BOBO@.dHAHAHA#?XH?l4$j" ?D-Z(Charles E. Miller, Jr.xHH(FG(HH(d'@>p X1M#,l@/j ##,``@ ? ?ڼbout ClaA#Help?A#Font/DA JugglerusT TOPS@.Acce2j>'Z Chooser on?n@4(|DSETr f e8A???=?Q?(U;%T+  2 4   ^ k P Q      L M N O P Q R S T U V a b A B d e f g     C D r s   & M n    4     i j   % 3      & ' P Q   * +        m x   & 1 y   &  8          P  c  g  h      %  D  I  s   !   p "      !    # i!ww2?R\@-N@. 6;%0?PUNIFORM CIRCULAR MOTION 1150 LAB NAME . PARTNER . In this experiment we will study F = ma as it applies to an object moving in a circle.  Before attaching the spring and the string, adjust the pointer for minimum R with M directly above as shown in the figure. Now attach the spring and the string and adjust m until M is directly above the pointer. From the force diagrams above, convince yourself that, since T2 has no horizontal component, the spring force T3=mg because you experimentally arranged for the spring and string forces to be horizontal (we can also find that T2 = Mg, but we do not really need that). Remove the string connecting M and m. Adjust the counterweight so the apparatus rotates smoothly. Now, with your fingers rotate the vertical rod at such a rate as to keep M directly above the pointer. If, as you maintain the rate of rotation which keeps M directly above the pointer, the unit rocks as it rotates, you will need to adjust the counter weight so that the center of mass is shifted to the axis of rotation. With a timer, find the tim, t, for 50 revolutions*, determine the period of revolution T, and the acceleration of M using the following equations: Period, T = t/50 Speed, v = 2R/T Acceleration, a = v2/R Repeat the above procedure, measurements, and calculations for four other values of R, five values of R total. Be sure to measure R from the center of the rotating shaft. Using a double pan balance, measure M. Use ClarisWorks to write your lab report. Inside your lab report, create a spread-sheet to handle these calculations: Let the spreadsheet in ClarisWorks do as much of the calculations as you feel comfortable with. You should be able to enter only the hanging masNs m, the time for 50 revolutions t, and the radius R, and let ClarisWorks calculate the rest of the data table for you. Now cut and paste into Graphical Analysis the column of data for the weight w=mgwhich is also the horizontal, centripetal force exerted by the springand the centripetal acceleration a. From Graphical Analysis, make a graph plotting centripetal force (or weight) on the vertical axis and centripetal acceleration on the horizontal axis? What does this graph look like? What do you expect it to look like? Why? That is, what equation can you find to support your answer? If the graph is a straight line, what is the slope of the line? What do you expect the slope to be? Why? That is, what equation can you find to support your answer? How close is your actual, experimental slope to your expected, theoretical slope? That is, find the percent difference. *When counting a periodic motion, it is helpful to count down to zero 5-4-3-2-1-0 and start the time on the count of zero and then continue with 1-2-3- . . . - 48-49-50. Use Claris Works to complete your lab report. Every lab report ought to have the following: Purpose: What did you start out to find, determine, or demonstrate? Why are you doing this? Procedure: What did you do? Three or four sentences Data Calculations Explain what you did with your data. Sample calculations (probably) Percent differences Comparisons with theory Conclusion: What did you find, determine, or demonstrate Why did you do this? What does it all mean?ZNDSET.H.?P@w?,$6*@xx'/ @ 12 8  @1)8/ 8 ffff1M*` 8 q&))) p&))) q" p" q">VJVV>>J p">VJVV>>J" (FM(M @ 1* 8 q p 1SZ 8 D"D"18J 8 "D"D1SZ 8 1 8(m 1  8(m Q X"""""W"j"j"""""V"#"#"" " ( hPointer"X"X"X (zR"J" E#" """$"J"E"J"A"<#""#+YMg (mg(T(FT+-"T +1(M2(3 (T +1 Q~ X Qnt X Qrx X Qv| X Qz X q p"""l"l"i""Y(-Counter* WeightDSET.H?@?R%6*?DSET.H????6*?DSET02 =l?L&H$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$@/?|4X4X4Z` rCTAB?m??QX;%?=T@.@ COLM@-CHNK 'hanging 'mass'm '(in kg) P P P P#* Q'#+ QC#, Q_ Q{ Q#) Q Q R^ R RA Rk R0 Rb R R S* SC* S_* S* S* S* Sx T= T+ TG9( Tcp Tq Tr Tt Tu U'v UCw U_x Uy COLM?lCHNK' weight of' hanging mass 'w = mg@' (in Newtons)  u v! v" w'# w$ x/% x& y7' y( z?) z* {G+ {, |O- |. }W/ }0 ~_1 ~2 g3 4 o5 6 w7 8 9 : ; < = > ? @ A #B C + COLM?CHNK' time for 50' revolutions't'(in sec)B ? o  #* #+ #,  ' 7#) G [ s  0 b + ?* O* _* * * x =p q r t /u Wv kw x z | ~   #\ K] COLM?CHNK' time for 1I' revolutionI'T = t/50'(in sec)B >Y ? ? @ A B_\ C] Cb D` EMa F' F=\ HC=6 Ih JQ K K Lc L M M7@ M' N P5 R V Vq W Y Z [\9) \9), ] = ]= ]/ ]A COLM?HCHNK 'radius@' of circle'R '(in m)@ImagesCommon Symbols Community Computers EducationEvents & HolidaysFlagsFoodsGlobesHandsRoad Signs - USA ShapeburstsStarsToolsTransportationUSA MapsWeather World Maps >D=  TcBPD>p  jyED>  jyDD>  jyDD>Ы 04=aa'DD> ̴ jy COLM?PCHNK 'speed' of mass M' v = 2R/T'(in m/s)zYZWXF[J\HS9P:Q7N8O0U+@-M@?'>fegjhmrltuz}]@_DC0 X=LayoutBrowseBFindFLayoutLListI-Define FieldsD Insert Field Insert Part Tab Order Show Multiple- New Layout Edit Layouts-p`0.DF ̔ jyE~DF ʹ jyBHpDG ͌ kz COLM=HCHNK' centripetal' acceleration ' a = v^2/R' (in m/s^2)IFu`FvFw`Fu`FvPpHH@.Fu`pFy= ??Fu`? m8Fw0@FyFu`Fw`Fx80(8hfFu`FwFxFu`FwFxFu`FwЫP(HH?PFw`P DSETT.Hn@.(=?@6*@FNTMCUTSDSUM/Charles E. Miller, Jr.HDNISTYL #@STYL=???l??nH??&        V                                     !  "  #  $  % !&"'&#HASH $(( ( (() *  ( ( ( (?(Zn(n(n(& & % &  % %x%p& (" (!A( A( C& L:Qhjazo}BodV CHAR?Q(    "    C  @    3  dHASH        z CELL?.HASH!!  GRPH?P`fn~4HASHogl RULR?` @@|+.P.|P.@+.P.P.dHASH  7O fz  º@ @B`(LKUP  !" $NAMEDefault Default SSHeaderBodyFooterFootnoteFootnote Index DFNTM HelveticaGeneva"New Century SchlbkNew YorkETBL@FNTM;fCUTS;nDSUM;vHDNI;STYL;ETBLM'