W=mg 1.1 define Weight as the force on an object due to a gravitational field

To change the G.P.E. of an object a force must be applied through a distance, i.e. work1.2 explain that a change in gravitational potential energy is related to work done

At r=infinity, E.P. = 0

To move an object away from the Earth we must do work on it. If after work is done, the potential energy is 0, then near the Earth the Ep must be negative.

1.3 define gravitational potential energy as the work done to move an object from a very large

distance away to a point in a gravitational field

1.4 perform an investigation and gather information to determine a value for acceleration due to gravity using pendulum motion or computer-assisted technology and identify reason for possible variations from the value 9.8ms-2

Aim: To find the value of g by measuring the period of a pendulum of known length

Theory: oscillation (T) of a simple pendulum is given by:

Tie a mass to the end of a piece of string and attach to horizontal support1.Measure the length of the pendulum2.Set pendulum in motion and measure 10 oscillations (1 = back and forth)3.Record results in a table like so:4.

Method:

Length (l) Time for 10 oscillations 10T (s) Period T (s) g (ms-2)

1.00 20.08 2.008 9.79

0.80 17.90 1.790 9.86

0.60 15.64 1.564 9.68

0.40 12.58 1.258 9.98

Average value for g is found to be 9.83 ms-2

Variations of local gExperimental error

Variations from expected is due to

1.5 gather secondary information to predict the value of acceleration due to gravity on other planets

Planet Mass ratio Radius ratio g

Mercury 0.06 2.63 4.1

Venus 0.82 1.05 8.9

Earth 1.00 1.00 9.8

Mars 0.11 1.89 3.8

Jupiter 318.0 0.09 24.8

Saturn 95.0 0.11 10.5

Uranus 14.5 0.25 9.0

Neptune 17.2 0.26 11.2

1. The Earth has a gravitational field that exerts a force on objects both on it and around itSaturday, 23 October 20109:05 AM

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ay = -gax = 0

2.1 describe the trajectory of an object undergoing projectile motion within the Earth's gravitational field in terms of horizontal and vertical components

Parabolic shape of the trajectory of a projectileShowed that horizontal and vertical motion are independent and combine to produce parabolic shape

2.2 describe Galileo's analysis of projectile motion

Gravitational constantMass and radius of the planet

2.3 explain the concept of escape velocity in terms of the:

Considered how a projectile could be launched horizontally from the top of a high mountain so it would not fall to Earth

As launch velocity increases, distance object travels before hitting Earth would increase until the object wouldn't hit the ground, and go into orbit

Curvature of Earth exactly matches curvature of projectile. Higher velocity = object escapingCannon fired horizontally cause an angle would lead to an ellipse therefore the object would always crash into earth

2.4 outline Newton's concept of escape velocity

Because on the surface of the Earth, humans experience an acceleration of g.Therefore, it is convenient to use multiples of this, as it is relatable to experience(and because g forces mean gravity forces, which is the downwards force on the astronaut)

2.5 identify why the term 'g forces' is used to explain the forces acting on an astronaut during launch

When a rocket takes off it starts vertically and then becomes parallel to the Earth's surface. Scientists take advantage of the easterly spin of the Earth to add to the velocity of the rocket so as to launch it into orbit; therefore a rocket will turn east

Higher latitudes mean less contribution

2.6 discuss the effect of the Earth's orbital motion and its rotational motion on the launch of a rocket

Law of Conservation of MomentumThe change in momentum of the system consisting of the rocket and its exhaust gases is zero.i.e.

Therefore

Therefore

2.7 analyse the changing acceleration of a rocket during launch in terms of the:

2. Many factors have to be taken into account to achieve a successful rocket launch, maintain a stable orbit and return to EarthSaturday, 23 October 20109:15 AM

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Therefore

is relatively constant and so as the mass of the rocket decreases (as fuel is burnt),

the velocity of the rocket must increase to compensate

Forces experienced by astronautsAs fuel is consumed, mass of system decreases.Acceleration is proportional to thrust and inversely proportional to mass, as mass decreases, accel increases; so force on astronauts increases

2 stage rocket: fires first rocket (g-forces increase), stops and fires second stage. When it stops, accel decreases again so as to manage the maximum g-force

Velocity ==> vector ==> magnitude and direction; acceleration = change in velocity; uniform circular motion = speed the same, direction changing therefore acceleration

Centripetal acceleration directed towards the centre of the circle:

If there is acceleration, there is a force (F=ma), therefore, centripetal force; towards the centre of the string

2.8 analyse the forces involved in uniform circular motion for a range of objects

A geosynchronous orbit is one in which the satellite has a period the same as the earthIf it is in the equatorial plane, the satellite appears to stay above the same point on the Earth -geo-stationary orbit

Geostationary orbit is about 35,800 km above the equator and have a period of 24 hoursSatellites in low earth orbit have a period of less than 24 hoursIf the orbit is polar, that is, orbits in a plane perpendicular to the plane of the equator, then the orbit's orientation is fixed and the earth rotates under the satellite.

