Newton`s laws of motion and model rocketry

16 Pages·0.763 MB·English

by  Cannon R.L.

by Robert L.Cannon
Updated and edited by
Ann Grimm and Jim Kranich
®
N ’ F L M :
EWTON S IRST AW OF OTION
Objects at rest will stay at rest and objects in motion will stay in motion
in a straight line unless acted upon by an unbalanced force.
W S
HY ATELLITES
There are nine of the ‘wanderers’ or d
S I O planets that have been discovered
TAY N RBIT
in our solar system.. Telescopes
(including the Hubble Space Telescope F
This booklet is designed to help you in Earth orbit) and mathematics have
understand some principles of rocket enabled modern astronomers to also G x M x m
F=
flight. To get the most from your identify and study numerous moons d2
Earth Moon
study, follow these instructions: accompanying the nine planets.
In addition to these nine planets and F= the gravitation force between the
Whenever ** appear, stop reading their moons, thousands of asteroids two objects
M= the mass of one object (Earth)
immediately and answer the question and a number of comets revolve
m=the mass of another object (Moon)
or perform the action which has just in orbits around the sun. d= the distance between both objects’
been suggested. Keep thinking and center of mass
G=gravitation at constant
try to reason out why the action was O
RBIT
performed. Try to answer each question
before going on with your reading...... P As can be seen from the formula, as
RODUCING
the mass of either object increases,
F so does the gravitational force
“Twinkle, twinkle, little star. ORCES
How I wonder what you are; between them. As the distance
Up above the world so high, between both objects increases,
Like a diamond in the sky.” ... An object in motion will continue the gravitational force decreases.
in motion at a constant speed in a
Moon’s actual motion as
straight line as long as no unbalanced influenced by Earth’s
force acts upon it. gravity. Moon
Earth
This bit of verse was probably one of
If your Estes rocket were
the first things you learned about
Moon’s motion
launched deep into space where
space. You now know that stars are if not affected by The
atmosphere (drag) and gravity Earth’s gravity.
huge bodies of extremely hot gases. force of
Stars other than Sol, our sun, are extremely (unbalanced forces) could not the Earth’s
far away. Atomic reactions consume affect it after engine burnout, gravity pulls
tremendous quantities of their matter it would travel a straight line at the moon toward Earth as the moon
every second, yet stars’ masses are so a constant velocity forever! revolves about Earth. In effect, the
great that millions of years go by before moon is falling toward Earth.
their sizes are significantly reduced. An object in space near another object The moon’s motion also causes the
is influenced by the gravitational field moon to move laterally (sideways) at
The early astronomers named many of of the other object. the same time. The moon’s velocity is
the stars. Eventually, some noticed For example, the moon is attracted just enough to keep it falling toward
that certain ‘stars’ did not stay towards Earth by the Earth’s gravita- Earth at the same rate that the Earth’s
where they belonged in the sky. tion. Mathematically, the gravitational curvature causes the Earth’s surface to
These migrants were named attraction that two objects have for become farther from the moon.
‘planets’ (wanderers). each other is as follows:
2
Mathematically, the expression which Trajectory of an Orbit set up by
Moon’s Position At a Given Moment
object which an object which
calculates the velocity needed to
Motion as influenced “falls”too fast. does not “fall”
by Earth’s gravity maintain a circular orbit around Earth fast enough to
A B Distance is as follows: remain in
moon “falls” circular orbit
because of
C
the Earth’s V= (u/r)1/2
gravity as it
moves from
Point on
A to C
Earth’s where, r is the distance between the
surface
directly Distance Earth’s satellite and Earth’s center (center of
below A surface “drops” mass) and u is the Universal Constant
below horizon line
(Gravitational Constant times
Point on Earth’s the Earth’s mass).
surface directly
below B
Circular
The velocity which a satellite must
Orbit
have to go into a circular orbit near
The moon’s velocity is just great enough the Earth’s surface is about 5 miles Since this is true, the higher an object is
to carry it farther away from Earth along
path AB in a certain time during which it per second. This is about 18,000 above the Earth’s surface, the slower is its
falls toward Earth a distance BC
miles per hour (5 miles/second x 60 rate of fall due to the Earth’s gravity. Since
Due to the distance between the seconds/minute x 60 minutes/hour). the object tends to fall at a slower rate the
Earth’s surface and center of mass, we To reach this high speed, artificial higher it is, it follows that the farther an
experience a gravitational acceleration (man-made) satellites must be object is from Earth, the slower it will have
of 9.81 meters per second per sec- launched by very powerful rockets. to move to stay in orbit.
