2. Leaving The Earth Flashcards
I) How would you calculate the work done on an object with mass ‘m’ in a uniform gravitational field of strength ‘g’ through a height of ‘h’?
W = mgh
I) Why does an objects weight vary as it rises above the earth?
Since the earth has a radial gravitational field, the gravitational field strength fall off with the square of the distances an object moves further from the surface of the earth. This means that the objects weight is reduced as it gets further away from the earth’s centre of mass.
I) When are radial gravitational fields produced?
They are always produced by spherical or point masses.
I) Define gravitational potential (V).
The work done per unit mass to move a small object from infinity to that point.
At a distance r from the centre of a spherical object’s mass M:
V = -GM/r and is measured in J/Kg
I) What are equipotential lines and equipotential surfaces?
Equipotential lines - Lines connecting points of the same potential.
Equipotential surfaces - Surfaces (spheres) connecting pints of the same potential.
I) What work is done when an object is moved over an equipotential surface?
NONE
I) How is the escape velocity equation derived?
It is assumed that in order for an object to escape from the earth’s gravitational field, the total energy of that object must be greater than or equal to zero (ignoring air resistance).
Therefore gpe + ke = 0 is the critical point at which the object leaves the earth. You can then rearrange this equation to derive the escape velocity equation.
I) Define the escape velocity of an object.
The escape velocity of an object is the minimum speed needed for an object to “break free” from the gravitational attraction of a massive body.
I) What is the approximate escape velocity on earth?
11.2 kms^-1
I) How would you use the earth’s rotation to help achieve escape velocity?
The speed of the earth’s rotation is nearly 500 ms^-1 going from west to east at the equator.
Therefore, an object travelling tangentially from the equator in an easterly direction requires an initial velocity of about 10.7 kms^-1 relative to the surface of the earth in order to escape.
I) Why are space launch sites often located at the equator.
Since the surface velocity of the earth decreases with latitude launch sites are positioned at the equator where the surface velocity is greatest.
I) What is the schwarzschild radius and what are the consequences of it?
The radius of a sphere such that, if all the mass of an object were to be compressed within that sphere, the escape velocity from the surface of the sphere would equal the speed of light.
This means that these objects would not emit or reflex EM radiation appearing ‘black’.
These objects are known as black holes.
I) Why does the earth retain its atmosphere?
Because its escape velocity if much larger than the mean speed of air molecules at temperatures found on earth.
I) What is the energy of a satellite in orbit?
Its combined kinetic and potential energy.
Remember that the potential energy is negative since it is relative to infinity where the potential energy is zero.
I) What is the 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 body.
I) Define momentum.
The product of an object’s mass and velocity (p = mv) and is a vector taking the direction of the velocity as its direction.
I) Define Impulse.
The product of the force and the time for which the force acts (Impulse = Ft).
Impulse is a vector and takes the same direction as the force.
It can also be defined as the change in momentum: mv-mu
I) What is newton’s third law?
For every action, there is an equal and opposite reaction.
Fa = -Fr
I) What is a perfectly elastic collision?
Collisions in which kinetic energy is conserved. In the macroscopic world these are very rare.
I) What happens if a moving particle elastically collides with a stationary particle of equal mass?
The moving particle stops and transfers all of its momentum and kinetic energy to the stationary particle.
I) What is a partially inelastic collision?
Collisions in which some of the kinetic energy is converted into internal energy or elastic potential energy. Pretty much all macroscopic collisions are inelastic.
I) What is a perfectly inelastic collision?
Collisions in which the colliding particles merge into one single particle.
I) What is an explosive collision?
Collisions in which there is an increase in kinetic energy due to the fact that then energy is converted from elastic, chemical potential or nuclear energy.
You could think of an explosion as a perfectly in elastic collision in reverse.
The sum of all the momenta will add up to zero.
I) What are the forces that act on a rocket?
What do they do?
Trust - Overcomes the weight of the rocket.
Lift - Stabilises the rocket.
Drag - Rockets have a high drag to lift ratio.
Weight - Due to the rockets mass.
I) How do the forces on a rocket change as it leaves the earth?
Thrust - as the fuel is used up the the rate at which the fuel is burnt changes causing the thrust to also change.
Drag - as the altitude increases, the air density decreases meaning that there is less drag due to air resistance the higher up the rocket goes.
Weight - as the altitude increases the rockets weight decreases due to the fact that the gravitational field strength decreases and that the fuel is used up.
I) What are the 4 major parts of a rocket?
The payload
The propellant
The combustion chamber
The nozzle
I) What considerations are taken into account when designing a combustion chamber and why?
When the fuel and the oxidiser react, they expand rapidly, creating intense pressure and a temperature high enough to melt the metal used for the construction of the rocket.
Therefore, the combustion chamber must have insulation and a cooling system in order to cope with such high temperatures.
The walls of the chamber must also be strong enough to withstand pressures 200 times atmospheric pressure.
I) How does rocket fuel propel the rocket upwards?
The exhaust gases from the fuel is ejected from the combustion chamber nozzle at the rear of the rocket.
It converts the high pressure of the gases into thrust by forcing the exhaust through a narrow opening, accelerating the exhaust to high speeds.
Since the rocket has no momentum before it takes off, and since no external forces act on it, its total momentum must remain at zero.
