8.7 Introduction to rocket propulsion  (Page 4/4)

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Professional Application

During a visit to the International Space Station, an astronaut was positioned motionless in the center of the station, out of reach of any solid object on which he could exert a force. Suggest a method by which he could move himself away from this position, and explain the physics involved.

Professional Application

It is possible for the velocity of a rocket to be greater than the exhaust velocity of the gases it ejects. When that is the case, the gas velocity and gas momentum are in the same direction as that of the rocket. How is the rocket still able to obtain thrust by ejecting the gases?

Problems&Exercises

Professional Application

Antiballistic missiles (ABMs) are designed to have very large accelerations so that they may intercept fast-moving incoming missiles in the short time available. What is the takeoff acceleration of a 10,000-kg ABM that expels 196 kg of gas per second at an exhaust velocity of $2\text{.}\text{50}×{\text{10}}^{3}\phantom{\rule{0.25em}{0ex}}\text{m/s?}$

$\text{39}\text{.}2\phantom{\rule{0.25em}{0ex}}{\text{m/s}}^{2}$

Professional Application

What is the acceleration of a 5000-kg rocket taking off from the Moon, where the acceleration due to gravity is only $1\text{.}6\phantom{\rule{0.25em}{0ex}}{\text{m/s}}^{2}$ , if the rocket expels 8.00 kg of gas per second at an exhaust velocity of $2\text{.}\text{20}×{\text{10}}^{3}\phantom{\rule{0.25em}{0ex}}\text{m/s?}$

Professional Application

Calculate the increase in velocity of a 4000-kg space probe that expels 3500 kg of its mass at an exhaust velocity of $2\text{.}\text{00}×{\text{10}}^{3}\phantom{\rule{0.25em}{0ex}}\text{m/s}$ . You may assume the gravitational force is negligible at the probe’s location.

$4\text{.}\text{16}×{\text{10}}^{3}\phantom{\rule{0.25em}{0ex}}\text{m/s}$

Professional Application

Ion-propulsion rockets have been proposed for use in space. They employ atomic ionization techniques and nuclear energy sources to produce extremely high exhaust velocities, perhaps as great as $8\text{.}\text{00}×{\text{10}}^{6}\phantom{\rule{0.25em}{0ex}}\text{m/s}$ . These techniques allow a much more favorable payload-to-fuel ratio. To illustrate this fact: (a) Calculate the increase in velocity of a 20,000-kg space probe that expels only 40.0-kg of its mass at the given exhaust velocity. (b) These engines are usually designed to produce a very small thrust for a very long time—the type of engine that might be useful on a trip to the outer planets, for example. Calculate the acceleration of such an engine if it expels $4\text{.}\text{50}×{\text{10}}^{-6}\phantom{\rule{0.25em}{0ex}}\text{kg/s}$ at the given velocity, assuming the acceleration due to gravity is negligible.

Derive the equation for the vertical acceleration of a rocket.

The force needed to give a small mass $\text{Δ}m$ an acceleration ${a}_{\text{Δ}m}$ is $F=\text{Δ}{\text{ma}}_{\text{Δ}m}$ . To accelerate this mass in the small time interval $\text{Δ}t$ at a speed ${v}_{\text{e}}$ requires ${v}_{\text{e}}={a}_{\text{Δ}m}\text{Δ}t$ , so $F={v}_{\text{e}}\frac{\text{Δ}m}{\text{Δ}t}$ . By Newton’s third law, this force is equal in magnitude to the thrust force acting on the rocket, so ${F}_{\text{thrust}}={v}_{\text{e}}\frac{\text{Δ}m}{\text{Δ}t}$ , where all quantities are positive. Applying Newton’s second law to the rocket gives ${F}_{\text{thrust}}-\text{mg}=\text{ma}⇒a=\frac{{v}_{\text{e}}}{m}\frac{\text{Δ}m}{\text{Δ}t}-g$ , where $m$ is the mass of the rocket and unburnt fuel.

Professional Application

(a) Calculate the maximum rate at which a rocket can expel gases if its acceleration cannot exceed seven times that of gravity. The mass of the rocket just as it runs out of fuel is 75,000-kg, and its exhaust velocity is $2\text{.}\text{40}×{\text{10}}^{3}\phantom{\rule{0.25em}{0ex}}\text{m/s}$ . Assume that the acceleration of gravity is the same as on Earth’s surface $\left(9\text{.}\text{80}\phantom{\rule{0.25em}{0ex}}{\text{m/s}}^{2}\right)$ . (b) Why might it be necessary to limit the acceleration of a rocket?