ond(9.81 m/s2) or 32.2 feet per Low Orbit: High orbital velocity,
second per second (32.2 ft/s2). Should an object receive a greater small orbital path
This means that a free falling object velocity than required to maintain
starting from an initial velocity of a circular orbit, even if launched
zero, will gain speed at the rate of in the proper direction, it will not
32.2 ft/s for each second of travel. stay in a circular path. It will instead
go into an elliptical orbit or escape
For the first second of free fall, entirely if the velocity is great enough.
an object will travel approximately High Orbit: Low orbital velocity,
large orbital path
16 feet. The Earth’s surface curves If the
“down” 16 feet in about 5 miles. object does A satellite which is in orbit far above
Therefore, an object moving not reach a Earth has a very long orbital path and
“horizontally” at 5 miles per second high is moving relatively slowly. The satel-
will fall at a rate which keeps it at a enough lite has a very long period (the time
constant distance above the Earth’s velocity to required to make one revolution).
surface. This situation produces an go into cir-
object which is a satellite of Earth cular orbit, A satellite in a lower orbit has a
and has a circular orbit. it will fall shorter orbital path. As can be seen
back to from the circular orbit and gravitation-
Satellite
Earth. al attraction equations, the satellite
Satellite
(an object in space must be moving faster since the gravi-
revolving about another
body in space) The farther an object is from Earth, tational attraction is greater due to
Orbit the weaker is the force with which the closer proximity with the primary.
(path of the
the Earth’s gravitation pulls on the If the actual velocity of the satellite is
satellite as it
Primary revolves about object (remember the earlier equation not increased accordingly for the lower
the primary)
that shows the gravitational force altitude, it will fall out of orbit and
The Moon
(Luna) is a being inversely proportional to the re-enter the Earth’s atmosphere.
satellite of
square of the distance?!). These factors cause the satellite to
Earth (Terra)
have a fairly short period.
Orbit
3
VELOCITIES AND PERIODS If you throw the ball as high and as MOMENTUM = MASS x VELOCITY
EARTH SATELLITES IN CIRCULAR ORBITS far as you can, you don’t have much of Mass is a property that all objects
AT VARIOUS ALTITUDES
a chance of getting the ball into orbit possess and is a measurement of
Altitude Velocity
Miles Miles per sec. Period even if you are very strong. Why not? that object’s resistance to a change in
motion. Because of the gravitational
0 4.92 1 hr.24 min.
* * attraction on Earth, we commonly use
100 4.85 1 hr.28 min.
You could the term weight instead of mass.
400 4.68 1 hr.38 min. not throw The more massive the object, the more
5,000 3.27 4 hr.47 min. the ball it weighs on Earth and obviously
with heavier objects are more difficult to
22,300 1.91 24 hr.-----
enough move. However, in space objects are
Man-made satellites are placed in energy to reach weightless yet they still possess mass.
orbits of varying altitudes depending escape velocity (the In this weightless condition, objects
upon the purpose of the satellite. minimum velocity that with more mass are more resistant to
Some are close to the Earth to make a moving object must a change in motion. It requires more
detailed observations and some are have to leave the force to change the motion as
Even “Atlas”
placed in very high orbits which vicinity of Earth compared to a less massive object.
has problems...
will remain in orbit for long and not return).
periods of time. The ball was pulled toward the center
of the Earth by the force of gravity.
From the velocities and periods chart,
you can see that one particular orbit Could you tell that the ball was
has a period of 24 hours. It makes slowing down as it went upward?
one revolution about the Earth every It was.
24 hours. The Earth also rotates about
its own axis once every 24 hour hours. Try this experiment in some open
This results in the satellite remaining place. Throw the ball as nearly
in a fixed position above the Earth and vertical (straight up) as you can.
is referred to as a “Geosynchronous Watch the ball as it goes up and
Orbit”. Communication satellites are comes down. If you have trouble
placed into this type of orbit to seeing the ball well and concentrating
provide continuous communication on observing its motion, have a friend
coverage for that section of Earth throw it while you stand to the side On Earth we can simply note that
below it. and observe. weight depends on mass, so the
greater the mass of something, the
Why would a satellite placed in a very * * more it will weigh.
low orbit close to the Earth, less than
200 miles, not stay in orbit for M
OMENTUM
many months?
* *
The ball starts slowing down the
You can answer this question yourself. instant it leaves your friend’s hand.
