# 8.7 Introduction to rocket propulsion  (Page 4/4)

 Page 4 / 4

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.

Calculate the work done by an 85.0-kg man who pushes a crate 4.00 m up along a ramp that makes an angle of 20.0º20.0º with the horizontal. (See [link] .) He exerts a force of 500 N on the crate parallel to the ramp and moves at a constant speed. Be certain to include the work he does on the crate an
What is thermal heat all about
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what is distance of A to B of the stations and what is the time taken to reach B from A
BELLO
the information provided is not enough
aliyu
Hmmmm maybe the question is logical
yusuf
where are the parameters for calculation
HENRY
there is enough information to calculate an AVERAGE acceleration
Kwok
mistake, there is enough information to calculate an average velocity
Kwok
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Abel
what is the unit of momentum
Abel
wha are the types of radioactivity ?
what are the types of radioactivity
Worku
what is static friction
It is the opposite of kinetic friction
Mark
static fiction is friction between two surfaces in contact an none of sliding over on another, while Kinetic friction is friction between sliding surfaces in contact.
MINDERIUM
I don't get it,if it's static then there will be no friction.
author
It means that static friction is that friction that most be overcome before a body can move
kingsley
static friction is a force that keeps an object from moving, and it's the opposite of kinetic friction.
author
It is a force a body must overcome in order for the body to move.
Eboh
If a particle accelerator explodes what happens
Eboh
why we see the edge effect in case of the field lines of capacitor?
Arnab
what is wave
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Muhammed
force is something which is responsible for the object to change its position
MINDERIUM
more technically it is the product of mass of an object and Acceleration produced in it
MINDERIUM
wave is disturbance in any medium
iqra
energy is distributed in any medium through particles of medium.
iqra
If a particle accelerator explodes what happens
we have to first figure out .... wats a particle accelerator first
Teh
What is surface tension
The resistive force of surface.
iqra
Who can tutor me on simple harmonic motion
on both a string and peldulum?
Anya
spring*
Anya
Yea
yusuf
Do you have a chit-chat contact
yusuf
I dont have social media but i do have an email?
Anya
Which is
yusuf
Where are you chatting from
yusuf
I don't understand the basics of this group
Jimmy
teach him SHM init
Anya
Simple harmonic motion
yusuf
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definition of mass of conversion
Force equals mass time acceleration. Weight is a force and it can replace force in the equation. The acceleration would be gravity, which is an acceleration. To change from weight to mass divide by gravity (9.8 m/s^2).
Marisa
how many subject is in physics
the write question should be " How many Topics are in O- Level Physics, or other branches of physics.
effiom
how many topic are in physics
Praise
Praise what level are you
yusuf
If u are doing a levels in your first year you do AS topics therefore you do 5 big topic i.e particles radiation, waves and optics, mechanics,materials, electricity. After that you do A level topics like Specific Harmonic motion circular motion astrophysics depends really
Anya
Yeah basics of physics prin8
yusuf
Heat nd Co for a level
yusuf
yh I need someone to explain something im tryna solve . I'll send the question if u down for it
a ripple tank experiment a vibrating plane is used to generate wrinkles in the water .if the distance between two successive point is 3.5cm and the wave travel a distance of 31.5cm find the frequency of the vibration
Tamdy
hallow
Boniface
Boniface
the range of objects and phenomena studied in physics is
Boniface