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INSERT DISK A AND PRESS A KEY.":A$:" ":5010F0:15:"STAND BY....":1023,200:"RUN COULOMB":E5500E::10:"PUT IN SIDE A OF THE FIRST DISK AND PRESS A KEY.":A$:" ":E::10:10:"PLEASE STAND BY... ...GETTING THE MENU!":"VERIFY MAIN MENU" F1023,6:216,0:"RUN M:"WRITE COULOMB INFO":F1$:F2$:F3$:F4$:"CLOSE COULOMB INFO"xD:10:"COULOMB FORCES/FIELDS SET-UP IS COMPLETE"D13:"DO YOU WANT TO TRY IT? _";:24:A$:A$"Y"A$"y"A$"n"A$"N"ĺ(7);(7):250D:DA$"N"A$"n"5000/E:1 Ci"NO"C22:"________________________________________":"SATISFIED WITH THE ABOVE CHOICES? _";:35:A$:A$"Y"A$"y"A$"n"A$"N"200CA$"N"A$"n"10C23:1:958:24:11:"<<< SAVING CHOICES >>>";C2:BD"OPEN COULOMB INFO":35:F3$:F3$"Y"F3$"y"F3$"n"F3$"N"ĺ(7);(7):70eBP15:35:F3$"Y"F3$"y"ĺ"YES":90oBU"NO"BZ18:"ALLOW EQUIPOTENTIAL DRAWING? _";:30:F4$:F4$"Y"F4$"y"F4$"n"F4$"N"ĺ(7);(7):90Cd18:30:F4$"Y"F4$"y"ĺ"YES":2007):30-A(9:35:F1$"Y"F1$"y"ĺ"YES":507A-"NO"A212:"SHOW CALCULATED FORCES? _";:12:25:F2$:F2$"Y"F2$"y"F2$"n"F2$"N"ĺ(7);(7):50A<12:25:F2$"Y"F2$"y"ĺ"YES":70AA"NO"=BF15:"DISPLAY CALCULATED FIELD RESULTS? _";a@"NOMON"E@ ::" SET-UP FOR COULOMB FORCES/FIELDS ":@:" PRESS Y OR N FOR EACH QUESTION"::" (NO NEED FOR THE RETURN KEY)"A9:"ARE THERE PADDLES OR A JOYSTICK ? _";:35:F1$:F1$"Y"F1$"y"F1$"n"F1$"N"ĺ(7);( w  (0 ѕнй`)JJ & & f)`ɀ`3PTUUUA ****-P@P@.     0@@@3  8@@A S@ ?  @@@@ J b Q@A  :@ @@4   1@ @@P.       <UTP<++++ @`,`X`0 0P. (0@ 0 @ @ /@`@@ @ 4 0 0  8`@ a@@ @@K `?@@  0 @0@8@@@  @@@P4@  (@(0P@  @@`@-       (  -UU      @@J  pK D]5pjs-p C08*0&  @`8`<'`F@p2o?`` @& 0 x `p@G A`@)@`A@@C|*`x@p  +@@!dpX!C W'8@'@ p"1b'|`p!@ ` '?b| A @(@`s0`),?@`08+)@` p@@P @@@ `. # !"%)2$$)9!\n.^/u*xΠ.  ,ΘX<V J |L ^``]|E  "CxHxD? r Q@0P0@AR +16p,݀,- )ؑ߀'& Aa;ր@\E DȈ CRR#Ȉ("ᅂ²&"'Ҁ)􀀀/*e a scope.":XX140:YY0:5:300:WD$"Oh, by the way.... the POWER switch is often combined with the INTENSITY knob!":YYYY10:15V,100:BACK11280`,1000 :WD$"Y":XX22:YY100:5:WD$"X":XX100:5:WD$"Gain":XX14:YY108:5B,XX92:5:WD$"Sync":XX53:YY110:5:WD$"Y-in":XX6:YY136:5:WD$"X-in":XX105:5:WD$"Trig":XX54:YY138:5L,L23:WD$"Well, there you have it. You should now be able to operate the signal here.":YYYY6:15:100:BACK11240.,::10:15:"HOLD ON...":"BLOAD SCOPE FACE,A$8D09"::0,9:1,141:38263E8,WD$"Int":XX13:YY5:5:WD$"Focus":XX3:YY28:5:WD$"X Pos":XX12:YY81:5:WD$"Y Pos":XX93:5:WD$"Sweep":XX50:YY61:5ignal into the X-INPUT and switch over to EXTERNAL triggering.":YYYY6:15:3000$,WD$"There are also situations where you are examining a signal related to the voltage in the wall sockets (at 60 cycles/s). The LINE setting usually will help synchronizThis is usually set to INTERNAL. The scope's internal circuits trigger the time sweep to synchronize with the vertical signal."P,WD$W$:YY10:15:300:WD$"If you are doing something that requires special synchronization you can feed that triggering sT,10015(T):,L15:WD$"Here is a wave that has had the SYNC adjusted to start displaying the wave at the half-cycle point.":YY50:15:L45:100:BACK11180,:W$"The only standard control we haven't discussed yet is the TRIGGER SOURCE switch. D$"The SYNC control (sometimes called TRIG LEVEL) adjusts where the wave starts being displayed. It adjusts the point along the wave that starts the time sweep going. This is called ''triggering'' the sweep.":YY10+15:4+T010.4.1:1009.7oscilloscope.":XX140:YY0:5:300:WD$"Oh, by the way.....the POWER switch is often combined with the INTENSITY knob!":YYYY30:5MV,100:BACK11280M`,1000Te wave cycle takes about 0.6 seconds to repeat.":YY25:15:L45:100:BACK11150چ+::W). The LINE setting usually will help synchronize the signal here.":YYYY6:15:100:BACK11240L.,::10:15:"HOLD ON...":"BLOAD SCOPE FACE,A$8BA9"::0,169:1,139:38263ML,L23:WD$"Well, there you have it. You should now be able to operate an al synchronization you can feed that triggering signal into the X-INPUT and switch over to EXTERNAL triggering.":YYYY6:15:300aL$,WD$"There are also situations where you are examining a signal related to the voltage in the wall sockets (at 60 cycles/st is the TRIGGER switch. It picks the source of triggering. When set to INTERNAL the circuits inside the scope trigger the time sweep to synchronize with the vertical signal."K,WD$W$:YY10:15:300:WD$"If you are doing something that requires speci15:41I+T010.4.1:1009.7T,10015(T):I,L15:WD$"Here is a wave that has had the SYNC adjusted to start displaying the wave at the half-cycle point.":YY50:15:L45:100:BACK11180J,:W$"The only standard control we haven't discussed ye5:L45:100:BACK11150H+::WD$"The SYNC control (sometimes called TRIG LEVEL) adjusts where the wave starts being displayed. It adjusts the point along the wave that starts the time sweep going. This is called ''triggering'' the sweep.":YY10I+09.7T,10015(T):sG+:22:"WHAT IS THE TIME PER CYCLE? ";A$:WD$"Wrong!":((A$).58(A$).62)WD$"Right!"H+L15:WD$WD$" One wave takes six centimeters. Each cm lasts 1/10 second so the wave cycle takes about 0.6 seconds to repeat.":YY25:1ve is about 3/4 of two cm or 7.5 Volts. You could also figure it out by taking 1.5 cm and multiplying by 5 V/cm.":YY25:15:L45:100:BACK11150F+::WD$"The Y-GAIN is set to 5 V/cm. The SWEEP is at 0.1 s/cm.":YY10:15F+4G+T010.4.1:10s set to 5 V/cm. The SWEEP is at 0.1 s/cm.":YY10:15>E+4E+T010.4.1:1009.7T,10015(T)::22:"WHAT IS THE LARGEST VOLTAGE VALUE? ";A$:WD$"Wrong!":((A$)7.3(A$)7.7)WD$"Right!"F+L15:WD$WD$" Two centimeters is 10 V and this wa0:BACK11090D+:WD$"Setting the SWEEP to 5 ms/cm gives this image. Two centimeters at 5 ms per centimeter still gives 10 ms for each wave cycle.":YY10:15D+4D+T031.60.1:1003.2T,10020(T)::100:BACK111207E+::WD$"The Y-GAIN i.32.1:10016T,10020(T)::100:BACK11060Cp+:WD$"Now set the SWEEP to 2 ms/cm. Note that one cycle takes up half the screen, five divisions or centimeters. This again gives 10 ms.":YY10:15Cz+4 D+T012.64.1:1008T,10020(T)::10m.":YY10:15B>+4PBH+T06.32.1:10016T,10010(T)::100:BACK11030BR+:WD$"Let's keep the same wave only now work with the SWEEP control. Now it is set at 1 ms/cm. The wave takes 10 ms to complete one cycle.":YY10:15B\+40Cf+T06re is the same -2 to +2 Volt wave. This time the Y-GAIN is set at 0.5 V/cm. (4 cm at 0.5 V/cm gives 2 V.)":YY10:15~A +4A*+T06.32.1:10016T,10040(T)::100:BACK11000B4+:WD$"Here is the -2 to +2 Volt wave with the Y-GAIN set at 2 V/ceen which shows the grid. This shows a wave which has voltage swings from -2 to + 2 Volts. The Y-GAIN knob is set at 1 V/cm.":YY10:15:100,50200,50200,150100,150100,50@+4@ +T06.32.1:10016T,10020(T)::100:BACK10940wA+:WD$"He*132,80:T011.75.25:1324T,80S(T)::A$:A$(32)11000?