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# Rockets - Rockets So far we have only considered situations...

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Rockets So far, we have only considered situations where the change in momentum is due to changes in velocity. What would happen if the mass changed instead? Or they both changed? This is the case of rocket motion. In order to determine a rocket's motion, we use conservation of linear momentum. We define the force exerted by the engines on the rocket as the thrust delivered by the engines. Consider a rocket sitting on the launch pad. The momentum of the rocket is zero. Now let the engines fire. v a F mg v r m We can treat the engines and the rocket as a combined system, so by the impulse equation we must have m ( t ) a dt = d p rocket + d p engine where d p engine = dm ( v + v r ), and v r is the velocity of the exhaust relative to the rocket. d p rocket = ( m - dm )( v + d v ) where v is the velocity of the rocket relative to the Earth. Thus, ( 29 ( 29 [ ] ( 29 [ ] dm v mdv dmdv dm v mdv dm v vdm mv dmdv vdm mdv mv mgdt v v dm mv dv v dm m mgdt r r r r - - - = - + - - - + = - - - + - + - = - 0 Dividing thru by dt and solving for the acceleration of the rocket, we get g m v dt dm

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Rockets - Rockets So far we have only considered situations...

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