Rocket PropulsionAP Physics C: Mechanics

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

Newton’s 2nd 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!

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

Conservation of MomentumThe total momentum before launch is zero.

Extremely massive moves up slowly. Small particles

move down very fast.

The rocket pushes down on gas particles. Gas particles push up on rocket with an equal

strength of force.

Blast-off…

Rocket Propulsion

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M + Δm( )v = M v + Δv( ) + Δm v − 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

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M + Δm( )v = M v + Δv( ) + Δm v − ve( )For blast-off, velocity at time t is zero:

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0 = MΔv + Δm −ve( )

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MΔv = Δmve

Rocket PropulsionFor the limit as Δt approaches zero:

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MΔv = Δmve

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Δv → dvΔm → dm

As ejected mass increases, rocket mass decreases:

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dm = −dM

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Mdv = −vedM

Rocket PropulsionIntegrate!

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Mdv = −vedM

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dvv i

v f

∫ = −ve1MMi

Mf

∫ dM

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vf − vi = −ve lnM f − lnM i( )

Rocket Propulsion

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vf − vi = −ve lnM f − lnM i( )

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vf − vi = ve −lnM f + lnM i( )

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vf − vi = ve lnM i − lnM f( )

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vf − vi = ve ln M i

M f

⎛ ⎝ ⎜

⎞ ⎠ ⎟

Rocket Propulsion

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vf − vi = ve ln M i

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.

ThrustThrust is the force exerted on a rocket by

exhausted gases.

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Fthrust = M dvdt

= vedMdt€

Mdv = −vedM

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F = dpdt

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?

€

vf − vi = ve ln M i

M f

⎛ ⎝ ⎜

⎞ ⎠ ⎟

€

vf = vi + ve ln M i

M f

⎛ ⎝ ⎜

⎞ ⎠ ⎟

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vf = 3×103m/s( ) + 5 ×103m/s( )ln M i

0.5M i

⎛ ⎝ ⎜

⎞ ⎠ ⎟= 6.5km/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

b) What is the thrust on the rocket if it burns the fuel at a rate of 50kg/s?

€

Fthrust = M dvdt

= vedMdt

€

Fthrust = vedMdt

= 5 ×103m/s( ) 50kg /s( ) = 2.5 ×105N