Transcript AP Rocket Propulsion

How do most vehicles propel
themselves?
 Tire pushes on ground,
ground pushes on tire…
 Normal Forces and
Friction
How do most vehicles propel
themselves?
 Plane pushes on air, air
pushes on plane.
Rockets have nothing to push off of…
Which physics principles are
related to rockets?
Which physics principles are
related to rockets?
Newton’s 1st Law
Upon exiting Earth’s atmosphere and
reaching a distance where Earth’s
gravitational field is negligible, the rocket
moves at high speeds without slowing
due to inertia!
Newton’s 2nd Law
Thrust of ejected gases must exceed the
force of gravity on an extremely massive
object!
Which physics principles are
related to rockets?
Newton’s 3rd Law
The rocket pushes down on gas
particles. Gas particles push up
on rocket with an equal strength
of force.
Conservation of Momentum
The total momentum before
launch is zero. Extremely
massive moves up slowly. Small
particles move down very fast.
Blast-off…
Rocket Propulsion
M  mv  Mv  v  mv  ve 
Mass of rocket
Mass of
fuel
Velocity at time t
Increase in
rocket velocity
after mass has
been ejected
Velocity of fuel
relative to the
rocket. (Quantity
is velocity of
ejected mass
with respect to
motionless
frame.)
Rocket Propulsion
M  mv  Mv  v  mv  ve 
For blast-off, velocity at time t is zero:
0  Mv  mve 

Mv  mv e
Rocket Propulsion
Mv  mv e
For the limit as Δt approaches zero:
v  dv
m  dm
As ejected mass increases, rocket mass decreases:
dm  dM

Mdv  v edM
Rocket Propulsion
Mdv  v edM
vf
Integrate!
Mf
1
 dv  ve  MdM
vi
Mi
vf  vi  ve lnMf  lnMi 
Rocket Propulsion
vf  vi  ve lnMf  lnMi 
vf  vi  ve lnMf  lnMi 
vf  vi  ve lnMi  lnMf 
M i 
vf  vi  ve ln 
M f 
Rocket Propulsion
M i 
vf  vi  ve ln 
M f 
Higher fuel ejection speed means greater
rocket acceleration.
Rocket without fuel should be as small as
possible and rocket should carry as much fuel
as possible to that mass ratio is high.
Thrust
Thrust is the force exerted on a rocket by
exhausted gases.
Mdv  v edM
Fthrust
dp
F
dt
dv
dM
 M  ve
dt
dt

A Rocket in Space:
1. A rocket moving in free space has a speed of 3x103m/s relative
to Earth. Its engines are turned on, and fuel is ejected at a speed
of 5x103m/s relative to the rocket
a) What is the speed of the rocket relative to Earth once its
mass is reduced to one half its mass before ignition?
b)
What is the thrust on the rocket if it burns the fuel at a
rate of 50kg/s?
A Rocket in Space:
1. A rocket moving in free space has a speed of 3x103m/s relative to
Earth. Its engines are turned on, and fuel is ejected at a speed of
5x103m/s relative to the rocket
a) What is the speed of the rocket relative to Earth once its mass is
reduced to one half its mass before ignition?
M i 
vf  vi  ve ln 
M f 
M i 
vf  vi  ve ln 
M f 
 M i 
vf  3 10 m/s 5 10 m/sln
 6.5km/s
0.5M i 

3
3
A Rocket in Space:
1.
A rocket moving in free space has a speed of 3x103m/s relative to Earth. Its
engines are turned on, and fuel is ejected at a speed of 5x103m/s relative to
the rocket
b) What is the thrust on the rocket if it burns the fuel at a rate of 50kg/s?
Fthrust
Fthrust
dv
dM
 M  ve
dt
dt
dM
3
5
 ve
 5 10 m/s50kg/s  2.5 10 N
dt