*A$"I"A$"i"SS4:0:Y6199:132,Y179,Y::3:S16S16:10970?*A$"D"A$"d"SS4:0:Y6199:132,Y179,Y::3:S0S0:10970?*10970@*:WD$"Here is an enlarged scr50:WD$"Keeping this in mind, try a few different settings for the Y-Gain knob.":YYYY10:15:WD$"(Press ''I'' or ''D'' to increase or decrease the Volts/cm setting. Hit SPACE when done.)":YY130:15:L45>*130,60180,60180,100130,100130,60:S0B?11324T,8016(T):11324T,120:1112,8016(T):(49152)12810930d=*TT.25:T11.75T0o=*10922~=*49168,0:=*:WD$"Now what you were watching was in super slow motion. A real oscilloscope is much, much faster.":YY10:15:300>*L*132,80:T011.75.25:1324T,8016(T)::T0j<*WD$"(Press SPACE when done watching.)":YY130:15<*WD$"Y-Input":XX60:YY75:5:WD$"Signal":XX65:YY85:5:WD$"Time Base Sweep":XX20:YY120:5<*49168,0K=*11324T,120:1112,8016(T):::100:BACK10820;*:WD$"By itself that is pretty boring! But when that motion is combined with a sweep coming from the TIME BASE GENERATOR we get a graph of the Y signal versus time.":YY10:15:300;*130,60180,60180,100130,100130,60:T03"(64OS:25:1110,YOS:105:1167,Y5OS:OSSl"(64OS:25:1110,YOS:105:1167,Y5OSw"(10410$#(0,9:1,141:38263:WD$"The voltage on the horizontal plates is controlled by either a horizontal amplifier circuit or a special ''tD")S2SS1:10420&!(A$" "104301!(10410k!(0:Z100118:Z,63Z,69:Z,87Z,99::XX100:YY63:3!(S0WD$"":I1(S):WD$WD$"+"::5:WD$"":I1(S):WD$WD$"-"::YY88:5 "(S0WD$"":I1S:WD$WD$"-"::5:WD$"":I1S:WD$WD$"+" to move up and down.":YY10:15:300 (WD$"Press ''U'' or ''D'' to control the beam. (Press SPACE when done.).":YY120:15:OS0:S0:Y79:232,96:233,3:16,Y134,Y:0:105:1167,Y (10:A$:" ":(A$"u"A$"U")S2SS1:10420!((A$"d"A$"3,83:59,7468,7468,78:59,8468,8468,80:62,7562,78:62,8062,83:[(100:BACK10060r(0,9:1,141:38263& (WD$"The VERTICAL DEFLECTION PLATES have voltages applied by a special vertical amplifier circuit. These plates cause the electron beam729,7459,74:29,8129,8456,84:39,7539,77:39,8139,83:53,7553,77:53,8153,83:59,7468,7468,78:59,8468,8468,80:62,7562,78:62,8062,83n(II115::3Fx(29,7729,7456,74:29,8129,8456,84:39,7539,77:39,8139,83:53,7553,77:53,815040:0,Y75,Y::3Z(WD$"The rest of the electrodes (called ANODES) serve to focus the beam. Their voltages are adjusted by the focus control knob.":YY10:15:WD$"Focus Control Anodes":XX70:YY40:5:45,7275,5063,72:300:300d(I115:0:29,7 to very high speeds.":YY10:15e2(WD$"Accelerating Grid":XX80:YY110:5:75,11024,86:300:300<(I120:0:25,7423,7423,78:23,8023,8425,84:II1100::3:25,7423,7423,78:23,8023,8425,84:F(100:BACK10060P(T0:B27:200:0:Y3ompared to the cathode. It is controlled by the intensity knob. It tends to push electrons back to the cathode.":YY10:15:3!((WD$"This grid has a potential of several thousand Volts positive. It pulls electrons off the cathode and accelerates themXX0:YY135:5:0,1307,85:300:300 (I120:0:5,7420,74:17,7517,78:17,8017,83:5,8420,84:II1100::3:5,7420,74:17,7517,78:17,8017,83:5,8420,84:(100:BACK10060(0:WD$"This little piece of metal is 5 to 20 Volts negative c'100:BACK10060(LAST17:150:WD$"This little piece of metal is 5 to 20 Volts negative compared to the cathode. It is controlled by the intensity knob. It tends to push electrons back to the cathode.":YY10:15:WD$"Intensity Control Grid"$(ilament":XX0:YY45:5:3,543,76:300'300:I120:0:1,787,78:9,78:11,78:13,78:8,79:10,79:12,79:13,79:1,807,80:9,8011,80:13,80'II1100::3:1,787,78:9,78:11,78:13,78:8,79:10,79:12,79:13,79:1,807,80:9,8011,80:13,80:13,8213,118:300y'300:I120:0:10,7615,7615,8210,82:3:II1100::10,7615,7615,8210,82::100:BACK10060&'LAST17:150:WD$"The FILAMENT warms the cathode. It is electrically heated to 1000 C.":YY10:15:WD$"o":XX166:YY8:5:WD$"FY:X166266S:1X,Y:1XS,Y::1268,Y::116,YR'0:Y3040:0,Y40,Y::3'LAST17:150:WD$"At the left end of the electron gun is the CATHODE. When it is heated, electrons ''boil off'' its surface.":YY10:15:WD$"Cathode":XX10:YY120:5:ns. As you might guess, the electron gun shoots the electrons out toward the screen.":YY10:15'0:1:232,96:233,3:864,1:865,0:866,4:867,0:868,5:869,03'300:S2:Y79:115,Y:I17:X16134S:1X,Y:1XS,Y::1136,Y:II1200::1166,s":XX0:YY120:5:80,117110,88:300:WD$"Horizontal Deflection Plates":XX100:YY140:5:200,135155,95:300:WD$"Screen":XX200:YY20:5:220,28260,60'100:BACK10060'0,9:1,141:38263a'WD$"A cathode ray is actually just a beam of electroE CRT...":"BLOAD CRT,A$8D09"::0,9:1,141:38263'L45:WD$"This is what the inside of a Cathode Ray Tube (CRT) looks like.":YY10:15:300:WD$"Electron Gun":XX10:YY30:5:38,4038,65:5,705,6570,6570,70:300'WD$"Vertical Deflection Plateeen.":XX140:YY0:5:WD$"SCREEN":XX60:YY30:5:300t'WD$"The screen is actually the end of the CATHODE RAY TUBE. In many ways it is like a television tube. Let's see what makes it work.":XX140:YY80:5:100:BACK100303~'::10:12:"OPENING THoscope face....":YYYY20:15:100:BACK10000L'::10:15:"HOLD ON...":"BLOAD SCOPE FACE,A$8BA9"::0,169:1,139:382635j'L23:WD$"Most scopes have at least this many controls! To help you learn what all the knobs do we must look behind the scr300:WD$"One problem with understanding oscilloscopes is the fact that no two look alike. Each manufacturer has their own ideas as to what the face of the scope should look like.":YYYY10:15.B'300:WD$"Let's look at an imaginary, but typical, oscill1000.':WD$"The first thing that strikes you when first seeing an oscilloscope is all the knobs and buttons. If you ever want to impress someone with your education just show them a ''scope'' and pretend you know how to make it work !"8'YY10:15:ctly or record them on a strip chart. Many things, however, change much too rapidly for your"$'YYYY10:15:WD$"eye