Given the following data for a fire extinguisher-toy wagon rocket experiment, calculate the average exhaust velocity of the gases expelled from the extinguisher. Starting from rest, the final velocity is 10.0 m/s. The total mass is initially 75.0 kg and is 70.0 kg after the extinguisher is fired.

How much of a single-stage rocket that is 100,000 kg can be anything but fuel if the rocket is to have a final speed of $8\text{.}\text{00}\phantom{\rule{0.25em}{0ex}}\text{km/s}$ , given that it expels gases at an exhaust velocity of $2\text{.}\text{20}×{\text{10}}^{3}\phantom{\rule{0.25em}{0ex}}\text{m/s?}$

$2\text{.}\text{63}×{\text{10}}^{3}\phantom{\rule{0.25em}{0ex}}\text{kg}$

Professional Application

(a) A 5.00-kg squid initially at rest ejects 0.250-kg of fluid with a velocity of 10.0 m/s. What is the recoil velocity of the squid if the ejection is done in 0.100 s and there is a 5.00-N frictional force opposing the squid’s movement. (b) How much energy is lost to work done against friction?

(a) 0.421 m/s away from the ejected fluid.

(b) $0\text{.237}\phantom{\rule{0.25em}{0ex}}\text{J}$ .

Unreasonable Results

Squids have been reported to jump from the ocean and travel $\text{30}\text{.}0\phantom{\rule{0.25em}{0ex}}\text{m}$ (measured horizontally) before re-entering the water. (a) Calculate the initial speed of the squid if it leaves the water at an angle of $\text{20}\text{.}0º$ , assuming negligible lift from the air and negligible air resistance. (b) The squid propels itself by squirting water. What fraction of its mass would it have to eject in order to achieve the speed found in the previous part? The water is ejected at $\text{12}\text{.}0\phantom{\rule{0.25em}{0ex}}\text{m/s}$ ; gravitational force and friction are neglected. (c) What is unreasonable about the results? (d) Which premise is unreasonable, or which premises are inconsistent?

Consider an astronaut in deep space cut free from her space ship and needing to get back to it. The astronaut has a few packages that she can throw away to move herself toward the ship. Construct a problem in which you calculate the time it takes her to get back by throwing all the packages at one time compared to throwing them one at a time. Among the things to be considered are the masses involved, the force she can exert on the packages through some distance, and the distance to the ship.

Consider an artillery projectile striking armor plating. Construct a problem in which you find the force exerted by the projectile on the plate. Among the things to be considered are the mass and speed of the projectile and the distance over which its speed is reduced. Your instructor may also wish for you to consider the relative merits of depleted uranium versus lead projectiles based on the greater density of uranium.

