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Unformatted text preview: Outline Outline c Momentum c Momentum and Impulse c Conservation of Linear Momentum c Collisions Chapter9 Impulse, Momentum & Conservation of Momentum….!!!! Momentum "momentu Definition: m" p mv ≡ = a a ; ; ; x x y y z z p mv p mv p mv = = = nd ( ) 2 Law: dv d mv dp F ma m dt dt dt = = = = a a a a a 2 1 2 1 ( ) t x x x x t p p p F t dt Δ = = ∫ Momentum is a vector quantity. Force changes momentum. 2 2 1 mv p mv v c γ ≡ = a a a 2 2 1 1 v c γ = Momentum and Impulse Profile of the force during a collision. Microscopic view of a “bounce”. Impulse 2 1 "impulse Defi " niti ( on: ) x t x t J F t dt ≡ = ∫ x avg J F t = Δ x x f i x p J p p J Δ = = + (area under force curve) (area under force curve) fx ix x ix fx fx ix p p J p p v v m m = + = + = = + Quiz!! 6 Non Quiz!! Quiz!! Example: A Bouncing Ball A 100 g rubber ball is dropped from a height of 2.0 m onto a hard floor. The floor exerts a force on the ball as shown above. How high does the ball bounce? 2 2 1 2 1 2 2 2 2(9.80 m/s )(2.0m) 6.26 m/s y y y v v g y g y v g y = Δ =  Δ =  Δ =  =  1 1 y y 2 2 J = F (t)dt= (base)(altitude) (300 N)(0.008 s) 1.20 Ns = = ∫ 2 1 (0.1 kg)( 6.26 m/s)+(1.20 Ns)=0.574 kg m/s y y y p p J = + = 2 2 / (0.574 kg m/s)/(0.1 kg)=5.74 m/s y y v p m = = 1 1 2 2 2 2 2 3y 2y 2y 2 2 v =v 2 0 so y= v (5.74 m/s) (9.80 m/s ) 1.68 m / g y g Δ = Δ = = Newton’s Second Law for a system of particles ( Reminder!!! ) • From the previous slide: • Here is a resultant force on particle i • According to the Newton’s Third Law, the forces that particles of the system exert on each other (internal forces) should cancel : • Here is the net force of all external forces that act on the system (assuming the mass of the system does not change) ∑ = i i com F a M a a net com F a M a a = i F a net F a tot net dP F dt = a a Conservation of Momentum 1 2 on 1 2 1 on 2 2 on 1 ( ) ( ) ( ) ( ) ( ) x x x x x d p F dt d p F F dt = = =  1 2 1 2 2 on 1 2 on 1 [( ) ( ) ] ( ) ( ) ( ) ( ) x x x x x x d p p d p d p dt dt dt F F + = + = = 1 2 ( ) ( ) constant x x p p + = 1 2 Before 1 2 After [( ) ( ) ] =[( ) ( ) ] x x x x p p p p + + The Law of Conservation of Momentum (derivable from Newton’s Laws and the definition of momentum.) In an isolated system, momentum is conserved. dP dt = a A System of N Particles The N=3 Case: For every pair of particles, the action/reaction pairs F j on k and F k on j are equal and opposite force vectors. In addition, each particle may be subjected to possible external forces F ext on k from agents outside the system....
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This note was uploaded on 02/21/2009 for the course PHY A10 taught by Professor Tawfiq during the Fall '08 term at University of Toronto Toronto.
 Fall '08
 TAWFIQ
 Physics, Momentum

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