or the strip chart pen to follow.":15:300:WD$"Luckily, an oscilloscope can follow very, very fast changes.":YYYY10:15:100:BACK of the most useful pieces of equipment found in the physics lab. The name actually means ''vibration viewer.''":YY10:15:300^'WD$"Many things vibrate or depend on time in a complicated way. If they don't vary too quickly you can observe them dire10:10:"PLEASE STAND BY... ...GETTING THE MENU!":1023,1:"VERIFY MAIN MENU" 1023,6:216,0:"RUN MAIN MENU": :10:"I CAN'T FIND THE MENU. INSERT DISK A AND PRESS A KEY.":A$:" ":1010 ':L45::WD$"An oscilloscope is one""ĺ" ":, m21:1:958:(7);(7):1022 nX 0:Y0LAST10:0,Y279,Y::3:x 0:YTB:0,Y279,Y::3: ,ZZ12000:: ZZ11000:: 1500 ::10:"PUT IN SIDE A OF THE FIRST DISK AND PRESS A KEY.":A$:" ":[ ::(WD$)LTR):99:XXXZ:YYYY10:67 XX0:YYYY10:5:B dBACK0 f49168,0:24:958:24::4:"<<< LEFT OR RIGHT ARROW OR ESC >>>";::1:A$:24:1:" "; hA$""ĺ" "::1000 jA$""BACK1:" ": kA$(249):0:Q4(231):1:XZXXs 100XX,YY:(WD$)LāQ1(WD$):((WD$,Q,1))31:99::232,Q1:233,Q2:Q3:Q4: LTRL11:X$(WD$,LTR,1):X$(32)X$"-"Ă W$(WD$,LTR(X$(32))):100XX,YY:QQ1(W$):((W$,QQ,1))31:99::WD$(WD$,E+1002:35752:"BLOAD SQUEEZE,A$9577"610000100,50200,50200,150100,150100,50:150,50150,150:100,100200,100:Y5015010:148,Y152,Y:50Y,9850Y,102:X10020010:X,Y:::100,100: F(0):Q1(232):Q2(233):232,0:233,8:Q3                                 Ӎ  "A$"n"5000IE:10:15:"STAND BY....":1023,200:"RUN FORCE TABLE"TE5500E::10:"PUT IN SIDE A OF THE FIRST DISK AND PRESS A KEY.":A$:" ":E::10:10:"PLEASE STAND BY... ...GETTING THE MENU!":"VERIFY MAIN MENU"%LE INFO":"WRITE FORCE TABLE INFO":F1$:F2$:F3$:F4$:UNITS$:"CLOSE FORCE TABLE INFO"D:10:"FORCE TABLE PROGRAM SET-UP IS COMPLETE."D13:"DO YOU WANT TO TRY IT? _";:24:A$:A$"Y"A$"y"A$"n"A$"N"ĺ(7);(7):250D: EA$"N200Ci"NO"C22:"________________________________________":"SATISFIED WITH THE ABOVE CHOICES? _";:35:A$:A$"Y"A$"y"A$"n"A$"N"200CA$"N"A$"n"10C23:1:958:24:11:"<<< SAVING CHOICES >>>";C2:ZD"OPEN FORCE TAB_";:28:F3$:F3$"Y"F3$"y"F3$"n"F3$"N"ĺ(7);(7):70hBP15:28:F3$"Y"F3$"y"ĺ"YES":90rBU"NO"BZ18:"ALLOW CALCULATION ASSISTANCE? _";:31:F4$:F4$"Y"F4$"y"F4$"n"F4$"N"ĺ(7);(7):90Cd18:31:F4$"Y"F4$"y"ĺ"YES":(7):30.A(9:36:F1$"Y"F1$"y"ĺ"YES":508A-"NO"A212:"DO YOU WANT TO SHOW THE EQUILIBRANT? _";:38:F2$:F2$"Y"F2$"y"F2$"n"F2$"N"ĺ(7);(7):50A<12:38:F2$"Y"F2$"y"ĺ"YES":70AA"NO"@BF15:"PERMIT A GRAPHICS DISPLAY? {@"NOMON"E@ ::" SET-UP FOR FORCE TABLE PROGRAM ":@:" PRESS Y OR N FOR EACH QUESTION"::" (NO NEED FOR THE RETURN KEY)"A9:"DO YOU WANT TO SHOW THE RESULTANT? _";:36:F1$:F1$"Y"F1$"y"F1$"n"F1$"N"ĺ(7);    !1 QRS QRS,P` 100:BACK11010+1000TO 1000L,Y:쓱+WD$"Start with a high scale to avoid overloading the meter. Then adjust to the lowest scale possible without overloading. This gives you as close to a full scale deflection as possible and reduces calibration error effects."+YY102:5:L45: the meter. Then adjust to the lowest scale possible without overloading. This gives you as close to a full scale deflection as possible and reduces calibration error effects."֒+YY102:5:L45:100:BACK11010+1000L1:5:XX10:Y104106:1,Y3$"When reading the potential difference between two points, attach the voltmeter to the points, in parallel with the circuit.":XX10:YY64:5:300ʑ+WD$"o":XX0:YY101:5:XX10:Y104106:1,Y3,Y:+WD$"Start with a high scale to avoid overloadingthese types of meters.":YY10:15:300ː+WD$"o":XX0:YY29:5:Y3234:1,Y3,Y::WD$"When measuring current, break the circuit and insert an ammeter in series with the circuit.":XX10:YY30:5:300+WD$"o":XX0:YY63:5:Y6669:1,Y3,Y:+WDt 100 mA!"я+:T110:B160:200:YY100:15:WD$"Each division is 1 mA. The calibration error is 3% of 25 mA or about 0.8 mA. So this setting is read as 12.0 0.8 mA.":YY110:15:7165,140:100:BACK10970'+:WD$"That's about all there is to using 300+22:"NOT COUNTING THE CALIBRATION ERROR, WHATDOES THIS READ ? ";A$:WD$"Afraid not! This reads 12 mA.":(A$,4)"12.0"WD$"Great !"ʎ+(A$)12(A$,3,2)".0"WD$"Don't forget the zero!" +(A$)48WD$"This is set to the 25 mA scale, nodle is on the 88 mark. It reads 88 3 mA.":YY110:15:755,150:100:BACK10970z+0:150,70220,38:3:207,44215,40:200:150,70148,10:WD$"We hook the meter into another circuit and it looks like this after switching to the 25 mA scale.":YY110:15: . 3 mA error)?":XX10:YY110:15:70,140f+22:"WHAT DOES THIS READ IN MILLIAMPS? ";A$:WD$"Wrong!":(A$)88WD$"Right!"Pp+:T110:B160:200:WD$WD$" The divisions are 0.4 mA apart. Starting at 80 we have 80, 84, 88, 92, 96, and 100. The neeR = - ";A$:WD$"NO!":(A$)3WD$"RIGHT!"R+:T110:B160:200:WD$WD$" 3% of 100 mA is 3 mA.":YY110:15:100:BACK10970+\+T110:B140:200:150,70220,38:WD$"The meter is still set to the 100 mA scale. What is this reading (not including the 5:WD$"( 3% of full scale)":XX93:YY90:5:7XX5,YYي>+WD$"Assume this meter is switched to the 100 mA scale. This time the calibration error is 3% of full scale. What is this error in milliAmps?":YY100:15*H+WD$"+":XX57:YY154:5:21:"ERRO5:WD$"15":XX175:YY5:5:WD$"20":XX215:YY22:5:WD$"25":XX235:YY45:5*+WD$"0":XX88:YY55:5:WD$"20":XX105:YY35:5:WD$"40":XX132:YY26:5:WD$"60":XX160:YY26:5:WD$"80":XX186:YY37:5:WD$"100":XX196:YY55:574+WD$"mA":XX145:YY80:7:R252:I3.56.1:COUNT5(COUNT5)R258+X1R1(I)279191150:Y110R1(I)60:X2R2(I)279191150:Y210R2(I)60:X1,Y1X2,Y2:COUNT5(COUNT5)R254L +COUNTCOUNT1::WD$"0":XX60:YY45:5:WD$"5":XX88:YY19:5:WD$"10":XX125:YY4: meter so that you are as close to full scale deflection as possible!":YYYY6:15:100:BACK10850߇+:50,0250,0250,10050,10050,0:FLAG0:R50:I3.56.1:XR(I)279191150:Y10R(I)60:FLAGēX,Y:FLAG1:11012+X,Y+- +COUNT0:R14V. This turns out to be 3% of our 3.3 Volt reading.":YYYY6:15:767,76:300ˆ*WD$"The calibration error on the 10 V scale was 0.2 V. This is 6% of the 3.3 V reading.":YYYY6:15:70,112:300c*WD$"The moral of the story is to always set the, the readings looked different. Probably the most common mistake made in physics labs is reading the wrong scale. Don't do it!":YY10O*15:300:WD$"Did you also see the difference in the calibration errors? On the 5 Volt scale our error was 0.1 eedle is between 3.2":YY100:15*WD$"and 3.6 V. (It is to the