Let’s pretend that you want to throw a At the moment the ball leaves the
baseball into orbit. You probably hand, it has a certain velocity upward.
realize that your chances of success The energy given to the ball by throw-
aren’t too great!! However, let’s go ing it caused the ball to have a certain
ahead and try. You can go outside amount of momentum at the point of The ball’s mass doesn’t change when
and try this if you wish, but let’s go hand release. The amount of momen- your friend throws it up into the air,
through the reasoning together first. tum possessed is calculated by yet the ball soon slows down to a
multiplying the ball’s mass times complete stop, then starts falling down
the ball’s velocity. to the ground. Can you observe any
4
pattern to the speed with which the depends upon the speed. Both forces a circular orbit (refer to the circular
ball falls? acted to reduce the ball’s upward orbit equation). This condition,
momentum. The force of gravity combined with the Earth’s gravity,
* * pulled the ball back to earth. causes the satellitein low orbit to soon
“fall” out of orbit and return to Earth.
As the ballstarts falling from the momen- Your Estes rocket encounters the same Satellites in extremely high orbits
tary pause at the top of its path, it forces during flight as did the ball. encounter much less drag and lower
falls faster and faster. This iscaused by When the engine burns out, the rocket gravity, so they will remain in orbit
the force of gravity pullingit downward. has a certain amount of momentum. for very long periods of time.
The forces of gravity and drag slow the
An unbalanced force is one
Your attempt to throw a ball into rocket down as it coasts upward and
which changes motion.
orbit around the earth didn’t work. eventually stops and starts coming
The moment the ball left your hand, down. What would your Estes rocket I
NERTIA
it had only so much kinetic (motion) do after engine burnout if there was
energy with which to go into orbit. no atmosphere or gravity?
The force of gravity was pulling the Inertia is the tendency of a body at
ball downward all the time, but from * * rest to remain at rest unless pushed
the instant the ball left your hand you or pulled by an unbalanced force,
could not supply force to the ball to Without gravity or air (producing drag) and a body in motion continues to
counteract the force of gravity. The to reduce the rockets momentum, move in the same direction at the
force of gravity pulled downward while it would behave according to Newton’s same speed unless acted upon by
the ball was moving upward. Result - First Law of Motion and continue in an unbalanced force.
the ball was slowed down. Was the motion, in a straight line, at constant
force of gravity the only force acting velocity unless an unbalanced force This definition is not as complicated
on the ball once it left your hand? acted upon it. In short, it would as it sounds. Many people refer to two
coast upward forever! types of inertia. One kind, which we
* * What forces exist on a satellite may call static inertia, is the inertia
D in orbit far above the Earth? possessed by non-moving bodies.
RAG
Can you think of an example of this?
* *
No. The ball moved through the air, * *
and the air produced drag on the ball The gravity of Earth is present, of
to slow it down. This drag is the course, although it is not very strong A book sitting on a desk is one good
resistance the air presents to the far from Earth. The closer the satellite example. As long as no unbalanced
movement of the ball through the air. is to Earth, the stronger is the force force acts on the book to move it,
You have felt this drag as you ran on of gravity acting on it. Remember the book stays where it is. Can you
a calm day and felt the wind in your from the gravitational force equation, think of a way to move the book?
face or as you rode your bicycle. the force of gravity is inversely
The faster an object is moving through proportional to the square of the * *
the air, the greater is the aerodynamic distance between the centers of mass
(moving air) drag on it. of both objects. In other words, the Any force, applied to the book in great
same satellite twice as far away enough quantity, will cause the book
LOW SPEED - LOW DRAG
(from the Earth’s center) would be to move. Picking up the book, push-
attracted only 1/4 as strongly. ing it along the desk with your finger,
or hitting the book hard enough to
As we go farther from the surface of knock it off the desk all qualify as
HIGH SPEED - VERY HIGH DRAG
our planet, the atmosphere gets thinner. forces great enough to move it.
The force of gravity on the ball was Yet there is a measurable amount of air
the same regardless of the speed even at an altitude of 1,000 miles up.
with which you threw the ball. The air resistance eventually slows the
The amount of drag encountered satellite down below that required for
5
Another kind of inertia is the inertia spool above your head with one hand. The whirling object and spool may be
possessed by a moving body, some- Hold the string with the other hand. compared to a satellite and Earth. The
times called kinetic inertia. This is Allow the object to pull about one foot string represents gravity, the whirling
the tendency for a moving body to (30.5 cm) of string through the spool object is the satellite and Earth is the
keep moving once in motion. before stopping the string’s movement spool. This is a model of the real situ-
with the other hand. Start whirling ation, although not an accurate one.
