212 Energy and Energy TransferP7.65If positive Frepresents an outward force, (same as direction as r), thenWdFrFrdrWFrFrWFrrFrrFrrFWrrrrWifrrrrfifififiifif=⋅=−=−−−=−−+−=−−−=×−−×−×−zz−−−−−−−−2212666661 03 101 89 101 03 101 88 10201313077013120760131212076 607013121277661341212776σσejej.....44 10101 89 103 54 105 96 10102 49 10112 101 37 10660134128120212121×−××−××+×= −×−−−WJ JJP7.66P∆∆∆tW Kmv== =af22The density isρ==∆mmAxvol.Substituting this into the first equation and solving for , since ∆∆xtv=,for a constant speed, we get=Av32.FIG. P7.66Also, since =Fv,FAv=22.Our model predicts the same proportionalities as the empirical equation, and gives D=1 for thedrag coefficient. Air actually slips around the moving object, instead of accumulating in front of it.For this reason, the drag coefficient is not necessarily unity. It is typically less than one for astreamlined object and can be greater than one if the airflow around the object is complicated.
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