Phys205A_Lecture25

# Physics for Scientists & Engineers with Modern Physics (4th Edition)

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Chapter 9 Motion of a System of Particles Rocket Propulsion

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Motion of a System of Particles z Assume the total mass, M, of the system remains constant z We can describe the motion of the system in terms of the velocity and acceleration of the center of mass of the system z We can also describe the momentum of the system and Newton’s Second Law for the system = v r CM 1 i i i mr M r
Velocity and Momentum of a System of Particles z The velocity of the center of mass of a system of particles is z The momentum can be expressed as z The total linear momentum of the system equals the total mass multiplied by the velocity of the center of mass CM CM 1 ii i d m dt M == r vv r rr CM tot i Mm = ∑∑ p p r r

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Acceleration of the Center of Mass z The acceleration of the center of mass can be found by differentiating the velocity with respect to time CM CM 1 ii i d m dt M == v aa r rr = r r CM i Mm
Forces In a System of Particles z The acceleration can be related to a force z If we sum over all the internal forces, they cancel in pairs and the net force on the system is caused only by the external forces CM i i M = aF r r

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Newton’s Second Law for a System of Particles z Since the only forces are external, the net external
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Phys205A_Lecture25 - Chapter 9 Motion of a System of...

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