AQA A2 Physics - Leaving the Earth Revision Notes

Notes for the 'Leaving the Earth' chapter in A2 Physics: Physics in Context for AQA specification B

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  • Created on: 27-04-11 18:46
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Leaving the Earth
Going Up:
GPE Change in a Uniform Field
Close to surface of the earth the gravitational field is almost completely uniform
o Meaning g is a constant value of 9.81 N kg-1
Meaning the work done in lifting an object through a distance h will be given by
E p = W ork Done = mgh
This is the equal to the amount of GPE that the object gains
o Assuming no work is being done in moving the atmosphere out of the way
o This can also be calculated from the area under a graph of weight against
distance from the centre of the earth
GPE Change in Radial Field
Gravitation field strength falls off with the square of distance as an object moves
further from the surface of the earth if the field is radial
o It is an inverse square law, meaning the weight of an object will vary as well
The change in GPE can be given by
o The area under the graph of weight against distance from the earth
EP = GM Em( r11 - r12 )
For an object moving away from the Earth's surface there will be an increase in
gravitational potential energy
o Meaning it is less negative
Radial gravitational fields are always produced by spherical or point masses

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Equipotential Surfaces
GPE of an object at a particular height depends on
o The mass of the object
o The mass of the earth
Gravitational field strength
o Useful to think of the space around the earth as having a property which
depends only on the mass of the earth
Another way of thinking of the field
o Potential at a point in a gravitational field is the potential energy experienced
per unit mass at that point
Therefore measured in J kg-1
o The gravitational…read more

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Escape from the Earth:
Escape Velocity
In order to escape from the earth's gravitational field the object needs to have
enough initial kinetic energy
o When added to the negative potential energy would need to make a total
energy of at least zero
In order to escape the total energy of a body must be at least zero
o Ignoring any energy transferred into the internal energy of the atmosphere or
the body
This means
o GP E + K E = 0
o Meaning…read more

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Mass increases
o Or Radius decreases
The escape velocity need to increase too
If a planet or star is sufficiently massive the escape velocity matches the speed of
light, such an object would not emit or reflect electromagnetic radiation
And would therefore appear black
It is not possible to exceed the speed of light in a vacuum. The Schwarzschild Radius
is where an object has the escape velocity of the speed of electromagnetic radiation
(a black hole).…read more

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Conservation of Energy
In any closed system the total energy remains constant although it may change form
and internal work may also be done when one body interacts with another
Momentum
momentum = mass ×velocity
Momentum is conserved providing no external forces act on the system before and
after the collision/event
o A snooker ball hitting a stationary snooker ball will collide and separate again
Momentum of each changes but overall the total momentum remains
constant
m1u1 + m2u2 = m1v1 + m2v2
o Newton's…read more

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Rocket Science:
Forces on a Rocket
Thrust opposes weight on a rocket when rocket is close
enough to the earth for gravity to be significant
Lift is used to stabilise the rocket
Forces vary throughout the flight
o Weight reduces as the fuel is used up
o Thrust changes as the fuel is burnt at different
rates
o Drag increases with the square of velocity
o Drag is also affected by the density of the air
which is affected by the temperature and altitude
o…read more

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No external force acts so momentum must stay at zero
As exhaust is ejected the gases have momentum in one direction and
the rocket must have an equal momentum in the opposite direction
Meaning the rocket will move
Loss of Mass
o Assuming the rocket can ejects its mass at a constant rate and with a
constant velocity relative to the rocket
Then the thrust will remain constant
o The mass of the rocket will be decreasing as the fuel is used up
o F=ma…read more

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Most efficient at the moment
Meaning a lot depends on the mass ratio
o Mass Ratio
Lighter materials can be used to improve the payload: fuel ratio by
making the payload lighter or eliminating some structure
The ratio is hard to improve as carrying more fuel means a bigger
structure, which means greater final mass
o Suggests current rockets powered by chemical propellants can
never achieve near-speed-of-light speeds due to the ratio
needed becoming unimaginably large
Rocket Equation can be rearranged to:
-V f
Mf…read more

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Combustion of the fuel in a chemical rocket produces a high pressure gas which
ejected through the rocket nozzle
o Accelerated exhaust gas is called the working fluid
Turbine engines and propeller powered aircraft used air from the
atmosphere as the working fluid, however, no atmosphere/air means
they won't work in space
In the combustion chamber the gas behaves just as any other gases
o Exhibits the macroscopic properties of
Pressure
Volume
Temperature
All due to microscopic properties of the gas molecules,
including the transfer…read more

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Pressure is defined as force per unit area
F
p= A
o This is rearranged to F=pA, meaning the work done by a gas expanding at a
constant pressure will be given by
W = pAs
If area is constant, As = V , the increase in volume.…read more

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