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Rockets&CM

# Rockets&CM - Physics 201 Lecture 15 Reprise on...

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3/27/08 Physics 201, UW-Madison 1 Physics 201: Lecture Physics 201: Lecture 15 15 Reprise on collisions and rocket motion Equilibrium Center of mass Dynamics of center of mass

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3/27/08 Physics 201, UW-Madison 2 Question Question Two balls--one heavy (basketball) and the other light (tennis ball) --are stacked on each other, lighter ball on the top of the heavier one, and dropped to the ground. The speed of the recoiling tennis ball will be: Smaller than Same as Larger than the speed attained by it if dropped by itself at the same height CORRECT
3/27/08 Physics 201, UW-Madison 3 Rocket Motion Rocket Motion "Professor Goddard does not know the relation between action and reaction and the need to have something better than a vacuum against which to react. He seems to lack the basic knowledge ladled out daily in high schools." -- 1921 New York Times editorial about Robert Goddard. • "Correction: It is now definitely established that a rocket can function in a vacuum. The 'Times' regrets the error." 1969 New York Times

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3/27/08 Physics 201, UW-Madison 4 Rocket Propulsion Rocket Propulsion The operation of a rocket depends on the law of conservation of momentum as applied to a system, where the system is the rocket plus its ejected fuel This is different than propulsion on the earth where two objects exert forces on each other » road on car » train on track The rocket is accelerated as a result of the thrust of the exhaust gases This represents the inverse of an inelastic collision Momentum is conserved Kinetic Energy is increased (at the expense of the stored energy of the rocket fuel)
3/27/08 Physics 201, UW-Madison 5 Rocket Propulsion Rocket Propulsion Initially after Δ t The rocket’s mass M M- Δ M The rocket’s speed v v v+ Δ v Momentum of fuel 0 (v-v e ) Δ M (The fuel, Δ M, is ejected at v e with respect to rocket -- v+(-v e ) in our coordinate system.) Δ p = Impulse V e

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3/27/08 Physics 201, UW-Madison 6 Rocket Rocket M dv = v e dM ! dv = v e dM M v f " v i = v e ln M i M f Integrate Δ p = Impulse v ! v e ( ) " M + M ! " M ( ) v + " v ( ) ! Mv = F " t momentum after " t - initial p = impulse
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