<< Chapter < Page Chapter >> Page >

A rocket’s acceleration depends on three major factors, consistent with the equation for acceleration of a rocket . First, the greater the exhaust velocity of the gases relative to the rocket, v e size 12{v rSub { size 8{e} } } {} , the greater the acceleration is. The practical limit for v e size 12{v rSub { size 8{e} } } {} is about 2 . 5 × 10 3 m/s size 12{2 "." 5 times "10" rSup { size 8{3} } `"m/s"} {} for conventional (non-nuclear) hot-gas propulsion systems. The second factor is the rate at which mass is ejected from the rocket. This is the factor Δ m / Δ t size 12{Δm/Δt} {} in the equation. The quantity ( Δ m / Δ t ) v e size 12{ \( Δm/Δt \) v rSub { size 8{e} } } {} , with units of newtons, is called "thrust.” The faster the rocket burns its fuel, the greater its thrust, and the greater its acceleration. The third factor is the mass m size 12{m} {} of the rocket. The smaller the mass is (all other factors being the same), the greater the acceleration. The rocket mass m size 12{m} {} decreases dramatically during flight because most of the rocket is fuel to begin with, so that acceleration increases continuously, reaching a maximum just before the fuel is exhausted.

Factors affecting a rocket’s acceleration

  • The greater the exhaust velocity v e size 12{v rSub { size 8{e} } } {} of the gases relative to the rocket, the greater the acceleration.
  • The faster the rocket burns its fuel, the greater its acceleration.
  • The smaller the rocket’s mass (all other factors being the same), the greater the acceleration.

Calculating acceleration: initial acceleration of a moon launch

A Saturn V’s mass at liftoff was 2 . 80 × 10 6 kg size 12{2 "." "80" times "10" rSup { size 8{6} } `"kg"} {} , its fuel-burn rate was 1 . 40 × 10 4 kg/s size 12{1 "." "40" times "10" rSup { size 8{4} } `"kg/s"} {} , and the exhaust velocity was 2 . 40 × 10 3 m/s size 12{2 "." "40" times "10" rSup { size 8{3} } `"m/s"} {} . Calculate its initial acceleration.

Strategy

This problem is a straightforward application of the expression for acceleration because a size 12{a} {} is the unknown and all of the terms on the right side of the equation are given.

Solution

Substituting the given values into the equation for acceleration yields

a = v e m Δ m Δ t g = 2 . 40 × 10 3 m/s 2 . 80 × 10 6 kg 1 . 40 × 10 4 kg/s 9 . 80 m/s 2 = 2 . 20 m/s 2 .

Discussion

This value is fairly small, even for an initial acceleration. The acceleration does increase steadily as the rocket burns fuel, because m size 12{m} {} decreases while v e size 12{v rSub { size 8{e} } } {} and Δ m Δ t size 12{ { {Δm} over {Δt} } } {} remain constant. Knowing this acceleration and the mass of the rocket, you can show that the thrust of the engines was 3 . 36 × 10 7 N size 12{3 "." "36" times "10" rSup { size 8{7} } `N} {} .

Got questions? Get instant answers now!

To achieve the high speeds needed to hop continents, obtain orbit, or escape Earth’s gravity altogether, the mass of the rocket other than fuel must be as small as possible. It can be shown that, in the absence of air resistance and neglecting gravity, the final velocity of a one-stage rocket initially at rest is

v = v e ln m 0 m r , size 12{v=v rSub { size 8{e} } "ln" { {m rSub { size 8{0} } } over {m rSub { size 8{r} } } } ,} {}

where ln m 0 / m r size 12{"ln"` left (m rSub { size 8{0} } /m rSub { size 8{r} } right )} {} is the natural logarithm of the ratio of the initial mass of the rocket m 0 size 12{ left (m rSub { size 8{0} } right )} {} to what is left m r size 12{ left (m rSub { size 8{r} } right )} {} after all of the fuel is exhausted. (Note that v size 12{v} {} is actually the change in velocity, so the equation can be used for any segment of the flight. If we start from rest, the change in velocity equals the final velocity.) For example, let us calculate the mass ratio needed to escape Earth’s gravity starting from rest, given that the escape velocity from Earth is about 11 . 2 × 10 3 m/s size 12{"11" "." 2 times "10" rSup { size 8{3} } `"m/s"} {} , and assuming an exhaust velocity v e = 2 . 5 × 10 3 m/s size 12{v rSub { size 8{e} } =2 "." 5 times "10" rSup { size 8{3} } `"m/s"} {} .

ln m 0 m r = v v e = 11 . 2 × 10 3 m/s 2 . 5 × 10 3 m/s = 4 . 48 size 12{"ln" { {m rSub { size 8{0} } } over {m rSub { size 8{r} } } } = { {v} over {v rSub { size 8{e} } } } = { {"11" "." 2 times "10" rSup { size 8{3} } `"m/s"} over {2 "." 5 times "10" rSup { size 8{3} } `"m/s"} } =4 "." "48"} {}

