pure form they have four outer electrons. These cause the structure to be covalently bonded. - Because all of the electrons are attached/bonded, there are few free electrons to move about or conduct. This leads to a high resistance. - When heated, imperfections in the lattice and thermal ionisation may cause a few electrons to become free and move. This will allow the material to conduct. A higher temperature will cause more electrons to become free and therefore the resistance is decreased and increases the conductivity. E.g. Thermistor

Definitions of (i) emf, (ii) tpd and (iii) lost volts

i) Emf is the energy given to each coulomb of charge as it passes the source. ii) V (tpd) is the effective output of the battery. It is the energy each coulomb of charge has as it exits the source after passing the internal resistance. iii) Lost Volts is the difference between the Emf and tpd. It is the voltage that is lost to the internal resistance of the battery.