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Chapter%207(1)

# Chapter%207(1) - COLLEGE PHYSICS Part I Chapter 7 Impulse...

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COLLEGE PHYSICS, Part I Chapter 7: Impulse and Momentum Conservation of Linear Momentum Elastic and Inelastic Collisions Impulse Center of Mass

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Momentum When a particle of mass m moves with velocity v , its momentum p is defined as follows: Momentum is a vector quantity, i.e. has both magnitude and direction, and its unit is kg . m/s p mv = r r Momentum and Kinetic Energy Two objects have the same momentum but different masses. A. The one with less mass has more kinetic energy B. Both have the same kinetic energy C. The one with more mass has more kinetic energy 2 2 2 1 1 2 2 2 2 p p K mv m m m p mK = = = = Determine the correct answer using these relationships: This quantity is called the linear momentum to distinguish it from the angular momentum; we will just call it momentum.
If the components of the velocity in the three dimensional space are v x , v y , and v z , then the components of the momentum are Newton’s Second Law and Momentum Newton’s second law can be presented like this: or, x x p mv = y y p mv = z z p mv = 0 lim t v F m t ∆ → Σ = r r 0 lim t m v F t ∆ → Σ = r r But, 2 1 2 1 2 1 ( ) m v m v v mv mv p p p = - = - = - = ∆ r r r r r r r r So, 0 lim t p F t ∆ → Σ = r r The vector sum of all forces acting on a particle equals the rate of change of momentum.

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The total momentum of two or more particles is defined as the vector sum of the momenta of the particles. ... A B C P p p p = + + + r r r r Similarly: , , , , , , , , , ... ... ... x A x B x C x y A y B y C y z A z B z C z P p p p P p p p P p p p = + + + = + + + = + + + r r r r r r r r r r r r
Example: A 1000 kg car that travels northbound with v = 15 m/s collides with a 2000 kg truck traveling eastbound with v = 10 m/s. Find the total momentum just before the collision. , 4 , , 4 , , , 0 1.5 10 / 2.0 10 / 0 A x A y A A y B x B B x A y p p m v kg m s p m v kg m s p = = = × = = × = After selection of an appropriate coordinate system, we can write: So, the total momentum has one x component and one y component (certainly there is no z component) 2 2 4 , , 2.5 10 / B x A y P p p kg m s = + = × , , tan 0.75 36.9 A y B x o p p θ θ = = =

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Conservation of Momentum When two objects (in this case two astronauts) interact, they exert force on each other. According to Newton’s third law, the two forces are equal in magnitude and opposite in direction; the sum of all forces is zero. Now consider Newton’s second law written in this form: When the components of a system interact with each other, the associated forces are called internal forces . The forces exerted on any part of the system by objects outside of the system are called external forces . A system free of any external forces is an isolated system . 0 lim t p F t ∆ → Σ = r r If the sum of all forces is zero then the change of total momentum is also zero. Hence, momentum remains constant, or, the total momentum is conserved .
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