Solving for m 0 / m r size 12{m rSub { size 8{0} } /m rSub { size 8{r} } } {} gives

Questions & Answers

A body travelling at a velocity of 30ms^-1 in a straight line is brought to rest by application of brakes. if it covers a distance of 100m during this period, find the retardation.
Pamilerin Reply
what is distribution of trade
Grace Reply
what's acceleration
Joshua Reply
The change in position of an object with respect to time
Mfizi
Acceleration is velocity all over time
Pamilerin
hi
Stephen
It's not It's the change of velocity relative to time
Laura
Velocity is the change of position relative to time
Laura
acceleration it is the rate of change in velocity with time
Stephen
acceleration is change in velocity per rate of time
Noara
what is ohm's law
Stephen
Ohm's law is related to resistance by which volatge is the multiplication of current and resistance ( U=RI)
Laura
how i don understand
Willam Reply
how do I access the Multiple Choice Questions? the button never works and the essay one doesn't either
Savannah Reply
How do you determine the magnitude of force
Peace Reply
mass × acceleration OR Work done ÷ distance
Seema
Which eye defect is corrected by a lens having different curvatures in two perpendicular directions?
Valentina Reply
acute astigmatism?
the difference between virtual work and virtual displacement
Noman Reply
How do you calculate uncertainties
Ancilla Reply
What is Elasticity
Salim Reply
using a micro-screw gauge,the thickness of a piece of a A4 white paper is measured to be 0.5+or-0.05 mm. If the length of the A4 paper is 26+or-0.2 cm, determine the volume of the A4 paper in: a). Cubic centimeters b). Cubic meters
Ancilla Reply
what is module
Alex Reply
why it is possible for an object(man) to stay on air without falling down?
akande Reply
its impossible, what do you mean exactly?
Ryan
Exactly
Emmanuella
it's impossible
Your
Why is it not possible to stand in air?
bikko
the air molecules are very light enough to oppose the gravitational pull of the earth on the man..... hence, freefall occurs
Arzail
because of gravitational forces
Pamilerin
this mostly occur in space
Stephen
what is physics
Joshua Reply
no life without physics ....that should tell you something
Exactly
Emmanuella
😎👍
E=MC^2
study of matter and energy and an inter-relation between them.
Minahil
that's how the mass and energy are related in stationery frame
Arzail
Ketucky tepung 10m
firdaus
Treeskin, 6m Cloud gam water 2m Cloud gam white 2m And buur
firdaus
Like dont have but have
firdaus
Two in one
firdaus
Okay
firdaus
DNA card
firdaus
hey am new over hear
Shiwani
War right? My impesilyty again. Don't have INSURAN for me
firdaus
PUSH
firdaus
I give
firdaus
0kay
firdaus
Hear from long
firdaus
Hehehe
firdaus
All physics... Hahahaha
firdaus
Tree skin and two cloud have tokside maybe
firdaus
Sold thing
firdaus
PUSH FIRST. HAHAHAAHA
firdaus
thanks
firdaus
Kinetic energy is the energy due to montion of waves,electrons,atoms, molecule,substances an object s.
Emmanuella
Opjective 0
firdaus
Atom nber 0
firdaus
SOME N
firdaus
10.000m permonth. U use momentom with me
firdaus
hi
Hilal
plz anyone can tell what is meteor and why meteor fall in night? can meteor fall in the day
Hilal
meteor are the glowy (i.e. heated when the enter into our atmosphere) parts of meteoroids. now, meteoroids are the debris resulting from the collision of asteroids or comets. yes, it occurs in daytime too, but due to the daylight, we cant observe it as clearly as in night
Arzail
thank's
Hilal
hello guys
Waka
wich method we use to find the potential on a grounded sphere
Noman
hello
Pamilerin
Physics is the science that studies everything around us from the smallest things like quarks to the biggest things like galaxies. It's simply everything.
Laura
Good day everyone
Divine
It talks mainly about matter with related topics such as forces energy gravity and time. It's amazing
Laura
Hi
Alpha
Physics generally is the study of everything around us.
Steven
physics is the branch of sceince
shafiu
physics is the branch of sceince that deal with motion
shafiu
physics is the branch of sceince that deal with motion &energy
shafiu
with out a physics the life is nothing to see
Yilma Reply
What do you want to talk about😋😋
Emmanuella
the study of all the natural events occuring around us..... this is Physics (until those events obey the laws of physics)
Arzail
Conservation of energy😰
Emmanuella
yeah, that too
Arzail
Energy, it always remains there in a physical system. it can only take the form either in motion (kinetic energy) or in rest (potential energy)
Arzail
In nature organisms feed on one another in an orderly way.
Emmanuella
that describes the food chain, in which we humans are at the top
Arzail
The energy that came initially from the sun 🌞is converted into a form in which it can be stored in green plant.
Emmanuella
Therefore, there is conservation of energy.
Emmanuella
DNA CARD
firdaus
"card"
firdaus
Darag
firdaus

Get the best College physics course in your pocket!





Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'College physics' conversation and receive update notifications?

Ask