PHYS L - Prncples of Physcs Laboratory I Laboratory Adanced Sheet Ballstc Pendulu. Objecte. The objecte of ths laboratory s to use the ballstc pendulu to predct the ntal elocty of a projectle usn the prncples of conseraton of lnear oentu and conseraton of total echancal enery.. Theory. The ntal elocty of the projectle wll be easured by two ndependent ethods. Those easureents wll then be copared. a. The frst easureent ethod wll use the rane of a projectle launched horzontally fro a en heht aboe the round to easure the ntal elocty of the projectle. Fro the results of the projectle oton laboratory: where s the ntal elocty of the projectle, s the acceleraton due to raty near the Earth's surface, x s the rane of the projectle, and y 0 s the ntal heht of the projectle aboe the round. b. Dere the expresson for the ntal elocty of a projectle n a ballstc pendulu syste (. Hnt: efer to Youn's dscusson of the ballstc (Exaple 8.3 pendulu. The pendulu we use wll be ery slar to that shown Fure 8.8 of your text. Explan all assuptons and show all steps. 3. Apparatus and experental procedures. a. Equpent. Ballstc pendulu apparatus Meter stck. 3 Carbon paper. 4 Mass balance.
b. Experental setup. The experental setup s shown n Fure (proded by the student. c. Capabltes. To be proded by the student. 4. equreents. a. In the laboratory. Usn the technques you learned n the projectle oton laboratory, deterne the ntal elocty of the launcher by easurn the ntal heht and rane of the ass when projected horzontally. (Warnn: Keep the pendulu porton of the apparatus out of the lne of fre durn ths part of the laboratory. Conduct fe rane trals. Measure the dstance fro the pot pont to the center of ass of the pendulu/ball syste. Conduct fe trals allown the projectle and the pendulu to collde. Measure the anle of the swn for the pendulu/ball syste. 3 Measure the asses of the projectle and the pendulu. b. After the laboratory. The tes lsted below wll be turned n at the bennn of the next laboratory perod. A coplete laboratory report s requred for ths laboratory. Para.. Theory. Prode the porton of the theory secton dealn wth the deelopent of the equaton used to calculate the ntal elocty ( of the projectle usn the ballstc pendulu. Use the follown sybols n your deelopent: The dstance fro the pot to the center of ass of the pendulu/ball syste s c. The anle of the swn of the ball and pendulu syste s. 3 The ass of the ball s ; the ass of the pendulu s. Para. 3. Apparatus and experental procedures. Prode a fure of the experental setup. Prode a descrpton of the capabltes of the equpent used n the experent.
Para. 4. Data. Prode a copy of your data (Annex A contans tables for data. Prode the follown calculatons n a spreadsheet (Annex B prodes equatons for calculatons whch are contaned n the ballstc.xls spreadsheet proded by your nstructor: a The ntal elocty of the projectle as deterned by the rane ethod. b The uncertanty n the elocty of the projectle as deterned usn the rane ethod. c The ntal elocty of the projectle as deterned usn the ballstc pendulu. d The uncertanty n the elocty of the projectle as deterned usn the ballstc pendulu. e The percent fractonal errors n the ntal elocty of the projectle deterned usn both the rane ethod and the ballstc pendulu. f The percent dscrepancy between the two ntal eloctes. Use the ntal elocty deterned usn the projectle oton easureents as the accepted alue n ths calculaton. Para 5. esults and Conclusons. Prode a stateent of the ntal eloctes deterned by each ethod and ther uncertantes. Prode a stateent of the percent fractonal error and percent dscrepancy n your results for the ntal elocty deterned usn the ballstc pendulu. 3 Assess the precson and accuracy of the experent. 4 Descrbe sources of rando error n the experent. 5 Descrbe sources of systeatc error n the experent.
Annex A Data. Intal heht of projectle (use botto of ass. y 0 ( y 0 (. ane of projectle. tral x ( 3 4 5 3. Mass easureents. ass (k (k 4. Pot-center of ass dstance. c ( c (
5. Swn anle. tral ( o 3 4 5
Annex B Calculatons The calculatons assocated wth the propaaton of error are soewhat tedous and are, therefore, coputed n a spreadsheet to aod nuercal stakes. The Excel TM spreadsheet fle s ballstc.xls. Deratons of the forulas used n the spreadsheet are proded.. The "accepted" ntal elocty s en by. The uncertanty n the "accepted" ntal elocty s en by where, wth = 9.800 /s and = 0.005 /s, and 3. The calculated alue of the ntal elocty easured usn the ballstc pendulu s en by (
4. The uncertanty n the easured ntal elocty s en by where, ( ( ( ( ( ( ( sn