Rockets
So far, we have only considered situations where the change in
momentum is due to changes in velocity.
What would happen if the mass
changed instead?
Or they both changed?
This is the case of rocket motion.
In
order to determine a rocket's motion, we use conservation of linear momentum.
We define the force exerted by the engines on the rocket as the thrust delivered
by the engines.
Consider a rocket sitting on the launch pad.
The momentum of
the rocket is zero.
Now let the engines fire.
v
a
F
mg
v
r
m
∆
We can treat the engines and the rocket as a combined system, so by the
impulse equation we must have
m
(
t
)
a
dt
=
d
p
rocket
+
d
p
engine
where
d
p
engine
=
dm
(
v
+
v
r
), and
v
r
is the velocity of the exhaust relative to the
rocket.
d
p
rocket
= (
m

dm
)(
v
+
d
v
) where
v
is the velocity of the rocket relative to
the Earth.
Thus,
(
29 (
29
[
]
(
29
[
]
dm
v
mdv
dmdv
dm
v
mdv
dm
v
vdm
mv
dmdv
vdm
mdv
mv
mgdt
v
v
dm
mv
dv
v
dm
m
mgdt
r
r
r
r

≈


=

+



+
=



+

+

=

0
Dividing thru by
dt
and solving for the acceleration of the rocket, we get
g
m
v
dt
dm
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 Spring '09
 Knott
 Physics, Mass, Momentum, Spacecraft propulsion, 0.5g, 25,000 kg, 27,000 kg, 18,000 kg

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