Let’s consider again a satellite in orbit the object about the spool.
far above the Earth. The force of What would happen to the object
gravity, while weak, still pulls on the revolving about the spool if you were
satellite. The satellite still encounters to suddenly release the string? This
some aerodynamic drag from the few compares to what inertia would do to
atoms, molecules and ions of the an artificial satellite if Earth’s gravity
atmosphere present this high above suddenly ceased to exist.
the surface. However, this aero- * *
dynamic drag force is very small.
SNAP!!
The satellite may weigh very little if
it is in a weak gravitational field.
Inertia causes
However, the satellite has the same an object to
mass when in orbit as it did when proceed at a
on the ground. constant speed
Feel the force with which the object in a straight line.
The kinetic energy possessed by the pulls on the string. Whirl the object
satellite due to its motion is equal to faster. Notice how the pull becomes
the product of 1/2 the mass of the greater.
satellite times the square of its
velocity. Due to its kinetic inertia * *
the moving satellite tries to travel in Moving objects possess momentum.
a straight line. Result - the satellite’s The amount of momentum an object By whirling the object faster or slower
kinetic inertia tries to keep it moving has is determined by multiplying its and by changing the length of the
in a straight line at a tangent away mass times its velocity. For example, a string, a number of interesting
from its position in orbit. 100 pound (mass) satellite moving at experiments are possible. This can
4.85 miles per second (orbital velocity help you get a “feel” for understanding
S
IMULATION OF for a satellite in circular orbit at a the forces at work on a satellite
height of 100 miles above the Earth’s in orbit.
surface) will have a momentum of
ORBITAL MOTION
2,560,800 foot-pounds/second (100lbs. One example which can be performed
x 4.85 miles/second x 5280 feet/mile). is to keep the pull on the string
An interesting way to experiment Similarly in the metric system of reasonably constant while measuring
with objects revolving about a point measurements, a 45 kilogram (kg) the period of revolution for a short
in space is to conduct the following satellite moving at 7790 meters/ length of string (low orbit) as
experiment. Obtain a thread spool second (m/s) will have a momentum compared to the period of revolution
(preferably empty), a long piece of of 350,550 kg-m/s. for a much longer length of string.
string (about four feet [122 cm]), and
a lightweight object (small rubber ball, The inertia a moving body possesses
eraser, or the like). Tie the object tries to keep it moving in a straight
securely to one end of the string. line at a constant velocity. The object
Pass the other end through the hole in the you are whirling is attempting to go in
spool and pull the string through as far a straight line, but the string exerts a
as possible without breaking the string. continual force on the object causing
Stand in an open area and hold the it to move in a circular path.
6
REVIEW
NEWTON’S FIRST LAW OF MOTION
Section I Section II
Read each statement and decide Multiple choice.
whether it is True or False Circle or underline the best word or
(write T or F). words to complete each statement.
______ 1. All satellites are man made. ______13. “Escape velocity” refers to 17. The inertia possessed by non
______ 2. Gravity has no effect on the force necessary to lift moving bodies may be called
satellites in orbit. a satellite off the (kinetic, constant, static) inertia.
______ 3. As we go farther from the Earth’s surface. 18. The velocity which a satellite
Earth the atmosphere gets ______14. An object which is in must have to go into circular
thinner, but,there is a motion continuesinmotion orbit near the Earth’s surface is
measurable amount of air at different speeds unless about (22,300, 18,000, 50,000)
even at an altitude of an unbalanced force acts miles per hour.
1000 miles. upon it. 19. The moon is attracted toward
______ 4. An unbalanced force is ______15. For any one specified earth by the (gravity, magnetic
one that does not change altitude of a satellite in a force, solar energy) of the earth.
motion. circular orbit, there is only 20. There are (eleven, nine, thirty)
______ 5. The speed at which a one specific velocity it planets in our solar system.
body passes through the air must maintain. 21. The force acting on a satellite
has no effect on the ______16. You would weigh less on which keeps it in orbit is
amount of drag produced. top ofMount Everest (high- (trajectory, orbital, gravity) .
______ 6. The mass of a satellite est mountain in theworld) 22. The resistance that results when
changes as its distance than you would in Death a body is moved through the air
from Earth changes. Valley (lowest elevation on is called (drag, thrust, lift).
