Download 11 Dyn and Space N3 rocket Theory

Dynamics and Space
Learning Intention
You will be able to:
Carry out Calculations involving the relationship
between weight, mass and gravitational field strength
during Interplanetary rocket flight.
Application of Newton’s third law to explain motion
resulting from a ‘reaction’ force.
Use Newton’s laws to explain free-fall and terminal
velocity.
THE EFFECT OF DISTANCE ON GRAVITY
As a spacecraft rises from the surface of the Earth, the pull of the
Earth’s gravity on it gets smaller and smaller. The table below shows
the values of the gravitational field strength at various distances from
the Earth.
As you can see from the table, the value of “g” quickly decreases with
distance from the Earth. You might think that it becomes zero at some
point in space – it does, but that point is infinity! However, beyond a
few million km, the effect of Earth’s gravitational pull has become very
small.
Plot a graph of gravitational field strength (y-axis) against the distance
from the Earth (x-axis). Use a whole sheet of graph paper, draw in
pencil and take care when sketching the free-hand curve through the
points. Stick the graph in your jotter.
Distance from
Earth (km)
Gravitational Field
Strength (N/kg)
0
1000
2500
5000
10
7.3
5.1
3.1
7500 10000
2.2
1.5
Gravitational Field
Strength/ N/kg
12
10
8
6
4
2
0
0
2000
4000
6000
8000
10000
Distance from Earth/ km
12000
1 From the graph, find out how far from the surface of the Earth you
would have to travel in order to experience gravitational field strength
exactly one quarter of what it is on the surface.
2 A space station, orbits the Earth at a height of 220 km. Use your
graph to find the gravitational field strength at this distance from
Earth.
3 An astronaut on board the space station has a mass of 60 kg. Find
her weight on board the space station.
4 The moon orbits the Earth at a distance of 384000 km from the
centre of the Earth. How do we know that the Earth’s gravity must
extend at least this distance out into space?
5 When you see videos of people on board space stations, you see
them “floating” in the cabin. They appear to be weightless.
True weightlessness can only happen where the pull of gravity is
zero.
Using the figures from the graph, explain why the cosmonauts
could not be truly weightless.
A person in a spacecraft in orbit above the Earth clearly appears to be
weightless but we know that the gravitational field strength there is not
zero.
To be truly weightless you must go so far away from any planet or star so
that the gravitational field strength is zero.
Astronauts in orbit appear to be weightless because they are “falling” to
Earth at exactly the same rate as the spacecraft they are in. They are in
permanent “free-fall”.
For example:
James is standing still in an aeroplane. In his right hand, he is holding a
force meter with a 3 kg mass hanging from it.
Due to its weight, the mass exerts a downward
force on the force meter.
James jumps out the airplane, still holding the force meter with the 3 kg
mass hanging from it.
Both the force meter and the 3 kg mass are now in free-fall.
They are both accelerating downwards towards the Earth
at the same rate of10 m/s2. Because the force meter and
The 3 kg mass are falling at the same rate, the mass does not exert a
downwards force on the force meter - So the reading on the force meter
is 0 N. (The 3 kg mass appears to be weightless as it falls freely.)
Newton’s third law is actually very simple.
“To every action there is always opposed an equal reaction.”
In other words if you push against a wall, the wall pushes against you.
When Newton was talking about actions and reactions he was talking
about forces.
Can you think up any more “Newton pairs” – two forces acting in
opposition to each other?
Here is one example:
The force of a swimmer backwards on the water.
The force of the water forwards on the swimmer.
Write any more you can think of in your jotter.
For each of the four diagrams, draw arrows clearly showing the two
forces acting at the contact point. Name the two forces (eg in
diagram 1 the forces will be – the force of the boot on the ball and the
forces of the ball on the boot).
1 While driving down the road, Anna
Litical observed a fly striking the
windshield of her car. Quite obviously, a
case of Newton's third law of motion.
The fly hit the windshield and the
windshield hit the bug. Which of the two
forces is greater: the force on the bug or
the force on the windshield?
You saw that any action force must have an equal and opposite reaction
force. This principle is used in the only type of motor capable of operating
in space – the rocket. All other types of motor require air to work.
Propellant gases force
the Rocket forwards
(action)
Rocket motors force
the propellant gases
backwards (action)
For a rocket to escape the Earth’s gravitational pull, it must reach a
speed of over 11000 m/s. Modern rockets use paraffin or hydrogen as
the fuel. To support the tremendous rate of fuel burn required, a large
supply of oxygen is needed. This will be carried in the form of liquid
oxygen.
1 (a) What is the only of motor that can be used in space?
(b) Why is this the only form of motor that can be used?
2 Why do rockets carry a supply of liquid oxygen?
3 What advantages might there be in using liquid fuel rather
than solid fuel?
4 Explain, using Newton’s 3rd law, how a rocket motor works
What is happening to the force, acting on the people, who are on
board the plane vomit comet as it accelerates to the ground at 10
m/s2
SQA I2 2003 Q22.
A spacecraft travels through space between planet X and planet Y.
Information on these planets is shown in the table below.
The spacecraft has a total mass of 2.5x 106 kg.
The spacecraft engines produce a total force of 3.8x107 N.
(a) The spacecraft is initially on planet X.
(i) Calculate the weight of the spacecraft when it is on the surface
of planet X.
(ii) Sketch a diagram showing the forces acting
on the spacecraft just as it lifts off from planet X.
You must name these forces and show their
directions.
(iii) Calculate the acceleration of the spacecraft
as it lifts off from planet X.
(b) On another occasion, the spacecraft lifts off
from planet Y.
The mass and engine force of the spacecraft are
the same as before.
Is the acceleration as it lifts off from planet Y
less than, more than or equal to the
acceleration as it lifts off from planet X?
You must give a reason for your answer
using information contained in the table
below.