POSTER PRESENTATION OF A PAPER BY: Alex Shved, Mark Logillo, Spencer Studley AAPT MEETING, JANUARY, 2002, PHILADELPHIA

Transcription

1 POSTER PRESETATIO OF A PAPER BY: Ale Shved, Mar Logillo, Spencer Studley AAPT MEETIG, JAUARY, 00, PHILADELPHIA

2 Daped Haronic Ocillation Uing Air a Drag Force Spencer Studley Ale Shveyd Mar Loguillo Santa Roa Junior College Departent of Engineering & Phyic 1501 Mendocino Ave Santa Roa, CA Superviing Intructor Youne Ataiiyan

3 Introduction An oject oving through fluid encounter a reitive force The nature of thi reitive force depend on the peed of the oject At low velocitie the drag force i due to the friction etween the oving oject and the fluid At high velocitie the drag force i ainly due to the fluid preure eerted on the oving oject The velocity of the oving oject, v, coined with the phyical propertie of the fluid i ued to define a dienionle quantity, called the Reynold nuer written a 1 : R = (vd/) In thi equation, i the denity of the fluid, i the vicoity of the fluid and D i the effective length or diaeter of the oving oject At low Reynold nuer, the drag force i linearly proportional to the velocity of the oject, F I =-v and at high Reynold nuer, the drag force i proportional to the quare of the velocity, F II =-v The ocillatory otion of a a attached to a pring would e a daped ocillation due to the drag force eerted y air on the oving oject The daping force i typically aued to e linearly proportional to the velocity of the oject The equation of the otion can e decried a: F v d dt d dt where K i the pring contant and X i the diplaceent of the oject fro it equiliriu poition By olving the aove differential equation, the olution i found to e in the t for of: X ( t) A e co( t )

4 where o t X ( t) A e co( t ) Figure 1: Typical daped haronic ocillation Procedure During the initial part of thi eperient a pring wa upended fro a rod, approiately eter fro the ground A otion enor wa connected to a coputer and placed directly underneath the pring The ai of the pring wa aligned a accurately a poile with the center of the otion enor Figure : Scheatic preentation of the eperiental et-up

5 The a of a thin circular di with a diaeter of 5 centieter wa eaured on an analytical alance Additional a wa added to the plate until the total a wa15 gra 1gra The circular plate wa then upended fro the otto of the pring, aove the otion enor The pring wa retracted downward a ditance of 10 centieter fro the equiliriu poition and releaed The oent the pring wa releaed and allowed to ocillate, the otion enor wa activated through the coputer and diplaceent-tie data wa collected and tored In the econd trial the pring wa retracted a ditance of 0 centieter downward and releaed again a the otion enor wa activated The ae procedure wa repeated, for the final trial, with the circular di retracted to a ditance of 30 centieter downward The releae of the di fro ultiple diplaceent ditance reulted in varying initial velocitie, enaling u to invetigate the air drag at everal different velocitie The aove procedure wa repeated for thin circular di with diaeter of 10c, 15 c and 0 c while aintaining a total a of 15 +/-1 gra for each di In the econdary tage of the eperient the pring contant wa deterined uing Hooe' law Thi wa accoplihed y upending variou ae fro the pring and eauring each vertical diplaceent fro the equiliriu poition The pring contant wa deterined fro the lope of the of weight veru the diplaceent curve and wa found to e +/- 001 / The diplaceent-tie data wa fit to the equation: X ( t) A e co( t ) t uing a progra called CurveEpert 3 verion 137 Thi proce wa perfored in two different tage In the firt tage, the entire range of the collected data wa ued for the curve fitting In the econd tage,

6 elected range of collected data correponding to a pecific velocity range wa ued for the curve fitting RESULTS The value of for each di and variou initial diplaceent were deterined directly fro the paraeter otained y the curve fitting It hould alo e noted that theoretically, the paraeter can e calculated fro o, where i deterined fro the curve-fit A hown in the OTE ection elow, the calculated uing thi ethod reult in a very large poile error, due to the cloe proiity of 0 and /() value In the firt attept, the curve fitting wa done on the entire range of the collected data for all the ituation decried in the procedure ection Plot of veru di area for all three di and for different diplaceent are hown in Figure 3 By generating the velocity-tie graph fro eaured ditance-tie data, the overall range of the velocitie for all the ituation wa found to e etween 13 to 03 / Uing thi range of velocitie and = 0013 g/c 3 for air, = g/(cs), the range of the Reynold nuer wa found to e in the to 300 range It ha een hown 4 that for a thin di oving through a fluid at high velocitie, correponding to the Reynold nuer of greater than 310 4, the drag force i proportional to the quare of the velocity according to : FD = ½(C D A V )

7 where C D, called the drag coefficient, i contant and equal to 11 for a high Reynold nuer In the aove equation, i the air denity and A i the area of v plate area (full data curve fit) y = R = FOR X=30 c y = R = FOR X=0 c (Kg/) y = R = FOR X=10 c the di plate area (^) Figure 3: Plot of veru di diaeter for variou diplaceent value The value of were found y curve fitting to the entire range of collected data for each cae To eparate the analyi into a high velocity region and a low velocity region, eparate value were otained y curve fitting the data correponding to the velocitie aove 1 / and elow 03 /, repectively Thi analyi wa perfored for the diplaceent of X=30 c data only Plot of thee new value veru di diaeter for the high and low velocity region are hown in figure 5

8 An ongoing invetigation aied at finding a correlation etween and the reported value of C D = 11 i in progre

9 06 04 CURVE FITTIG AT DIFFERET SPEED RAGES curve A, High peed curve B, Full Range 0 curve C, low peed t(sec) Figure 4: Reult of the curve fitting to the low velocity range, high velocity range and the full range for the 0 c diaeter di ocillation fro a 30 c diplaceent

10 Variation of with plate area (partial curve fit) High peed region y = R = (Kg/) Low Speed y = E-05 R = Plate Area () Figure 5: Plot of deterined fro curve fitting to the low velocity range and high velocity range data Thee value are deterined fro a 30c diplaceent for each of the di REFERECES: 1- JK Vennard, RL Street, Eleentary Fluid Mechanic, 6th ed Page 83, John Wiley and Son, 198 -RA Serway, RJ Beichner, Phyic for Scientit and Engineer, 5th Ed, P408, Sounder College Pulihing, CurveEpert v 137 wwweiconet/~dhya/cvptht 4-ae a 1, page 631

11 OTE: Error calculation for fro g g g g g g g g g g g g g g