Lecture_5 - 4.7 Free-fall equations Earlier we established...

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1 4.7 Free-fall equations Earlier we established that the motion of a object in free fall is motion with uniform acceleration (the acceleration due to gravity ) So, just do the stuff in section 4.6 with |a|=g=9.8m/s 2. Note g is always positive (it is the magnitude of the acceleration due to gravity) Acceleration ( a ) can be either positive or negative , depending on the choice of the x-axis
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2 4.7 Free-fall equations • The direction of the acceleration due to gravity is always downward . • If you choose a positive x-axis to be straight up , ONLY then is the acceleration due to gravity negative!!! • In vector notation… a =-g i Remember i is our unit vector for the x direction
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3 4.8 Inclined planes • It was hard to measure falling objects with the equipment of the time, but Galileo slowed this motion with inclined planes – That when a ball rolls down an incline, the ratio of the distance covered to the square of the time duration necessary to cover that distance is constant . x 1 t 1 2 x 2 t 2 2 x 3 t 3 2
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4 4.8 Inclined planes Remember… – If we have a uniformly accelerating object starting from rest: – Rearranging (chose down slope +): x ( t ) 1 2 at 2 x ( t ) t 2 1 2 a •So Galileo’s ratio is directly proportional to the acceleration x 1 t 1 2 x 2 t 2 2 x 3 t 3 2
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5 4.8 Inclined planes • Since the ratio does not change as the ball goes down the incline the acceleration must be constant! x 1 t 1 2 x 2 t 2 2 x 3 t 3 2 x ( t ) t 2 1 2 a
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4.8 Inclined planes • If you increase the angle of the incline , the ratio of… Increases . • For any
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This note was uploaded on 06/04/2009 for the course PHYS 2054 taught by Professor Stewart during the Spring '08 term at Arkansas.

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Lecture_5 - 4.7 Free-fall equations Earlier we established...

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