For example, if T = 6 hours, one polar revolution will rotate the orbit 90 degrees to the west, as the Earth rotates. In a couple of days the whole earth could be mapped

2.9 compare quantitatively low Earth and geo-stationary orbits

Orbital Velocity: the period (T) of an object in circular motion is the time for one complete revolution. Velocity = distance/time, and in T seconds, a satellite has orbited 2r. Therefore

Kepler's Law of Periods:

Substituting

for T and solving for v, gives:

Speed is inversely proportional to the square root of the radiusSmaller the radius, the faster the satellite must travel to stay in orbit at that radius

Thus the orbital velocity of a satellite depends on radius of the orbit, the mass of the planet and G, and therefore is independent of the mass of the satellite.

2.10 define the term orbital velocity and the quantitative and qualitative relationship between orbital velocity, the gravitational constant, mass of the central body, mass of the satellite and the radius of the orbit using Kepler's Law of Periods

Friction occurs between satellite and atmosphereLoss of energy as heatObject moves closer to Earth where atmosphere is thicker, cycle continuesAs geostationary orbits are so far up, friction is negligible

2.11 account for the orbital decay of satellites in low Earth orbit

Heat generated as spacecraft meets with Earth's atmosphere

2.12 discuss issues associated with safe re-entry into the Earth's atmosphere and landing on the Earth's surface

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When a blunt end hits the atmosphere, it sets up a shockwave that carries away much of the heat

Use of an ablation shield

Heat generated as spacecraft meets with Earth's atmosphere

Retarding forces which need to be kept in safe limits for humansRadio blackout

Optimum angle for re-entry for Mercury, Gemini and Apollo missions was -6.2 1Angle too shallow, spacecraft bounce of atmosphere back into spaceToo steep, g-forces will be too great for the crew to survive, and temperatures will make spacecraft burn up

2.13 identify that there is an optimum angle for safe re-entry for a manned spacecraft into the Earth's atmosphere and the consequences of failing to achieve this angle

2.15 perform a first-hand investigation, gather information and analyse data to calculate initial and final velocity, maximum height reached, range and time of flight of a projectile for a range of situations by using simulations, data loggers and computer analysisAim: To predict the landing point of a ball launched horizontally from a table top at any speedTheory: The ball leaves the edge of the table top, its horizontal motion is given by: and its

vertical motion is given by

Combining the two to eliminate (t) gives:

And

Set up an inclined plane so that a ball can roll down it, onto a table top and off the edge unobstructed

1.

Release the ball and time, using a data logger, the time it takes the ball to roll 1.0m along the table, with the ball being caught each time (repeat 5 times releasing the ball from the same position)

2.

Calculate the horizontal speed of the ball3.Measure the table top height4.Calculate the distance the ball would land5.Place a Styrofoam cup at the calculated distance to test the results6.

Method:

Results example:Time to roll 1.0m was recorded: 0.9 s; 1.0 s; 1.1 s; 1.0 s; 1.1 s. Average = 1.1 0.1 s. Horizontal velocity of the ball = 1.0/1.1 = 0.9091 0.91 ms-1. Height of the table top = 0.86 mHence:

2.16 identify data sources, gather, analyse and present information on the contribution of one of the following to the development of space exploration: Tsiolkovsky, Oberth, Goddard, Esnault-Pelterie, O'Neill or von Braun

Developed V-2 guided missile used in attacks on LondonHeaded the team that put America's first satellite into spaceHelped develop the Saturn V rocket that carried the first men to the moonResponsible for the idea of the space station and space shuttleLiquid fuel rockets

Von Braun:

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A field can be described as a way of explaining 'action at a distance'Masses experience a force when placed in the gravitational field of another mass

3.1 describe a gravitational field in the region surrounding a massive object in terms of its effects on other masses in it

Newton proposed that 'any two objects in the universe attract each other with a force which is proportional to the product of their masses and inversely proportional to the square of their separation' (see formula)

G is the universal gravitational constant G = 6.67 x 10-11 Nm2kg-2

3.2 define Newton's Law of Universal Gravitation:

Orbital velocity is given by:

The force acting on a satellite in order to give it its changing velocity is given by

Combining these two equations with Newton's Law of Gravitation

Kepler's Law of Periods,

can be derived.