left of halfway between 3.2 and 3.6 so it is less than 3.4 V.)":15:L45*100:BACK10830*:WD$"You should have noticed that even though we were reading the same voltage each time Volts = 0.2 Volts.":YY110:15:7163,130:71,140J*100:BACK10830S*L48 *T120:B150:200:150,70115,10:788,110:WD$"This reads 3.3 0.2 V. Each division is 0.4 V. Starting at 2.0 V the marks are 2.0, 2.4, 2.8, 3.2, 3.6, 4.0, etc. The nV the marks are 3.0, 3.2, 3.4, 3.6, etc. The needle is between the 3.2 and 3.4 marks."w*YY100:15:100:BACK108305*T110:B160:200:0:150,70185,17:3:180,23:WD$"If we set the meter to the 10 Volt scale our calibration error becomes 2% of 10e are using the 5 V scale, the error is 2% of 5 V = 0.1 V.":YY110:15:7122,130:7203,130:L45:100:BACK10830W*T120:B150:200:150,70185,17:790,110:WD$"This reads 3.3 0.1 Volts on the 5 V scale. Each division is 0.2 V. Starting at 3.0 :YY55:5:WD$"2":XX105:YY35:5:WD$"4":XX135:YY28:5:WD$"6":XX165:YY28:5:WD$"8":XX192:YY38:5:WD$"10":XX204:YY55:5׀*WD$"Volts":XX135:YY80:5:WD$"( 2% of full scale)":XX93:YY90:5:7XX5,YYv*L50:WD$"Consider this meter. If wX2R2(I)279191150:Y210R2(I)60:X1,Y1X2,Y2:COUNT5(COUNT5)R254v*COUNTCOUNT1::WD$"0":XX60:YY45:5:WD$"1":XX88:YY19:5:WD$"2":XX129:YY4:5:WD$"3":XX177:YY5:5:WD$"4":XX215:YY22:5:WD$"5":XX235:YY45:5*WD$"0":XX88ACK10810~b*:50,0250,0250,10050,10050,0:FLAG0:R50:I3.56.1:XR(I)279191150:Y10R(I)60:FLAGēX,Y:FLAG1:10852~c*X,Y~d*~l*COUNT0:R147:R252:I3.56.1:COUNT5(COUNT5)R258Nq*X1R1(I)279191150:Y110R1(I)60: to some kind of standard. As the comparisons get better, the equipment price goes up!" ~X*YY10:15:300:WD$"Most electrical meters have calibration errors of 2 or 3 percent of the full scale reading. Let's look at an example...":YYYY10:15:100:Bers all line up. It they aren't you will read the wrong value from the scale.":YYYY10:15:100:BACK10780X}N*:WD$"An error that is usually even bigger than parallax error is the calibration error of the meter. All measuring devices compare readingsle on a meter takes a little practice. It is very important that you always keep your eye lined-up directly over the needle to reduce parallax error.":YY10:15:300m|D*WD$"A good meter has a mirror scale to make sure your eye, the needle, and the numb5214,89:300:WD$"Some electronic meters have digital scales rather than meter movements. This eliminates some of the problems with the movements and also makes them easier to read.":YYYY10:15z5*100:BACK10750{:*:WD$"Reading a non-digital scarly.":YY10:15:300y&*WD$"The major advantage of electronic meters is that they have very little effect on the circuits being measured. For example, a typical electronic voltmeter has an input resistance of more than 10,000,000 !":YYYY10:15z0*ok the terminals up to the points, in parallel to the circuit.":YYYY10:15:100:BACK10700y*:WD$"Electronic meters are different internally but function the same way as electrical meters. You must still make sure you have connected the meter propeis connected to the circuit depends on what you are measuring.":YY1w*15:300:WD$"If you are measuring current, break the circuit and insert the meter in series.":YYYY10:15:300]x*WD$"When reading the potential difference between two points, hoe to compensate for an aging battery. It zeros the ohmmeter.":YY120:15:100:BACK10620Ew):WD$"A multimeter is one device that combines the functions of an ammeter, a voltmeter, and an ohmmeter. Even though it has all three capablities, the way it :5:YY96:5:WD$"+":YY70:5:145,120165,105160,105u)165,105165,108:WD$"The regular resistor can be switched to measure different ranges of resistance.":YY120:15:100:BACK10620Zv)T130:B150:200:WD$"The resistor with the arrow is adjustablXX154:YY64:5:139,67150,67:164,67190,67190,72:16:3190,72:0:130,62130,72:133,65133,70:136,62136,72:139,65139,706u)190,108190,113170,113:32:3170,113:0:134,113110,113110,10090,100:90,80110,80110,68130,68:WD$"o":XX88:YY76$"An ohmmeter has a built in power supply--usually just a battery--that applies a known voltage to the device being measured. The resistance is determined by measuring the current that flows and applying Ohm's Law.":YY10t)15:300:1150,60:WD$"G":nto the plus terminal again.)":YY120:15:100:BACK10530r)T130:B160:200::WD$"The resistance of the voltmeter must be high enough so that the current flowing through it is small compared to the circuit current.":YY120:15:100:BACK10530s):WD unbroken circuit with a PARALLEL CONNECTION. Current flowing from the positive terminal of the battery splits up and flows in two parallel paths.":YY10:15:300:r)WD$"One path is through the resistors, the other is through the voltmeter. (Flowing ivoltmeter is connected to read the potential difference across the resistors.":YY10:15:WD$"+":XX134:YY59:5:Y6790:100,Y:190,Y:I1100::p)WD$"o":XX98:YY86:5:XX188:5:100:BACK10530q)LAST30:150:WD$"Voltmeters are attached to the,67140,67:154,67190,67:100:BACK10530o)3110,90:3147,90:140,12090,12090,90110,90:184,90200,90200,120149,120:140,115140,125:143,118143,122:146,115146,125:149,118149,122:WD$"+":XX133:YY110:5p)LAST40:150:WD$"Watch how the ):WD$"We will create a new symbol for this combination of a galvanometer and multiplier resistor. Let's use our voltmeter to measure the potential difference across a pair of resistors in a circuit.":YY10:15*o)1140,60:WD$"V":XX144:YY64:5:100plier'' since it multiplies the voltage that can be safely attached to the terminals. This one gives a 10-fold increase. Other resistors would be switched in on a real voltmeter"mw)YY80:15:WD$"to give different volt ranges.":15:100:BACK10500n|or must have a value of 9000 .":YY120:15:5120,129:553,139:5130,149:100:BACK10500lh)LAST20:150:T90:B160:200:WD$"R = 9 k":XX130:YY20:5:WD$"multiplier":XXXX8:YYYY5:5:5229,19mr)WD$"This resistor is called a ''multi0000":XX40:YY100:5:WD$"total":XX48:YY105:5:WD$"V 10 Volts":XX98:YY94:5:WD$"I 0.001 A":XX99:YY107:5:91,103109,103:122,103171,103:5222,99]l^)300:WD$"Since we need 10000 total, and the meter has 1000 itself, the extra resist100:15:100:BACK10500jJ)LAST20:150:T110:B150:200:WD$"Don't forget that we already