Disclaimer: This lab write-up is not

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1 Diclaier: Thi lab write-up i nt t be cpied, in whle r in part, unle a prper reference i ade a t the urce. (It i trngly recended that yu ue thi dcuent nly t generate idea, r a a reference t explain cplex phyic neceary fr cpletin f yur wrk.) Cpying f the cntent f thi web ite and turning in the aterial a riginal aterial i plagiari and will reult in eriu cnequence a deterined by yur intructr. Thee cnequence ay include a failing grade fr the particular lab write-up r a failing grade fr the entire eeter, at the dicretin f yur intructr. Anything included in thi reprt in RED (with the exceptin f the equatin which are in black) wa added by e (Bill) and repreent the data btained when the experient wa run. Ue yur wn data yu cllected and perfr the calculatin fr yur wn data! Newtn Law II -

2 Newtn Law II Nae PES 50 Reprt Objective The purpe f thi lab i t exaine and analyze tatic and dynaic yte uing Newtn Law. A tatic yte i ne where the ttal acceleratin i zer and there i n tin ccurring. A dynaic yte i ne where the ttal acceleratin i nn-zer and the cpnent f the yte ve. urtherre, we will deterine if Newtn Law are applicable baed upn the eaureent recrded and reult btained via the experiental prce. Data and Calculatin Part A rce bard The experient huld be et up a fllw: pulley T get the frce,, and 3 attach the a,, and 3 repectively. a: a: a: 3 igure : Experiental etup f a tatic yte ued t prve the validity f Newtn Law Experientally it i difficult t eaure the angle, and 3. Newtn Law II -

3 igure : Analytical rientatin f angle at the center f the tatic yte in a plar crdinate frae fr the experiental etup The prble arie when we try t eaure thee angle relative t the hrizntal axi, which nly exit n paper. S, we need t find ething ele. Hw abut eauring the angle ade between the tring, A, B, and C. igure 3: Analytical rientatin f angle at the center f the tatic yte in a nndicriinate crdinate frae fr eae f eaureent Newtn Law II - 3

4 Meaured value fr three eparate trial: ALL THESE VALUES HAVE A +/- 0.5 Trial Nuber 3 A B C kg kg 0.7 kg kg kg kg kg 0.35 kg kg Calculated value fr the three different frce bard cnfiguratin: Trial Nuber N N.037 N N N.5657 N N.5 N N Shw ne exaple f each f the perviu calculatin We ued the fllwing ethd t calculate the rce acting at the ae: g kg N We ued the fllwing ethd t calculate the Theta 3: 70 3 (N calculatin neceary.) We ued the fllwing ethd t calculate the Theta : C We ued the fllwing ethd t calculate the Theta : 45 B B C We wuld nw like t tet Newtn law. Yu have direct eaureent and an equatin that relate the. Newtn Law II - 4

5 r the hrizntal cae: r the vertical cae: c = - c 3 = in + in ill in bth halve f thee equatin with the eaureent yu have taken. Hw de Newtn law hld up If bth ide are equal then Newtn law i valid. Trial : r the hrizntal cae: c = - c Nc37 = Nc N N With cnideratin f reanable errr intrduced by huan eaureent, angle and a runding, the fact that the tring are nt ale, and the fact that the pullie are nt frictinle thee value are alt identical. S, Newtn Law fr rce in the x-directin appear t hld true fr trial. r the vertical cae: 3 = in + in.037 N = Nin Nin N = N 0.63 N.037 N N Again, with cnideratin f reanable errr intrduced by huan eaureent, angle and a runding, the fact that the tring are nt ale, and the fact that the pullie are nt frictinle thee value are alt identical. S, Newtn Law fr rce in the y-directin appear t hld true fr trial. Newtn Law II - 5

6 .Recrd all f yur reult and yur wrk. Al, lit any urce f errr that ay have cntainated thee reult. Surce f errr culd have been fr the a value r angle value. Huan errr accunt fr bth f thee thing. It ight have been fr the a f the weight nt being prperly recrded r the balance wa nt giving prper reading. It al culd have been fr nt reading the prtractr right. Repeat part A tw re tie uing different ae Trial : <Sae a abve> Trial 3: <Sae a abve> Part B Atwd Machine Recrd the value f the ae: = 0.49 kg = kg igure 4: Experiental et-up f the Atwd Machine Newtn Law II - 6

7 Pitin [] The graph f the pitin v. tie huld be quadratic, Right! Reeber the kineatic equatin, x = Inert a cpy f jut ne f the graph yu ade. a t + v t + x. Thi i a quadratic equatin. Pitin v. Tie y = x +.3x R = Tie [ec] igure 5: Graph f Experiental Data Cllected f Pitin veru Tie it the pitin v. tie graph t a quadratic equatin uing the deling ftware within the Lgger Pr prgra fr thi find experiental value fr acceleratin. The bet fit line fr the data we cllected wa given a: y t.3 t It i f particular interet t nte the regrein deterined by Excel. Thi cae ut t be a value f.0. Thi ean that the quadratic nature f the data i extreely gd. If we cpare the equatin fr kineatic D tin fr the y-pitin with the fund trendline, we can eaily ee by evaluatin that the fllwing cntant crrelate directly: y a yt v, y t y y t.3 t Newtn Law II - 7

8 Thu: a y [/ ] v, y [/] y [] Hence the eaured acceleratin i: a y 0.69 Calculate the theretical value f a uing the ae invlved. a y g a y 49. g 69.7 g 69.7 g 49. g 9.8 Hence the expected acceleratin i: a y Are thee tw value in agreeent Lit all pible urce f errr. T cpare the eaured value with the expected value, we ut d a percent difference. a y, MEASURED a y, EXPECTED Uing the percent difference, we can cpare the eaured acceleratin with the expected acceleratin. % difference a Expected a a Expected Meaured x00% x00% % difference.3499% By exaining ur reult f the percent difference calculatin, we can ee that we are nt far ff fr the expected value f the acceleratin. The value i jut lightly lwer (by exactly.3%) Newtn Law II - 8

9 than the expected value. Again, with cnideratin f reanable errr intrduced by huan eaureent, a runding, the fact that the tring are nt ale, and the fact that the pully i nt frictinle thi percent difference i well within reanable liitatin. Cncluin Thi cling paragraph i where it i apprpriate t cnclude and expre yur pinin abut the reult f the experient and all it part. Only the final reult() need t be retated. Yu are intelligent cientit. llw the guideline prvided and write an apprpriate cncluin ectin baed n yur reult and deductive reaning. See if yu can think f any pible caue f errr. ** NOTE: There are everal cpnent f errr which culd ignificantly dify the reult f thi experient. Se f thee are lited belw: Actual v Aued acceleratin due t gravity (Altitude, Earth Oblatene, ee prelab and 3 fr exaple) [9.76 / v. 9.8 / ] Technique Meaureent rictin Drag and air reitance Snagging and catching Calibratin Senr liitatin paraeter Cputer prcer peed and reading regitratin Trque Senr Alignent Other A few f the ptential errr lited abve ay be applicable t YOUR experient Newtn Law II - 9