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Transcript

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 mv Mv v mv 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 mv Mv v mv ve For blast-off, velocity at time t is zero: 0 Mv mv e Mv mv e Rocket Propulsion Mv mv e For the limit as Δt approaches zero: v dv m dm As ejected mass increases, rocket mass decreases: dm dM Mdv vedM Rocket Propulsion Mdv vedM vf Integrate! Mf 1 dv ve MdM vi Mi v f v i v e ln M f ln M i Rocket Propulsion v f v i v e ln M f ln M i v f v i v e ln M f ln M i v f v i v e ln M i ln M f M i v f v i v e ln M f Rocket Propulsion M i v f v i v e 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 vedM dp F dt dv dM Fthrust 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 v f v i v e ln M f M i v f v i v e ln M f M i vf 3 10 m/s 5 10 m/sln 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? dv dM Fthrust M ve dt dt dM 3 5 Fthrust ve 5 10 m/s50kg /s 2.5 10 N dt