have 1000 inside the galvanometer. This plus the un-known resistance limits the current to 1 mA.":YY9:15:5241,0:300kT)WD$"R = = = 1:5?i6)WD$">":XX179:5:WD$"10 V":XX125:5:100:BACK10500j@)T110:B130:200:WD$"The 10 Volts being measured must drive a current of 1 mA through the meter. We can apply Ohm's Law again to find the total resistance needed for this to happen.":YY00,40:114,40130,40:167,40190,40190,70:WD$"G":XX104:YY37:5i,)WD$"o":XX78:YY69:5:XX188:5:300:WD$"We want to be able to apply a potential difference of 10 Volts to the terminals.":YY100:15:Y73:90,Y120,Y:150,Y180,Y:WD$"<":XX90:YY70make a voltmeter that can read up to 10 Volts without ''frying'' the galvanometer!":YYYY10:15:L45:100:BACK10470Bh"):WD$"Once again, here is our galvanometer, only this time in series with a resistor.":YY10:15:1100,34:3130,40:80,7080,401l voltmeter must be able to measure higher voltages than our galvanometer can handle. If we put a big resistor in series with our galvanometer most of the voltage would drop across it instead of the sensitive meter."vg)YYYY10:15:300:L50:WD$"Let's Y100:15:5159,139:100:BACK10440e):WD$"So if we never ran into potential diff-erences higher than 1 Volt we could just use our galvanometer. But what if we wanted to check the output of a transistor radio battery?":YY10:15:300f)WD$"A rea001 A) x (1000 )":YYYY20:5:5246,69:400:WD$"V = 1 Volt":YYYY20:5:300%e(WD$"This means that a potential difference of 1 Volt applied to the terminals of our galvanometer will drive a current of 1 mA through the internal 1000 resistance.":Y .":YYYY10:15:0:548,893c(100:BACK10350c(:WD$"Ohm's Law allows us to find the voltage that causes full deflection.":YY10:15:WD$"V = I x R":XX120:YYYY20:5:300Pd(WD$"V = (1 mA) x (1000 )":YYYY20:5:5229,49:400:WD$"V = (0.to do to a galvanometer to turn it into a voltmeter?":YY10:15:300c(WD$"Consider our imaginary galvanometer. Recall that a current of 1 mA caused a full scale deflection of the meter needle. Also remember that it had an internal resistance of 1000 the circuit. If its resistance was too large, the current in the"a(YY90:15:WD$"circuit would be reduced by the meter.":15:100:BACK10300Eb(:WD$"What about when we want to measure the potential difference between two points? What do we have ough the ammeter. (The current flows INTO THE PLUS terminal.)":YY110:15:100:BACK10300Ca(B160:200:WD$"The combination of the galvanometer and shunt resistor has a low overall resistance. This is important since we don't want the ammeter to affect73,42:100:BACK10300_(T110:B140:200:WD$"We break the circuit and insert the ammeter.":YY100:15:0:180,87192,87:3:300:1192,93:WD$"A":XX183:YY83:5[`(WD$"+":XX195:YY78:5:WD$"This series connection insures that the current flows thrce which end of the battery is the positive terminal. This causes a clockwise flow of current in the circuit.":YY100:15^(CX150:CY60:FLAG0:R20:I.56.4:XR(I)279191150:YR(I)60:FLAGēX,Y:FLAG1:10392^(X,Y_(:165,48:174,481;]x(0:70,5390,53:75,5685,56:70,5990,59:75,6285,62](80,5380,30150,30:3150,30:182,30220,30220,40:16:3220,40:32:220,75220,87150,87:3150,87:114,8780,8780,62z^(WD$"Battery":XX10:YY55:5:300:WD$"+":XX95:YY50:5:WD$"NotiNECTION. The current flows through a series of components in the circuit. One of the components is the ammeter.":YYYY6:15\d(100:BACK10170]n(:WD$"For example, let's say that a battery is pushing a current through several resistors.":YY10:15r to measure current, the current must flow through the ammeter. That's not too hard to understand! But how do you make that happen?":YYYY6:15:300~\Z(WD$"You actually have to ''break the circuit'' and insert the ammeter. This is called a SERIES CON combination of galvanometer and switchable shunt resistors is given this symbol:":YY10:15:170,20:WD$"A":XX74:YY23:5:50,2770,27:84,27104,27ZF(WD$"The ''A'' stands for ammeter, of course.":YY30:15:300[P(WD$"When you are using an ammete$"10":XX226:YY65:5:100:BACK10130Y2(T100:B160:200:WD$"In a real ammeter, the shunt resistors are switched by a knob or pushbuttons. This allows you to measure a wide range of currents quite easily.":YY90:15:100:BACK10130Z<(0::WD$"The"All we do is put in a different shunt resistance, this time allowing 99 mA to bypass the meter. Our resistance will be 1/99 of the meter's internal resistance or 1000/99 = 10 . (We round 10.1 to get a common resistor size.)"'Y((YY90:15:578,139:WD0:WD$"But what if we really wanted to measure up to 100 mA? Then what do we do?":YYYY10:15tW (100:BACK10130W(T90:B150:200:0:WD$"10 mA":XX28:YY45:5:WD$"111":XX224:YY65:5:3:WD$"100 mA":XX23:YY45:5:WD$"9":XX102:YY62:5X(WD$unt":XX135:YY145:5:100:BACK10130V'WD$"R = 111":XX170:YY65:5:WD$"shunt":XX179:YY70:5:5240,64:T110:B160:200_W(WD$"That's simple enough isn't it? The shunt resistor allows most of the current to bypass the meter.":YY80:15:3062:5:100:BACK10130U'T80:B160:200:WD$"Since we want 9 times as much current in the shunt resistor, it must have 1/9 the resistance of the galvanometer. By taking 1/9 of 1000 we get R = 111 .":YY100:15:570,139:5197,139&V'WD$"sh,48:300T'WD$"10 mA":XX28:YY45:5:232,0:233,21:163,39:232,93:233,23:WD$"If we pick the right shunt resistance 9 mA will flow through it and 1 mA will go through the galvanometer.":YY100:15U'WD$"1 mA":XX115:YY28:5:WD$"9 mA":XX109:YYistance):":YY10:15:582,9:1140,30:WD$"G":XX144:YY34:5:120,37140,37:154,37174,37T'300:WD$"We will put in a SHUNT RESISTOR to bypass the meter.":YY70:15:300:3130,60:120,37120,60130,60:167,60174,60174,37:90,48120,48:175,48205WD$"The way to do this is to ''shunt'' 9 mA though a side circuit so that only 1 mA of the original 10 mA current flows through the galvanometer.":YYYY10:15:100:BACK10100]S':WD$"Here is our galvanometer (1 mA maximum current, 1000 internal resYY10:15:WD$"galvanometer is 1000 .":15:5130,49Q'WD$"Let's say we want to be able to measure up to 10 mA with our ammeter. The problem is to prevent all that current from running through our galvanometer and ruining it.":YYYY10:15:300R'20:15:100:BACK10070P':WD$"Let's use a galvanometer to build an