is there a formula for magnitudes of displacement
A Body of maas m slides down an incline and reached the bottoms with a velocity v
What is mass
mass is the amount of matter a body contains.
prakash
what is model
what is a dimension
John
When using the Conservation of Energy equation, do we substitute the energy as a negative quantity when the energies on a single object are exerting forces opposite to one another?
Ex. On an inclined plane, gravitational potential energy, friction energy/work and spring potential energy. (Let's say that the spring is keeping the box from sliding down the slope.) How do we use this in the equation? I'm so confused
Jennifer
Oh! And if there's kinetic energy that is exerting a force opposite to the spring, what do we do?
Jennifer
Then we subtract the k.e. from force exerted from newton's 2nd law.
Prem
Subtract energy from force? They're different units
Jennifer
why is it dat when using double pan balance the known and unknown mass are the same
discuss the uses of energy in the following sectors of economy security and education
amajuoyi
why the current produce during dc motot is not use for its working rather we have to supply current outside
Tanveer
is there more then 4 dimensions
hii
princy
hi
Miguel
hello I kinda need help in physics... a lot
Brown
Brown. what kind of help
Jeff
when it comes to physics stick with the basics don't overthink things
Jeff
yes
ayesha
sticking to the basics will take you farther than overwhelming yourself with more than you need to physics is simple keep it simple
Jeff
thk u Ayesha
Jeff
for real....? so I've got to know the fundamentals and use the formula to solve any problem
Brown
read Stephan hawkings a brief history of time
ayesha
ayesha
physics isn't hard it's just understanding and applying the formulas if u need help ask any question
ayesha
okay...because I've got an exam next year February a Computer based exam
Brown
ayesha
ayesha
hi
Varun
hello
Ibrahim
yeah
oyeronke
how can we find absolute uncertainty
it what?
Luke
in physics
ayesha
the basic formula is uncertainty in momentum multiplied buy uncertainty In position is greater than or equal to 4×pi/2. same formula for energy and time
Luke
I have this one question can you please look it up it's 9702/22/O/N/17 Question 1 B 3
ayesha
what
uma
would you like physics?
Suthar
yes
farooq
precision or absolute uncertainty is always equal to least count of that instrument
Iram
how do I unlock the MCQ and the Essay?
what is the dimension of strain
Is there a formula for time of free fall given that the body has initial velocity? In other words, formula for time that takes a downward-shot projectile to hit the ground. Thanks!
hi
Agboro
hiii
Chandan
Hi
Sahim
hi
Jeff
hey
Priscilla
sup guys
Bile
Hy
Kulsum
What is unit of watt?
Kulsum
watt is the unit of power
Rahul
p=f.v
Rahul
watt can also be expressed as Nm/s
Rahul
what s i unit of mass
Maxamed
SI unit of mass is Kg(kilogram).
Robel
what is formula of distance
Maxamed
Formula for for the falling body with initial velocity is:v^2=v(initial)^2+2*g*h
Mateo
i can't understand
Maxamed
we can't do this calculation without knowing the height of the initial position of the particle
Chathu
sorry but no more in science
Imoreh
2 forces whose resultant is 100N, are at right angle to each other .if one of them makes an angle of 30 degree with the resultant determine it's magnitude
50 N... (50 *1.732)N
Sahim
Plz cheak the ans and give reply..
Sahim
50 N...(50 *1.732)N
Ibrahim
show the working
usiomon
what is the value of f1 and f2
Syed
what is the value of force 1 and force 2.
Syed
.
Is earth is an inertial frame?
The abacus (plural abaci or abacuses), also called a counting frame, is a calculating tool that was in use in Europe, China and Russia, centuries before the adoption of the written Hindu–Arabic numeral system
Sahim
thanks
Irungu
Most welcome
Sahim
Hey.. I've a question.
Is earth inertia frame?
Sahim
only the center
Shii
What is an abucus?
Irungu
what would be the correct interrogation "what is time?" or "how much has your watch ticked?"
prakash
hmmmm
oyeronke
coming
oyeronke
time is the distance measured on clock
KINGSFORD
time is that in which events are distinguishable with reference to before and after
Omo
time measure of duration interval of period
Sewmeho
please guys I really don't know physics and am a science student in my final year
bella
you'll be fine Bella. I am taking Physics as well and all u need to do is have drive to learn.
Joshua
how
bella
Study. are u taking Algebra Based Physics or Calc based?
Joshua
am in high school
bella
An American highschool?
navid
I love physics too, but I have a problem of finding time to study more than I usually do, help me out on how much time I need for physics to better understand it.
Prince
So basically, Physics is the study of the laws of motion, and mathmatical calculations to show and figure out forces on an object or certian parts of that force
Joshua
you'll learn 3 laws of motion
Joshua
guys, physics is more than what you think it's
Abdulraheem
YES Sir! it's fun
Joshua
READ stephen hawking a brief history of time it got me into physics it talks about the curiosity of the world beyond our knowledge and the history it's all related to physics yet in a fascinating way
ayesha
not only fun, it tells you what life is and how life is
Abdulraheem
When you start you won't stop
ayesha
Joshua are you on hangout?
bella
no im not
Jeff
Yes
Joshua
I'm in college, so I'm taking a different type of physics but I still love physics in general
Joshua
Guy what do mean by different type of physics
Micheal
quantum physics nuclear physics and metaphysics those are the types of physics that there are
Jeff
metaphysics is basically just Theory
Jeff
a load of 20N on a wire of cross sectional area 8×10^-7m produces an extension of 10.4m. calculate the young modules of the material of the wire is of length 5m
Young's modulus = stress/strain strain = extension/length (x/l) stress = force/area (F/A) stress/strain is F l/A x
El
so solve it
Ebenezer
Ebenezer