______ 7. A satellite has inertia. and in the world). 23. The momentum of a body
______ 8. A satellite actually falls moving through the air is
around the Earth. measured by multiplying
______ 9. Satellites placed in higher (force, height, mass) times
orbits remain in orbit for velocity.
longer periods of time than 24. The path followed by a satellite
those placed in lower moving around the Earth is
orbits. called its (vertigo, orbit,
______10. Momentum is the only trajectory).
major force acting on a 25. The time that it takes a satellite
satellite. to make one revolution around
______11. A satellite in a high the Earth is called its (segment,
circular orbit has a higher particle, period).
orbital velocity than one 26. The velocity required by a space
in low orbit. craft to leave orbit and head for
______12. The ‘period’ of a satellite the moon is called (separation,
refers to its time in orbit escape, momentum) velocity.
before falling.
7
N ’ S L M :
EWTON S ECOND AW OF OTION
Force is equal to mass times acceleration.
U
NBALANCED The previous section (Newton’s First the motion; the greater the mass, the
Law) examined the condition when lower the acceleration.
unbalanced forces were not present.
F
ORCES AND That is commonly referred to as a If a football player charges into
static condition; no acceleration. another player who is not expecting
An unbalanced force is a force which the charge, the player who is hit
R
OCKETS is not matched by an opposing force. receives an unbalanced force. He
Let’s examine the effect when probably gets knocked several feet!
unbalanced forces exist which cause
This section is designed to help acceleration (a change in velocity)
you better understand some creating a dynamic condition.
ideas which are important to
rocketry and model rocketry. Mathematically, Newton’s Second Law
Follow the instructions is expressed as follows:
carefully.
F = m x a
If you hold an object at arms length
and release it, what happens?
where: The object _______.
F = force (newtons or pounds) ———————————————
m = mass (kilograms or slugs) sllaf
a = acceleration A
CCELERATION
(m/s2 or ft/s2)
You will need a pencil Any time the speed at which an object
and a strip of cardboard or If we had a static situation (accelera- is moving is changed,
thick paper that is four inches wide tion is zero), the right side of the the object is
and ten inches long. Place this strip equal becomes zero. The net sum of accelerated.
over the next column and move the the forces then equals zero too. If the object is
paper down until it comes to the first This shows that we have no unbal- made to move
dotted line. Study the material, then anced forces. In a dynamic situation at a greater
fill in the blank(s). where unbalanced forces are present speed, we say
(net sum of all forces not equal to that the object
Move the paper down to uncover the zero), the quantity m x a, has anactual receives positive
answer and check your response. value indicating the object of mass acceleration.
Your answer does not need to be m will accelerate by the amount a. Conversely, a
in the exact words given as long as moving object
it expresses the correct idea. You can see that the amount of accel- that is slowed
If your response was incorrect, review eration is directly proportional to the down would
the material, correct the answer and magnitude of the unbalanced forces; undergo
move on to the next paragraph. the greater the force, the greater the negative
Follow these steps throughout acceleration. The magnitude of the acceleration
this section. acceleration is also inversely propor- (deceleration).
tional to the amount of mass resisting
8
An unbalanced force acting on an M The more massive an object is, the
OMENTUM
object causes the object to greater is the force needed to achieve
____________. a given acceleration (rate of velocity
——————————————— All moving objects possess momentum. change). In other words, a
etarelecca The momentum of a moving object is given force will accelerate an
determined by multiplying the mass object of low mass more than
of the object (its quantity of matter) it would accelerate an
C
When you release the object you were times the velocity (speed in a certain object of greater mass.
holding, it receives ___________ accel- direction) of the object.
eration because of the force of D The engines of rockets
______________. MASS x VELOCITY = MOMENTUM C and D produce the
——————————————— same thrust. Rocket C
ytivarg evitisop Which has more momentum, a ball mov- has much more mass
ing at a given velocity or an identical than Rocket D.
ball moving at a higher velocity? The Rocket _______ will
To properly describe a force we need to ball moving at the ___________ have a greater acceleration
know the magnitude (amount) of the velocity has a greater momentum. than the other rocket.
force and the direction in which the ———————————————— ————————————————
force is acting. rehgih D
T
HRUST
An unbalanced _____________ A rocket engine can produce a
accelerates an object in the direction certain amount of thrust. To cause a
in which the ____________ is acting. The greater the unbal- satellite to reach the desired velocity,
——————————————— anced force acting on an the rocket must accelerate the satellite
ecrof ecrof object, the greater is from zero velocity to the desired
the acceleration the velocity.
force produces.
