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Solutions to Physics 325 Midterm Exam
15 Nouember
2006
PROBLEM
1 (20 points)
A rocket has a mass ,4,1 when empty of fuel. It is filled with fuel of rnass 8.4.1
in orcler
to tnake a specific
journey
through intergalactic space (i.e no need to consider
leaving
and
joining
the gravitational fields of stars or planets). All the fuel is used up during
the journey.
The rocket is started from rest and brought back to rest at the end of the
journey.
At first the thruster engines
at the back of the rocket are activated. These have
an exhaust velocity of u. After a time the back engines are turned off and thc fbrrvard
ettgines
are activated. Thel' also have an exhaust speed of u. but in the opposite directioti.
How much fuel is burned on the first part of the
journey,
the part u'hele
tire back engirres
are buruing and the rocket
is acceleratinrr
fn^r,rd?
SOLUTiON:
Since
the rocket experiences
no other force other than the thrust of the engrncs.
the
equation of motion is given by:
mb:
h1,",
n'here u", is the exhaust velocity, and the positive direction is in the direction of tlie
rocket's motion.
We note tliat until a certain point in the
journey,
uer
:
2.
ancl afterwards we havc that
't.'",
changes
sign,
that is, uer
:
u, utitil the rocket comes
to rest at the end of the
jouluc'r'.
As the tocket is started from rest, at this special point irr the
journcS',
the velocity
is
ur
:
tLIn(9A,[
lm1)
r,r,here
nr,1
is the total mass of the rocket at this point.
After this point, the rocket will be decelerated
and the velocit5.
rvill be given bv:
u(t):utuln(rylm(t))
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This note was uploaded on 02/23/2009 for the course PHYS 325 taught by Professor Lamb during the Fall '09 term at University of Illinois at Urbana–Champaign.
 Fall '09
 Lamb
 mechanics, Mass

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