lecture10 - Physic 231 Lecture 10 Main points of todays...

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Physic 231 Lecture 10 Main points of today’s lecture: Elastic collisions in one dimension: ( ) () 10 1 20 1 2 2 20 2 1 2 10 2 1 2 1 1 2 2 v m v m m v v m m m v m m m m v f f + = + + + = Multiple impulses and rocket propulsion. 2 1 2 1 m m m m + + ropellant f 0 F t mv Δ=Δ ⋅ −Δ ⋅ propellant propellant f 0 m F v v Thrust t Δ =− = Δ Motion in a circle ( ) 0f m Thrust v v t Δ Δ θ tan ; 1 2 2 y y x r = + = () () sin ; cos r y r x x = =
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Review Conceptual Question the demonstration, one car is heavier than the other, but both In the demonstration, one car is heavier than the other, but both experience the same force and both run for the same distance . Which car has the greater final momentum? A. The lighter car. B. The heavier car. C. They have the same momentum. Slide 9-33
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Totally elastic collisions To calculate the result of an elastic collision in one dimension, we considered e constraints of total momentum and energy conservation: the constraints of total momentum and energy conservation: f f tot v m v m v m v m p , 2 2 , 1 1 0 , 2 2 0 , 1 1 : 1 Eq. + = + = 2 1 2 1 2 1 2 1 q , 2 2 2 , 1 1 2 0 , 2 2 2 0 , 1 1 2 : 2 Eq. f f tot v m v m v m v m E + = + = We rearrange both equations to get object 1 on the left and object 2 on the right: q earranged = ( ) ( ) 0 , 2 , 2 2 , 1 0 , 1 1 : 1 Eq. Rearranged v v m v v m f f () 2 0 , 2 2 , 2 2 2 1 2 , 1 2 0 , 1 1 2 1 : 2 Eq. Rearranged v v m v v m f f = = ( )( ) ( )( ) 0 , 2 , 2 0 , 2 , 2 2 , 1 0 , 1 , 1 0 , 1 1 v v v v m v v v v m f f f f + + ( ) 0 , 2 , 2 , 1 0 , 1 : 2 New Eq. v v v v f f + = + Combining the last equation and the rearranged Equation 1, we have two equations and 2 unknowns which we can solve to get v 1,f and v 2,f : 0 , 2 2 1 2 0 , 1 2 1 2 1 , 1 2 v m m m v m m m m v f + + + = 0 , 1 2 1 1 0 , 2 2 1 1 2 , 2 2 v m m m v m m m m v f + + + =
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Example A 2 kg cart moves with a velocity of 3 m/s to the right on a frictionless track. It collides elastically with a stationary 1 kg cart. a) What are the final velocities of the two carts? kg m s m s m kg kg kg v m m m m v f 2 2 2 / 1 / 3 3 1 2 a) 0 , 1 2 1 2 1 , 1 = = + = b) In a frame moving with the initial velocity of the first cart, what are e initial and final velocities of the two carts?
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lecture10 - Physic 231 Lecture 10 Main points of todays...

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