ammeter (which can measure higher currents). We will use a galvanometer which will undergo full scale deflection with only 1 mA. The internal resistance of the coils inside the"7Q' of current flowing through them.":YYYY10:15:1140,100:WD$"G":XX144:YY103:5P'100,107140,107:154,107190,107:WD$"Since galvanometers are so sensitive, you must be very careful when attaching them to a circuit so you don't burn them out!":YY1to a box with wire attachment terminals you get a device which can measure very small currents. We call this a GALVANOMETER.":YY10:15:300SO~'WD$"Here is the symbol for one. The most common galvanometers undergo full scale deflection with only 50 mASO BE CAREFUL!":YYYY10Mj'15:300:WD$"Because it is so easily damaged, it is very important that you learn the proper way to connect a meter into a circuit to be measured.":YYYY10:15:100:BACK10040Nt':WD$"When you put a d'Arsonval movement ined by Edward Weston in 1888.":YY10:15:300M`'WD$"The coil and aluminum frame in a d'Arsonval movement are supported by two spiral springs. As you might guess, this arrangement is very delicate. If dropped or overloaded the movement could be ruined. $"calibrated numbers. This is what you look at when you ''read the meter.''":15:100:BACK10000-LV':WD$"This type of meter movement is named after it's inventor, Arsene d'Arsonval, although modern day devices actually use an improved version developoil.":15:300JB'WD$"When a small current flows through the coil it acts like an electomagnet and responds to the magnetic field passing through it. As it turns in this field a pointer which is attached to it moves along a scale of":YYYY10:15cKL'WD:WD$"Let's discuss the electrical meters first. The heart of this type of device is the meter movement. This is just a very fine coil of wire wrapped around a lightweight aluminum frame. A strong magnetic field"J='YY10:15:WD$"passes through the c two versions--electrical and electronic. Electrical meters are basically meter movements and resistors. Electronic meters may have things like vacuum tubes, transistors, and integrated circuits in them."H)'WD$W$H.'YYYY10:15:100:BACK1000I8'(in Amps), potential difference (in Volts), and resistance to current flow (in Ohms).":YY10:15G'300:WD$"These functions are often combined into one piece of equipment which is called a multimeter.":YYYY10:15:300H$'W$"All these meters come inY 1,2,3, OR 4!";:2030$F" ":" "_F21:31:A$:22:1:958:23:12:"PLEASE STAND BY..."~F(A$)2000,3000,4000,5000aG':L45::WD$"This lesson is about the use of ammeters, voltmeters, and ohmmeters. These devices measure electrical current . YOU MAKE SETTINGS"::10:"3. YOU READ SETTINGS"::10:"4. RETURN TO EQUIPMENT MENU"E1:21:" WHAT IS YOUR CHOICE? [ ]"::" (NO NEED TO PRESS 'RETURN')":21:31:A$FA$"1"A$"2"A$"3"A$"4"ĺ(7);(7):::9:"PRESS ONL:10:"I CAN'T FIND THE MENU. INSERT DISK A AND PRESS A KEY.":A$:" ":1010WD:D:5:" ":5:" READING LABORATORY BALANCES ":5:" ":ZE9:10:"1. INSTRUCTIONS"::10:"2:CZZ11000::!C1500oC::10:"PUT IN SIDE A OF THE FIRST DISK AND PRESS A KEY.":A$:" ":C::10:10:"PLEASE STAND BY... ...GETTING THE MENU!":1023,1:"VERIFY MAIN MENU"C1023,6:216,0:"RUN MAIN MENU":OD;::1:A$:24:1:" ";VBhA$""ĺ" "::1000pBjA$""BACK1:" ":BkA$""ĺ" ":Bm21:1:958:(7);(7):102BnB0:Y0LAST10:0,Y279,Y::3:B0:YTB:0,Y279,Y::3:C,ZZ12000:(WD$,LTR,1):X$(32)X$"-"ĂAW$(WD$,LTR(X$(32))):100XX,YY:QQ1(W$):((W$,QQ,1))31:99::WD$(WD$,(WD$)LTR):99:XXXZ:YYYY10:6AXX0:YYYY10:5:AdBACK0=Bf49168,0:24:958:24::4:"<<< LEFT OR RIGHT ARROW OR ESC >>>"R<@1002:"BLOAD SHAPES,A$175D":232,93:233,23:3:0:1G@10000@F(0):Q1(232):Q2(233):232,0:233,8:Q3(249):0:Q4(231):1:XZXX@100XX,YY:(WD$)LāQ1(WD$):((WD$,Q,1))31:99::232,Q1:233,Q2:Q3:Q4: ALTRL11:X$                                          ~`@ <?@! H " @@@@D 0C@p| aB 7xx gcb 5pp|y`b4v?@@""@5px# " 5 @~?p@@`  @;@ 6@ | 4  E @`@`0`8A>Lp8M#~|N`p0cO F VM@ @ ~=@ 0| Da#A; ?8G Cpv  @?p =px @@@ :0: ; 6Č DA``BBšB D @  @S`  `NpM0@H B Ā? <ё:s'z⒆Ap\ <}B@|5?ő:|~đ6xxaiS OLLS̐NOĀOM =ì ;E ĀC< @   CȐɐʐː؀ـڀۀҀӀԀՀրȐ ɐʐːLĐh‰׭̐  ؀؀L؀۩؀Ҁ〽Ҁ J eJJKȐJȭɐJȭʐJȭːJL_`  Az"#<       ŠҠ> ˠ  ӠV ŠN ŠŠ ҠŠŠ ӠԮàŠ  ԭРԠ ĠҠ ŠŠO ŠŠϠ ŠŠԭР ĠŠŠ Ҡˠ0ҠˠӠ"ǠԠ Ӡ Ԡ N Ϡ@!B!B!D$"That's all there is to using a force table. You should find it a big help in understanding vectors and vector addition.":YY20:15:WD$"You are now finished with this lesson!":YYYY10:15:100:BACK30260}fv1000'force'' vector you add up the total mass on the weight hanger and the mass of the hanger itself":YYYY10|Rv15:WD$"(probably 50g). The direction of the vector can be read right off the angle scale. What could be easier!":15:100:BACK30240}\v:Wlling on a weight is equal to the mass in kilograms multiplied by the":YY10:15{>vWD$"acceleration due to gravity.":15:300j|HvWD$"Your instuctor may allow you to pretend that GRAMS is a force unit, sparing you a lot of calculating. To specify a 'e on the force table! Your instructor may NOT want you to do it this way.":YYYY10:15mz/v100:BACK30210Q{4v:WD$"One other thing is often done to simplify calculations. The proper metric unit for force is NEWTONS. The force supplied by gravity pus counter clockwise from the X-axis, the trigonometry of finding vector components is easy. The x components always use COS and the y components always use SIN.":YYYY10:15Xz*vWD$"This trick ONLY works when you consistantly measure the angle as is don:WD$"You will probably be comparing this experimentally determined EQUILIBRANT (the force which keeps the ring centered) to the theoretical EQUILIBRANT which you calculate mathematically.":YY10:15:300y#vWD$"Since the angle scale is marked in degreeite direction. Do you see why?":15:300wvWD$"Placing the EQUILIBRANT vector on the table cancels the others and the ring centers itself on the pin and doesn't fly off to the side. That's what you should try to do.":YYYY6:15:100:BACK30180x ve single force which cancels out the original forces is called the EQUILIBRANT because it brings the system into equilibrium. (All the forces add up to":YYYY6:15)wvWD$"zero.) It is the same size as the RESULTANT force vector, but in the exact oppos't