198010 - Frederiksen

ExercisePrepare a spreadsheet with the exact expression forv(t) and for s(t) using the difference equation s 1= s 0+ v(t 1)·∆t, and compare the result with the correspondingexpression without air resistance. Compare(t,v) and (t,s) graphs for various values ofk = 1 /2 ·D ·A · CwTheory and real data can be compared using theFrederiksen free fall apparatus. The density of air D= 1,293 kg/m 3 and the cross sectional area A can bedetermined, the value of the air resistance coefficientCW can be found. This is readily done by checkingwhich value of CW in the expression for v(t) whichgives the best agreement with the measured datawhen s(t) is computed in the spreadsheet using thedifference equation.ExerciseWith knowledge of CW it is possible to compute theterminal velocity for a falling body, for in this casem·g - k · v 2 = 0:This is also apparent for the limiting value of v(t) for tgoing towards infinity. Perform an experiment by lettingthe ball fall from a high spot (e.g. Top of a building).Does the object approach a constant speed.?FrederiksenViaduktvej 35 – 6870 Ølgod – Tlf. 75 24 49 66 – Fax 75 24 62 82e-mail: sflab@sflab.dk – www.sflab.dk