The ejected exhaust gases have momentum in the downwards direction so the rocket must have an equal momentum in the opposite direction.
I) On average, what percentage of a rocket is fuel?
What takes up the rest?
90% fuel
5% payload
5% Rocket-only mass
I) How are rockets designed to improve the payload to take off mass ratio?
Multi stage rockets are used. Once the fuel in one stage has been used up, it detatches from the rest of the rocket and falls back down to earth. The remaining rocket is therefore lighter and requires less force to accelerate it to a greater velocity since F = ma.
I) What is the rocket equation?
vf = ve ln(mo/mf) where: vf is the maximum velocity of the rocket in gravity-free, drag-free flight. ve is the exhaust velocity of the gas. mo is the total rocket mass mf is the empty rocket mass
I) What two things affect the maximum velocity of a rocket?
The exhaust velocity:
The larger the exhaust velocity, the higher the maximum velocity.
The mo/mf ratio:
The higher the mo/mf ratio, the higher the maximum velocity.
I) For general info on water rockets read the textbook
Textbook m9
I) What is the accelerated exhaust gas called in a rocket?
The working fluid
I) What is the first law of thermodynamics?
ΔU = Q + W Where: ΔU is the change in internal energy W is the work done Q is the heat
I) How would you calculate the work done by a gas expanding at a constant pressure enclosed inside a piston?
W = pAs or W = pΔV Where: p is the pressure A is the cross-sectional area of the piston s is the distance moved by the piston
I) How does an increase in internal energy affect the temperature?
Since the internal energy is proportional to temperature, the temperature increases.
I) In the thermodynamics of rocket propulsion, which quantities are considered positive (hint: use ΔU = Q + W)?
If there is an increase in internal energy of the working fluid.
If work is being done on the working fluid.
If heat is being transferred to the working fluid.
i.e. if it is being done TO THE WORKING FLUID, the sign is POSITIVE.
I) When considering the exhaust gases exiting a rocket, it the expansion isothermal or adiabatic?
Adiabatic - The system looses internal energy and cools as a result of doing work on the rocket and the expansion occurs in such a short time that no heat can transfer out of the rocket’s nozzle.
I) Since the exhaust gas is modelled as an ideal gas what does that mean about the relationship between pressure and temperature?
The gas obeys the ideal gas equation:
pV = nRT
Where p is the pressure, V is the volume, r is the number of moles of gas, R is the molar gas constant and T is the temperature in Kelvin.
Therefore, because the V, n and R all stay the same, it can be said that pressure is proportional to temperature.
I) Describe how a solid fuel system works stating the advantages and disadvantages.
This type of propulsion system provides large amounts of thrust but can’t be turned off once ignited.
The are safe and stable until ignited so are used to power model rockets as well as boosters for the space shuttle.
The fuel combines with oxidiser to generate high temperatures and pressures.
The solid fuel burns from the inside outwards so the cavity inside the engine increases in volume.
The temperature of the combustion is constant and therefore, using the ideal gas equation pV = nRT, when the volume increases causing a decrease in pressure. This means that the rocket motor works less efficiently.
I) Describe how a cold gas system works stating the advantages and disadvantages.
This is the simplest form of propulsion, consisting of a single gas and a nozzle.
It is the safest of all the chemical propulsion systems but is less efficient. As gas is used the pressure goes down, reducing both trust and efficiency.
This system operates in the same way as when an inflated balloon is released. In terms of the ideal gas equation
pV = nRT,
p, V and n all fall
I) Describe how an ionic propulsion system works stating the advantages and disadvantages.
This is a form of electric propulsion where very small amounts of ionised gas are accelerated by an electrostatic field to produce a high speed exhaust, unlike chemical systems which eject large amounts of gas at a slow speed.
This means that the ionic system uses much less field than other chemical systems.
However, it is not effective in the atmosphere or as a launch vehicle, but is extremely useful in space where a small amount of thrust acting over a long period of time can result in a big difference in velocity.
The source of electrical energy can either be from solar or nuclear.
Explain the meanings of g and G
- G is the gravitational constant and g is the gravitational field strength
- g is the force on 1kg on or close to the earth’s surface
- G is the universal constant relating attraction of any two masses with their separation/ constant in Newton’s laws of gravitation
(3 marks)
Explain why gravitational potential energy has a negative value.
- GPE is zero at infinity
- loss of energy from zero means negative
- attractive force
- work is done on an object bringing it from infinity to the earth’s surface/ to raise the object from gravitational potential well.
(4 marks)
Name four main features of a commercial liquid propellant rocket.
any 4 from
- fuel/fuel tank
- payload
- nozzle
- combustion chamber
- oxidiser/ oxidiser tank
- fuel pump/ injector
(6 marks)
Explain how propulsion is achieved with a liquid propellant rocket. Make reference to the main features of the rocket and the conservation of momentum.
- fuel combined with oxidiser
- fuel oxidised and combusted in combustion chamber
- fuel additional mass to payload
- wasted gases ejected through nozzle
- initial total momentum zero
- momentum of waste gases must equal that of rocket
- in opposite direction
- total momentum still zero
- Newtonís third law
(2 marks)
Explain why launching the space shuttle using a multistage rocket is inefficient
- large rocket mass means it needs a lot of fuel
- increases mass over and above payload/ adds extra
