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PHY183-Lecture7 - Position velocity and acceleration...

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August 31, 2006 Physics for Scientists&Engineers 1 1 Physics for Scientists & Engineers 1 Engineers 1 Fall Semester 2006 Lecture 7 August 31, 2006 Physics for Scientists&Engineers 1 2 Position, velocity and acceleration vectors ! Related through derivatives and integrals ( ) ( ) ( ) ( ) ( ) x t dx t v t dt dv t a t dt ! = ! = 0 0 0 0 ( ) ( ') ' ( ) ( ') ' ( ) t t x t x v t dt v t v a t dt a t = + ! = + ! " " August 31, 2006 Physics for Scientists&Engineers 1 3 Summary: Five Kinematical Equations Summary: Five Kinematical Equations ! One-dimensional motion with constant acceleration : ! Can solve practically all one-dimensional problems 0 2 1 0 0 2 1 0 0 2 0 0 2 2 0 0 ( ) ( ) [ ( )] ( ) ( ) 2 [ ( ) ] t t v t v at x t x v t at v v v t x t x v t v t v a x t x ! ! = + = + + = + = + " = " August 31, 2006 Physics for Scientists&Engineers 1 4 Free Fall ! Particular motion with constant acceleration in 1 d a = - g, with g = 9 . 81 m/s 2 Conventional notation: call vertical axis y axis ! Kinematic equations for this case 0 2 0 0 1 0 0 2 0 0 2 2 0 0 1 2 ( ) ( ) [ ( ) ] ( ) ( ) [ ( ) ] 2 t t v t v t y t y v t t v v t v y t y v t v t v y t y g g g ! ! = = + = + " = + " = " " " g y F mg mge = = ! ! ! ! x y g F ma mg ma g a = ! = ! = ! ! Newton’s Second law Use those for constant acceleration: X -> y a -> -g
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August 31, 2006 Physics for Scientists&Engineers 1 5 Remarks on Free Fall ! All objects fall at the same rate, because a = -g = constant Need to get rid of air resistance effects to see this Experiment => calculation of g ! In space, there is almost no gravity Why all objects float around Not net force: constant velocity, independent of the mass 0 2 0 0 1 0 0 2 0 0 2 2 0 0 1 2 ( ) ( ) [ ( ) ] ( ) ( ) [ ( ) ] 2 t t v t v t y t y v t t v
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