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Unformatted text preview: 1 The Effect of Air Resistance Harvey Gould Physics 127 2/06/07 I. INTRODUCTION I simulated the motion of a falling body near the earth’s surface in the presence of gravity and air resistance. I used the Euler, EulerCromer, and EulerRichardson algorithms and considered both a linear and quadratic dependence of the drag force on the velocity. Of particular interest is the rise and fall of a pebble and the relative times of ascent and descent. II. METHOD As shown in the text, Newton’s laws of motion can be written as two coupled firstorder differential equations. The Euler algorithm for the numerical solution of the latter equations can be written in the form v n +1 = v n + a n Δ t (1a) y n +1 = y n + v n Δ t. (1b) The EulerCromer algorithm modifies Eq. (1) slightly and can be expressed as v n +1 = v n + a n Δ t (2a) y n +1 = y n + v n +1 Δ t. (2b) A more sophisticated version of the Euler algorithm evaluates the acceleration and the velocity at the time Δ t/ 2 = t + Δ t/ 2. The EulerRichardson algorithm can be written as follows: a m = F ( y m , v m , Δ t/ 2) /m (3a) v m = v n + a n Δ t/ 2 (3b) y m = y n + v n Δ t/ 2 , (3c) 2 and v n +1 = v n + a m Δ t (4a) y n +1 = y n + v m Δ t. (4b) The total force on a falling body in the presence of air resistance can be written in the convenient form F = mg (1 v 2 /v 2 t ) (quadratic drag force) (5a) or F = mg (1 v/v t ) (linear drag force) (5b) The signs in Eq. (5) are for a falling body with the vertical coordinate increasing upward.The signs in Eq....
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This note was uploaded on 10/05/2011 for the course ME me352 taught by Professor Koraykadirsafak during the Spring '11 term at Yeditepe Üniversitesi.
 Spring '11
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