The harder you throw a ball, all other The forward The entire rocket (satellite, engine,
A
factors being constant, the farther it force a rocket propellant, body, etc.) is accelerated
B
will go. When you throw the ball with engine by the engine’s thrust.
only a little force, the ball receives creates is
only a small acceleration. called The total momentum achieved by a
If you throw the ball as hard as you thrust. rocket is equal to the total momentum
can, it receives a large acceleration. achieved by the rocket’s exhaust gases.
3rd
As we have learned, momentum equals
2nd
A large force produces a __________ mass times velocity. The exhaust
acceleration than a smaller force on gases of an Estes rocket have low
the same object. mass, but their velocity is extremely
——————————————— 1st fast. Because the total momentum is
regral Stage the same, a rocket having mass greater
Engine
than the exhaust gases will achieve a
velocity lower than the exhaust gases.
A larger acceleration produces a
___________ speed change than Which rocket will accelerate more if the
a small acceleration for the same individual engines produce equal thrust
length of time. and the rockets have equal total mass-
——————————————— es? Rocket _______ will accelerate
retaerg more than the other rocket. ACTION REACTION
————————————————
A
9
If the same thrust is applied to a rocket F = m dv a (acceleration) is _______ in the rockets acceleration.
dt
of small mass as to one of greater the first derivative of
esaercni
mass, which will achieve a higher velocity with respect to time
acceleration - the smaller mass or The greater the mass of a rocket, the
greater mass rocket? F dt = m dv multiplying both _______________ is the acceleration
———————————————— sides of the equation by dt produced for a given total thrust.
tekcor ssam rellams ehT ———————————————
F ∆t = m ∆v a derivative repre- rewol
If Newton’s second law of motion is sents a change, ∆ M -
ULTI STAGED
rewritten as F/m=a, it is apparent
that reducing a rocket’s mass which an Σ F ∆t = m(v - v)
f i R
engine’s thrust must accelerate will The sum of all forces times OCKETS
enable the rocket to achieve greater the length of time they act is
acceleration. This results in the rocket equal to the mass of the
attaining higher velocities. object times the change in
velocity. Initial velocity is v
i
The less the total mass of the rocket, and the final velocity is v. As the
f
the __________ the velocity the propellant in
payload can reach when the rocket’s The left side of the equation represents each stage of a
engine is operated for a specified time. impulse (force times time) and the multi-stage rocket is
———————————————— right side represents momentum (mass used, that stage can
retaerg times velocity). This equation shows be dropped. This
that the sum of all impulses is equal to reduces the mass of the
The mass of a satellite does not the change in momentum. Because our rocket (by removing the
change as it moves from its position smaller engine operated for a longer engine and other parts of
atop a rocket on the launch pad to period of time, the rocket was able to that stage). As a result, the
achieving orbit. Since the satellite reach greater velocities. A larger engine thrust of the next stage’s engine
had zero momentum (its mass times producing greater thrust could make the pushes a smaller mass. This allows
zero velocity equals zero momentum) same payload mass reach the same that engine to give the rocket more
on the launch pad but a large momen- velocity by operating for a __________ acceleration than it could were the
tum as it follows its orbit, the satellite period of time. rocket more massive. It also allows
has undergone a tremendous change in ———————————————— the engine’s thrust to be reduced to
its momentum. The momentum retrohs maintain the current velocity. This
possessed by all objects on Earth A small rocket engine producing a permits the engine to operate longer
because of the Earth’s motion is not small thrust may not be able to lift a using a given amount of fuel to reach
covered in this booklet. rocket with the payload and the neces- a higher altitude.
sary propellant, so a large engine or a
T
HRUST cluster of small engines are often necessary As a rocket’s stages separate from the
to lift the rocket off the launch pad. rest of the rocket, the rocket’s total
A small engine producing a small mass ______ .
thrust but operating for a long period ————————————————
of time can make a given payload mass sesaerced
reach a high velocity (assuming the
thrust is greater than the rocket’s Staging allows a payload to reach
weight and drag combined). This As the a _______________ velocity for a
is the principle of impulse which is rocket’s specific mass of propellant than would
derived from Newton’s second law. engine operates, the be achieved by using only a single-stage
For those with the appropriate math propellant is converted to rocket.
and physics background, the derivation gases which leave the rocket which ————————————————
is as follows: reduce the rocket’s mass. As a result, retaerg
F = m x a Newton’s second law a steady thrust level can produce an
10