325MTFa06_solutions - Solutions to Physics 325 Midterm 15...

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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):ut-uln(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.

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325MTFa06_solutions - Solutions to Physics 325 Midterm 15...

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