Kepler's Law of Periods applies to planets, comets and satellites, as well as spacecraft and other orbiting things

Therefore, Newton's Law of Universal Gravitation is essential to understanding and calculating the motion of satellites

3.3 discuss the importance of Newton's Law of Universal Gravitation in understanding and calculating the motion of satellites

Slingshot effect involves bringing a space probe closer to other planets to increase the probe's velocity

As a probe passes a planet, its speed reduces as it interacts with the planet's gravitational fieldThe probe picks up angular momentum from the planet (which in turn the planet loses, under the conservation of angular momentum but due to the size of the planet, this is negligible) in much the same way as a collision functions

The velocities of the satellite and planet add together to give the satellite extra speed

3.4 identify that a slingshot effect can be provided by planets for space probes

The strength of a gravitational field (and hence the gravitational force) is proportional to the mass creating the field and inversely proportional to the square of the distance from the source

The field is uniform if the mass distribution is uniformVariations in mass distributions such as the presence of or bodies, or oil and gas fields lead to variations in the strength of the field

3.5 present information and use available evidence to discuss the factors affecting the strength of the gravitational force

3. The Solar System is held together by gravitySaturday, 23 October 20109:32 AM

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Light as a wave; waves need a medium for transmission --> aetherSupposed to permeate all matterLight was shown to be a transverse wave, and as transverse waves cant travel through liquids or gases, it had to be a solid

But, if it were solid, the planets would have been brought to rest a long time ago due to friction, so therefore, it had to have an extremely low density or else be a tenuous fluid (thin consistency)

Paradox overcome by suggestion that the aether acted somewhat like wax, which is rigid for rapidly changing forces but is fluid under the action of continuous forces

Aether wind - as the earth was moving through the aether, it was thought that the speed of light should change relative to the movement of light through the aether 'wind'

4.1 outline the features of the aether model for the transmission of light

Used the phenomenon of interference of light to measure minute changes in speed of lightLight sent from a source and split into two perpendicular beams by a half silvered mirror. The two beams are sent back by two mirror and recombined in observers eye

4.2 describe and evaluate the Michelson-Morley attempt to measure the relative velocity of the Earth through the aether

Beam AM1 is going against the aether wind whilst AM2 is traveling with and then against. The times to do this can be shown to be different and so should induce an interference pattern between the beams

No interference pattern was noticed even when the apparatus was rotated through 90 degrees, and the experiment repeated at different altitudes and different times of the year

Therefore, the result was No motion of the Earth relative to the aether was detectable

Science progresses as a result of validation of hypotheses by experimentationFrom a hypothesis, predictions are made as to what would happen if an experiment were to be performed

If when the experiment was performed, the results are not in agreement with prediction, the hypothesis is incorrect

A null result from the MM experiments showed that the hypothesis was incorrect

4.3 discuss the role of the Michelson-Morley experiments in making determinations about competing theories

4. Current and emerging understanding about time and space has been dependant upon earlier models of the transmission of lightSaturday, 23 October 20109:35 AM

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A null result from the MM experiments showed that the hypothesis was incorrectThe MM experiment did however give evidence for Einstein's theory, which required no aether to function

An inertial frame of reference is one that is moving with constant velocity or is at rest; that is, the Law of inertia holds

A non-inertial frame of reference is one that is accelerating. In such frames observers have to postulate the existence of pseudo forces to maintain Newton's Laws

4.4 outline the nature of inertial frames of reference

"The laws of mechanics are the same for a body at rest and a body moving with constant velocity"

Therefore, no experiment can be done in an inertial frame of reference to determine whether it is stationary or moving with constant velocity

Time regarded independent of spaced and a fixed frame of reference to which all motion could be compared - Newtonian relativity

4.5 discuss the principle of relativity

Constant speed of light (3x10^8m/s)No need for an absolute frame of reference, therefore aether not neededComes to conclusions of length contraction, mass dilation and time dilation which are unobservable at speeds other than significant fractions of the speed of light

4.6 describe the significance of Einstein's assumption of the constancy of the speed of light

Consider a spacecraft travelling at 0.5c and someone shines a light beam in the direction of motion. Prior to Einstein these two speeds would have added together, so that the light beam was said to be going 1.5c

