2. Leaving The Earth

Question 1

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’?

Answer 1

W = mgh

Question 2

I) Why does an objects weight vary as it rises above the earth?

Answer 2

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.

Question 3

I) When are radial gravitational fields produced?

Answer 3

They are always produced by spherical or point masses.

Question 4

I) Define gravitational potential (V).

Answer 4

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

Question 5

I) What are equipotential lines and equipotential surfaces?

Answer 5

Equipotential lines - Lines connecting points of the same potential.

Equipotential surfaces - Surfaces (spheres) connecting pints of the same potential.

Question 6

I) What work is done when an object is moved over an equipotential surface?

Answer 6

NONE

Question 7

I) How is the escape velocity equation derived?

Answer 7

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.

Question 8

I) Define the escape velocity of an object.

Answer 8

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.

Question 9

I) What is the approximate escape velocity on earth?

Answer 9

11.2 kms^-1

Question 10

I) How would you use the earth’s rotation to help achieve escape velocity?

Answer 10

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.

Question 11

I) Why are space launch sites often located at the equator.

Answer 11

Since the surface velocity of the earth decreases with latitude launch sites are positioned at the equator where the surface velocity is greatest.

Question 12

I) What is the schwarzschild radius and what are the consequences of it?

Answer 12

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.

Question 13

I) Why does the earth retain its atmosphere?

Answer 13

Because its escape velocity if much larger than the mean speed of air molecules at temperatures found on earth.

Question 14

I) What is the energy of a satellite in orbit?

Answer 14

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.

Question 15

I) What is the conservation of energy?

Answer 15

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.

Question 16

I) Define momentum.

Answer 16

The product of an object’s mass and velocity (p = mv) and is a vector taking the direction of the velocity as its direction.

Question 17

I) Define Impulse.

Answer 17

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

Question 18

I) What is newton’s third law?

Answer 18

For every action, there is an equal and opposite reaction.

Fa = -Fr

Question 19

I) What is a perfectly elastic collision?

Answer 19

Collisions in which kinetic energy is conserved. In the macroscopic world these are very rare.

Question 20

I) What happens if a moving particle elastically collides with a stationary particle of equal mass?

Answer 20

The moving particle stops and transfers all of its momentum and kinetic energy to the stationary particle.

Question 21

I) What is a partially inelastic collision?

Answer 21

Collisions in which some of the kinetic energy is converted into internal energy or elastic potential energy. Pretty much all macroscopic collisions are inelastic.

Question 22

I) What is a perfectly inelastic collision?

Answer 22

Collisions in which the colliding particles merge into one single particle.

Question 23

I) What is an explosive collision?

Answer 23

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.

Question 24

I) What are the forces that act on a rocket?

What do they do?

Answer 24

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.

Question 25

I) How do the forces on a rocket change as it leaves the earth?

Answer 25

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.

Question 26

I) What are the 4 major parts of a rocket?

Answer 26

The payload
The propellant
The combustion chamber
The nozzle

Question 27

I) What considerations are taken into account when designing a combustion chamber and why?

Answer 27

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.

Question 28

I) How does rocket fuel propel the rocket upwards?

Answer 28

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.

Question 29

I) On average, what percentage of a rocket is fuel?

What takes up the rest?

Answer 29

90% fuel
5% payload
5% Rocket-only mass

Question 30

I) How are rockets designed to improve the payload to take off mass ratio?

Answer 30

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.

Question 31

I) What is the rocket equation?

Answer 31

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

Question 32

I) What two things affect the maximum velocity of a rocket?

Answer 32

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.

Question 33

I) For general info on water rockets read the textbook

Answer 33

Textbook m9

Question 34

I) What is the accelerated exhaust gas called in a rocket?

Answer 34

The working fluid

Question 35

I) What is the first law of thermodynamics?

Answer 35

ΔU = Q + W
Where: 
ΔU is the change in internal energy
W is the work done 
Q is the heat

Question 36

I) How would you calculate the work done by a gas expanding at a constant pressure enclosed inside a piston?

Answer 36

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

Question 37

I) How does an increase in internal energy affect the temperature?

Answer 37

Since the internal energy is proportional to temperature, the temperature increases.

Question 38

I) In the thermodynamics of rocket propulsion, which quantities are considered positive (hint: use ΔU = Q + W)?

Answer 38

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.

Question 39

I) When considering the exhaust gases exiting a rocket, it the expansion isothermal or adiabatic?

Answer 39

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.

Question 40

I) Since the exhaust gas is modelled as an ideal gas what does that mean about the relationship between pressure and temperature?

Answer 40

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.

Question 41

I) Describe how a solid fuel system works stating the advantages and disadvantages.

Answer 41

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.

Question 42

I) Describe how a cold gas system works stating the advantages and disadvantages.

Answer 42

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

Question 43

I) Describe how an ionic propulsion system works stating the advantages and disadvantages.

Answer 43

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.

Question 44

Explain the meanings of g and G

Answer 44

• 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

Question 45

(3 marks)

Explain why gravitational potential energy has a negative value.

Answer 45

• 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.

Question 46

(4 marks)

Name four main features of a commercial liquid propellant rocket.

Answer 46

any 4 from

• fuel/fuel tank
• payload
• nozzle
• combustion chamber
• oxidiser/ oxidiser tank
• fuel pump/ injector

Question 47

(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.

Answer 47

• 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

Question 48

(2 marks)

Explain why launching the space shuttle using a multistage rocket is inefficient

Answer 48

• large rocket mass means it needs a lot of fuel

- increases mass over and above payload/ adds extra