If c is constant however, time and distance need to change to compensate. That is, space and time become relative

4.7 identify that if c is constant then space and time become relative

The metre was originally one ten millionth of the distance between the equator and the North Pole this distance was marked on a platinum-iridium bar and copies were made

Following advances in accurate measurement of light wavelength this measure was changed to one defined by the wavelength of the light emitted by krypton-86 when excited in a discharge tube

Today, the metre is defined as 'the distance light travels in a vacuum in 1/299,792,458 of a second'

This means that distance is defined in terms of time, and acknowledges the relativity of space and time

4.8 discuss the concept that length standards are defined in terms of time in contrast to the original metre standard

The relativity of simultaneityTwo events A and B separated by a distance 'l' will be simultaneous if the observer at A records event at A occurring at time t, and that from B occurring at time t + l/c (or alternatively, the light arrives at the mid-point at the same time)

When the mid-point of the train is exactly lined up with the observer outside, two lightning bolts hit the ends of the train

The observer on the track sees the light at the same time, and so perceives it simultaneously

The observer inside however, sees the front flash first because the train 'catches up' to the light, and the back flash has to travel faster

Therefore, the events are not necessarily simultaneous in all reference frames, in fact, in most cases, they are not

Assume a train travelling at relativistic speed with an observer in the carriage and an observer standing on the side of the tracks

4.9 explain qualitatively and quantitatively the consequence of special relativity in relation to:

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most cases, they are not

The equivalence between mass and energy

As speed approaches c, work is still done but the amount of kinetic energy added is smaller

This goes into E=mc2

Where m=

Length contraction

When work is done on an object its kinetic energy is increased

The length of a moving object appears to contract in the direction of motion relative to a stationary observer with the following relationship: where lv is the moving length and l0 is the stationary length

Time dilationA moving frame of reference appears to go slower relative to a stationary observer with the following relationship where tv is the 'moving' time and t0 is the 'stationary' time

Mass dilation A moving objects mass is greater than when its stationary with the following relationship where mv is the moving mass and m0 is the stationary mass

Time dilation and length contraction could theoretically allow exceptionally long space journeys within reasonable periods of time, as judged by the travellers. However, relativity also indicates that the cost of energy to do this would be prohibitive (mass dilation)

4.10 discuss the implications of mass increase, time dilation and length contraction for space travel

4.11 gather and process information to interpret the results of the Michelson-Morley experiment

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4.12 perform an investigation to help distinguish between non-inertial and inertial frames of referenceAim: To distinguish between inertial and non-inertial frames of reference

Place a set of scales in a lift1.Measure the weight of a person before they enter the lift (i.e. in a stationary frame of reference)

2.

Make measurement of the weight of the person when the lift is accelerating, at constant speed and decelerating to rest

3.

Method:

Theory: in all inertial frames of reference, the measured weight should be the same as there are no external forces that don't cancel out, whereas in an accelerating frame, pseudo forces apply and so the measured weight changes

Idea behind thought experiments is that the logic is sound even though the ideas cannot be scientifically tested due to technical limitations

If yes, then an outside observer would see the light travelling at 2c, violating the constancy of light

If no, then the light could not 'catch up' to the mirror and he could tell he was moving, violating relativity

e.g. imagine himself on a train travelling at the speed of light while holding a mirror at arms length in front of his face. Would he see his reflection in the mirror?

Such thought experiments assisted Einstein in his formulation of the special theory of relativity

4.13 analyse and interpret some of Einstein's thought experiments involving mirrors and trains and discuss the relationship between thought and reality

4.14 analyse information to discuss the relationship between theory and the evidence supporting

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Many of Einstein's predictions were not able to be verified for years after he first postulated them

Mostly this was due to the lack of appropriate technologyNevertheless scientists came to accept Einstein's work and in time all his predictions were experimentally corroborated

In particle accelerators, designers need to account for the increasing mass of charged particles as they are accelerated to higher and higher speeds to ensure they are synchronised to continue to gain speed

Energy released in radioactive decay and nuclear reactors and explosions provides irrefutable evidence for the conversion of mass into energy

Mass dilation and mass-energy transformations:

4.14 analyse information to discuss the relationship between theory and the evidence supporting it, using Einstein's predictions based on relativity that were made many years before evidence was available to support it

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Potential Energy in a gravitational field

Force due to gravitational field (on Earth)

Projectile Motion Equations

Kepler's Third Law

Newton's Law of Universal Gravitation

Relativity Equations

Centripetal force

FormulasSaturday, 23 October 201010:15 AM

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