know the difference!":uuYYYY10:15:100:BACK30160uv:WD$"A pin holds the ring from flying off the table in response to the forces on it. The pulleys let you select directions for these forces from the angle scale.":YY10:15:300v vWD$"Thl different directions at once.":YYYY10:15:300uuWD$"These forces add up (as vectors) to form the RESULTANT FORCE. You could actually replace all the loads on all the hangers with this single force in the proper direction and the center ring wouldnweight hangers. The strings transfer the downward pull of gravity on the weights to a sideways pull on the ring.":YY10:15:3002tuWD$"By putting different loads on the hangers you will have a variety of forces trying to pull the center ring in severa":XX90:YY90:5:105,85145,50:300ruWD$"Pulley":XX0:YY70:5:40,7064,60:300:WD$"Leveling":XX10:YY130:5:WD$"Screw":XX15:YY140:5:60,14090,135:100:BACK30140su:WD$"Strings run from the center ring, over the pulleys, and down to the rce table.":YY10:15:300~quWD$"Table Top":XX20:YY30:5:80,3595,44:300:WD$"Pin":XX100:YY20:5:118,25150,40:300quWD$"Angle Scale":XX210:YY10:5:240,20195,45:300:WD$"Weight":XX220:YY105:5:WD$"Hanger":YY115:5:300$ruWD$"Ringh them.":YY10:15:300puWD$"That's why you will be using a force table. It makes it easy to see how vectors combine. Let's look at one and identify its main parts....":YYYY20:15:100:BACK30090qu:0,60:1,144:38263:WD$"Here is a typical fohe Pythagorean Theorem!)":L20:XX175:YY50:5:L45:WD$"?":XX60:YY90:0:5:3:WD$"5 m":5:100:BACK30040pu:WD$"That shouldn't be news to you. You have probably covered vectors in class already. But now you need some ''hands-on'' experience witYY70:5:300nu50,4040,50:100,130110,120:45,45105,125:WD$"?":XX60:YY90:5:22:"HOW FAR ARE YOU FROM THE START ? ";A$:WD$"Wrong!":(A$,1)"5"WD$"Right!":nouWD$WD$" This is a standard 3,4,5 triangle. (If you're into mathematics, use tu do this?":YY10:15:300muD1:Y40:X501104:X,YD:DD:I1500:::50,30110,30:50,2550,35:110,25110,35:WD$"3 m":XX70:YY20:5:300 nuY401204:XD,Y:DD:I1500:::120,40120,120:115,40125,40:115,120125,120:WD$"4 m":XX130:100:5:300lvuX1101904:X,YD:DD:I1500:::110,110190,110:190,105190,115:WD$"4 m":XX140:YY100:5:300:50,130190,130:50,12550,135:190,125190,135:WD$"7 m":XX110:YY135lu5:100:BACK30000mu:WD$"But how far do you get if yo300kbuWD$"Well if both excursions were in the same direction you end up 7 meters from where you started. Simple enough!":YYYY10:15 lluD1:Y120:X501104:X,YD:DD:I1500:::50,110110,110:50,10550,115:110,105110,115:WD$"3 m":XX70:YY For example...":YYYY10:152jNu100:BACK1000qjXu:WD$"What do you get if you add 3 + 4 ?":YY10:15:300k\uWD$"It depends! Let's say you step off 3 meters. From there you walk another 4 meters. How far are you from your starting point?":15:unity to work with vectors and verify their addition rules.":YYYY10:15:300jDuWD$"This is important because as you probably already know, vectors don't add up like numbers do. Vectors not only have a size, but they also have an associated direction. in your physics career you are exposed to the concept of vectors. They are used so often that you must thoroughly understand them right from the start.":YY10:15:300Ni:uWD$"The force table is a simple piece of lab equipment which gives you an opport"= ";A((YX)1703.14159);" DEGREES";gu-100:BACK10090ogv-22:25:"= ";A((YX)1703.14159);" DEGREES"gw-22:" = ";A(R);" GRAMS"gx-23:"(ANGLE MEASURED CCW FROM +X-AXIS = ";A(TH);")"g-100:BACK10090g-10090h0u:L45::WD$"EarlyR);" GRAMS" ff-100:BACK10090?fg-22:" = ";A(R);" GRAMS"fi-WD$"O = tan (Ry/Rx)":XX155:YY130:5:1203,128:198,130201,130:155,133158,133fn-WD$"= tan ("(A(Y))"/"(A(X))")":XX167:YY150:5:1202,148:197,150201,150&gs-22:25:25,13030,14040,125110,125:232,0:233,3:0:2:263,128:2104,128:WD$" = ("(A(X))")":YYYY10:15eK-WD$"+ ("(A(Y))")":XX79:5eP-2506((A(X))),148:21036((A(Y))),148:18,15023,15028,16038,145130,145 fd-22:" = ";A((B)))(A(Y(C))))Vd(-YYYY10:XX50:WD$"= "(A(X)):5:WD$"= "(A(Y)):XX175:5kd2-100:BACK10090d<-0:YY110160:10,YY279,YY::3:WD$"= "(A(X)):XX70:YY110:5:WD$"= "(A(Y)):XX190:5neF-WD$"R = (Rx) + (Ry)":YY120:15:20,130):A(X(C))0WD$WD$"+"jc,WD$WD$(A(X(C))):5:XX175:WD$"= "(A(Y(A))):A(Y(B))0WD$WD$"+"c-WD$WD$(A(Y(B))):A(Y(C))0WD$WD$"+"c -WD$WD$(A(Y(C))):5c-QX((A(X(A)))(A(X(B)))(A(X(C))))d-QY((A(Y(A)))(A(YR Ax + Bx + Cx Ay + By + Cy":15Eb,100:BACK10090Ob,YY55Zb,IACb,XX70:WD$"= "(A(X(I))):5:WD$"= "(A(Y(I))):XX190:5:YYYY20b,b,YY120:XX50:WD$"= "(A(X(A))):A(X(B))0WD$WD$"+"c,WD$WD$(A(X(B))$"X-Components Y-Components":XX50:YY32:5:0,41279,41:YY35Vat,YY25:IACa~,YYYY10:WD$(I64):15:WD$(A(R(I)))"cos("(A(TH(I)))")":XX55:5:WD$(A(R(I)))"sin("(A(TH(I)))")":XX175:5a,a,0,105279,1050b,YY100:WD$"`8,:R`B,WD$"A = "(A(R(A)))" g at "(A(TH(A)))" degrees":XX60:YY0:5`L,WD$"B = "(A(R(B)))" g at "(A(TH(B)))" degrees":XX60:YY10:5`V,WD$"C = "(A(R(C)))" g at "(A(TH(C)))" degrees":XX60:YY20:5``,0,30279,30Eaj,WD@_+:21:"RESULTANT R = ";A(R);" GRAMS, ANGLE = ";A(TH)O_+I110:0u_+XC,YCXCAXBXCX,YCAYBYCY:3_,J1100:_,XC,YCXCAXBXCX,YCAYBYCY::I1100:_,100:BACK10090_,11040_$,XSC17:YSC17:10550`., HELP PAGENGLE = ";A(TH(C))^+I15:0:XCAXBX,YCAYBYXCAXBXCX,YCAYBYCY:F1100::3:XCAXBX,YCAYBYXCAXBXCX,YCAYBYCY:J1100::^+100:BACK10090^+11040^+A$"R"10090_+:F1$"Y"F1$"y"Ė14:21:"RESULTANT VECTOR":112505:"VECTOR B = ";A(R(B));" GRAMS, ANGLE = ";A(TH(B))]+I15:0:XCAX,YCAYXCAXBX,YCAYBY:F1100::3:XCAX,YCAYXCAXBX,YCAYBY:J1100::]+100:BACK10090]+11040]+A$"C"11220^+:21:5:"VECTOR C = ";A(R(C));" GRAMS, A(7):11040\R+A$""ī113100\\+A$"A"11140r\f+:21:5:"VECTOR A = ";A(R(A));" GRAMS, ANGLE = ";A(TH(A))\p+I15:0:XC,YCXCAX,YCAY:F1100::3:XC,YCXCAX,YCAY:J1100::\z+100:BACK10090\+11040\+A$"B"111806]+:21: THE VECTOR"V[*+F4$"Y"F4$"y"Ģ22:"PRESS RIGHT ARROW------ CALCULATION HELP";:1:[4+23:"PRESS LEFT ARROW ------ MAKE NEW VECTORS";:1:[>+A$:A$"A"A$"B"A$"C"A$"R"A$""A$""ĺ(7);(7):11040 \H+A$""(F4$"N"F4$"n")ĺ(7);H150)),YCAYBYCY30YSC(B(TH150)):XCAXBXCX,YCAYBYCYXCAXBXCX30XSC(B(TH210)),YCAYBYCY30YSC(B(TH210))Z+XXXC50XC505:XX,YC::YYYC50YC505:XC,YY:Z +100:BACK10090Z+ [ +21:"PRESS A,B,C,OR R ------ FLASHESULTANT R = ";A(R);" GRAMS, ANGLE = ";A(TH)UY*XC,YCXCAXBXCX,YCAYBYCYdY*I110:0Y*XC,YCXCAXBXCX,YCAYBYCY:3Y*J1100:Y*XC,YCXCAXBXCX,YCAYBYCY:J1100::Z*XCAXBXCX,YCAYBYCYXCAXBXCX30XSC(B(TAYBYCYXCAXBXCX30XSC(B(TH(C)210)),YCAYBYCY30YSC(B(TH(C)210))X*XXXC50XC505:XX,YC::YYYC50YC505:XC,YY:X*100:BACK10090X* PLOT RESULTANTX*:F1$"Y"F1$"y"Ė14:21:"RESULTANT VECTOR":109502Y*:21:"RAXBXCX,YCAYBYCY:3:XC,YCXCCX,YCCY:J1100:W*0:XC,YCXCCX,YCCY:3:XCAXBX,YCAYBYXCAXBXCX,YCAYBYCY:J1100::PX*XCAXBXCX,YCAYBYCYXCAXBXCX30XSC(B(TH(C)150)),YCAYBYCY30YSC(B(TH(C)150)):XCAXBXCX,YC0090?Vb*21:1:958:21:"MOVE TAIL OF VECTOR C TO HEAD OF B"Vl*0:XCCX,YCCYXCCX30XSC(B(TH(C)150)),YCCY30YSC(B(TH(C)150)):XCCX,YCCYXCCX30XSC(B(TH(C)210)),YCCY30YSC(B(TH(C)210)):35Wv*I17:0:XCAXBX,YCAYBYXC100::UD*XCAXBX,YCAYBYXCAXBX30XSC(B(TH(B)150)),YCAYBY30YSC(B(TH(B)150)):XCAXBX,YCAYBYXCAXBX30XSC(B(TH(B)210)),YCAYBY30YSC(B(TH(B)210))UN*XXXC50XC505:XX,YC::YYYC50YC505:XC,YY:VX*100:BACK1(B)150)),YCBY30YSC(B(TH(B)150)):XCBX,YCBYXCBX30XSC(B(TH(B)210)),YCBY30YSC(B(TH(B)210))T0*I17:0:XCAX,YCAYXCAXBX,YCAYBY:3:XC,YCXCBX,YCBY:J1100:U:*0:XC,YCXCBX,YCBY:3:XCAX,YCAYXCAXBX,YCAYBY:J1*XCCX30XSC(B(TH(C)150)),YCCY30YSC(B(TH(C)150)):XCCX,YCCYXCCX30XSC(B(TH(C)210)),YCCY30YSC(B(TH(C)210))S*100:BACK10090S*21:1:958:21:"MOVE TAIL OF B TO HEAD OF VECTOR A"pT&*0:XCBX,YCBYXCBX30XSC(B(TH:XCBX,YCBYXCBX30XSC(B(TH(B)210)),YCBY30YSC(B(TH(B)210))^R)100:BACK10090wR) PLOT VECTOR CR)21:1:958R)21:5:"VECTOR C = ";A(R(C));" GRAMS, ANGLE = ";A(TH(C))R)CXXSCX(C):CYYSCY(C)R)XC,YCXCCX,YCCYS(TH(A)210))!Q)100:BACK100909Q) PLOT VECTOR BJQ)21:1:958Q)21:5:"VECTOR B = ";A(R(B));" GRAMS, ANGLE = ";A(TH(B))Q)BXXSCX(B):BYYSCY(B)Q)XC,YCXCBX,YCBYIR)XCBX30XSC(B(TH(B)150)),YCBY30YSC(B(TH(B)150)))21:1:958MP^)21:5:"VECTOR A = ";A(R(A));" GRAMS, ANGLE = ";A(TH(A))jPh)AXXSCX(A):AYYSCY(A)Pr)XC,YCXCAX,YCAY Q|)XCAX30XSC(B(TH(A)150)),YCAY30YSC(B(TH(A)150)):XCAX,YCAYXCAX30XSC(B(TH(A)210)),YCAY30YSC(BO(X0TH180TH:*O(Y0TH360TH:?O)A(TH)360TH0EO)]O) DRAWING SECTIONvO)11300: SCALE DOWN|O")O,)XSC14:YSC14O6)O@)3:XC2802:YC1302:XXXC50XC505:XX,YC::YYYC50YC505:XC,YY:OJ) PLOT VECTOR A PT5:100:BACK10090Nx(11310(N(10090CN( CALCULATE RESULTANTXN(XX(A)X(B)X(C)mN(YY(A)Y(B)Y(C)~N(R(XXYY)N(R50R500ġ:10100N(TH(YX):TH180TH3.14159N(10480N((THTH(A))10(THTH(B))10(THTH(C))1010100O((F3$"N"F3$"n"10330}MP(WD$"Press LEFT ARROW for more vectors or RIGHT ARROW for a drawing.":YY130:15:100:BACK10090MU(10520MZ(F4$"N"F4$"n"İ100:10090Nd(WD$"Press LEFT ARROW for more vectors or RIGHT ARROW for calculations.":YY130:1)):XX210:5'L(F2$"N"F2$"n"10310=L((A(TH)18010300L2(WD$"Equilibrant ":A$(A(R)):YY60:15:WD$A$:XX100:5:WD$(A(TH)180):XX210:5:10310L<(WD$"Equilibrant ":A$(A(R)):YY60:15:WD$A$:XX100:5:WD$(A(TH)180):XX210:5MF20:5:WD$A$:XX100:5:WD$(TH(C)):XX210:5?K(0,55279,55K(WD$"* Angles measured in degrees counter clockwise from positive X-axis.":YY90:15K (F1$"N"F1$"n"10270 L(WD$"Resultant ":A$(A(R)):YY50:15:WD$A$:XX100:5:WD$(A(THJ'0,10279,10279,110,11xJ'WD$"A ":A$(R(A)):YY20:XX20:5:WD$A$:XX100:5:WD$(TH(A)):XX210:5J'WD$"B ":A$(R(B)):YY30:XX20:5:WD$A$:XX100:5:WD$(TH(B)):XX210:5.K'WD$"C ":A$(R(C)):YY40:XXTH(C))10)10100BI'X(A)R(A)(B(TH(A))):Y(A)R(A)(B(TH(A)))tI'X(B)R(B)(B(TH(B))):Y(B)R(B)(B(TH(B)))I'X(C)R(C)(B(TH(C))):Y(C)R(C)(B(TH(C)))I'10380J'L47::WD$" Vector Magnitude (g) Direction *":YY10:15:L451:B2:C31Hj'::11:13:"PLEASE STAND BY...."XHt'R(A)(300(1)):TH(A)(360(2))H~'R(B)(300(3)):TH(B)(360(4))H'R(C)(300(5)):TH(C)(360(6))H'R(A)50R(B)50R(C)5010100I'((TH(A)TH(B))10)((TH(A)TH(C))10)((TH(B)dG::10:10:"PLEASE STAND BY... ...GETTING THE MENU!":1023,6:"VERIFY MAIN MENU"G216,0:38400:"RUN MAIN MENU":G|:10:"I CAN'T FIND THE MENU. INSERT DISK A AND PRESS A KEY.":A$:" ":5010G' MAKE VECTORS H$'A...":"RUN FORCE TABLE SET-UP":/F " ":" "jF21:31:A$:22:1:958:23:12:"PLEASE STAND BY..."F(A$)30000,10000,5000F5500G::10:"PUT IN SIDE A OF THE FIRST DISK AND THENPRESS A KEY. (OR ESC TO CANCEL)":A$:" ":A$""1000MENU"hE1:21:" WHAT IS YOUR CHOICE? [ ]"::" (NO NEED TO PRESS 'RETURN')":21:31:A$EA$""A$"1"A$"2"A$"3"ĺ(7);(7):::9:"PRESS ONLY 1,2, OR 3!";:1030!F A$""ĉ::"SET-UP COMMAND RECOGNIZED.":10:10:"STAND BYZZ11000::"D:: MENUD:5:" ":5:" THE FORCE TABLE ":5:" ":E9:10:"1. INSTRUCTIONS"::10:"2. GENERATE VECTORS"::10:"3. RETURN TO EQUIPMENT >>>";::1:A$:24:1:" ";ZChA$""ĺ" "::1000tCjA$""BACK1:" ":CkA$""ĺ" ":Cm21:1:958:(7);(7):102CnC ERASE WORDS C0:Y0LAST10:0,Y279,Y::3:C,ZZ12000:: D2)X$"-"ĂBW$(WD$,LTR(X$(32))):100XX,YY:QQ1(W$):((W$,QQ,1))31:99::WD$(WD$,(WD$)LTR):99:XXXZ:YYYY10:6BXX0:YYYY10:5:Bd ARROWS AND ESCBeBACK0ACf49168,0:24:958:24::4:"<<< LEFT OR RIGHT ARROW OR ESC AD SQUEEZE,A$9577":"BLOAD TABLE,A$903C"3A1000AF(0):Q1(232):Q2(233):232,0:233,8:Q3(249):0:Q4(231):1:XZXXA100XX,YY:(WD$)LāQ1(WD$):((WD$,Q,1))31:99::232,Q1:233,Q2:Q3:Q4: BLTRL11:X$(WD$,LTR,1):X$(3MX@1002:36921:D$(13)(4):3:L45:F1$"N":F2$"N":F3$"N":F4$"N":(1023)2002@D$;"OPEN FORCE TABLE INFO":D$;"READ FORCE TABLE INFO":F1$:F2$:F3$:F4$:D$;"CLOSE FORCE TABLE INFO":1023,6@A(X)(X.5):B(X)3.14159X180)A"BLO                        UP"{UX(16384):16368,0<{VíX1272000: JUMP OUTa{Wí(0)125Ģ10:22:" IS ":50015t{Yâ10:22:"NOT"{[X(16384):16368,0{]íX1272000: JUMP OUT{_í(1)125Ģ12:22:" IS ":50019{aâ12:22:"NOT"{cë500050125Ģ12:22:B]íX12720005B_í(1)125Ģ12:22:" IS ":50019HBaâ12:22:"NOT"SBcë50005:zRâ20:"ONCE SENSORS ARE PROPERLY POSITIONED, PRESS 'ESC' TO RETURN TO THE MENU."zSÖ6:10:"PHOTO-SENSOR #1 NOT LINED UP"{TÖ6:12:"PHOTO-SENSOR #2 NOT LINEDITIONED, PRESS 'ESC' TO RETURN TO THE MENU."YASÖ6:10:"PHOTO-SENSOR #1 NOT LINED UP"ATÖ6:12:"PHOTO-SENSOR #2 NOT LINED UP"AUX(16384):16368,0AVíX1272000AWí(0)125Ģ10:22:" IS ":50015AYâ10:22:"NOT"B[X(16384):16368,0300:WD$"You have now completed this lesson and should return to the menu.":YYYY40:15n@)100:BACK10520x@)2000@PÉ:::10:" ":10:" LINE UP PHOTOCELLS ":10:" ":.ARâ20:"ONCE SENSORS ARE PROPERLY POS values allows us make graphs, find slopes and intercepts, and generally do all the things a good lab student should do.":YY10:15:300Y@)WD$"The key point to remember is that the average speeds occur halfway through the time intervals.":YYYY20:15:260,40>h)L10:XX70:YY50:WD$"0.247 0.521 0.795 1.07 1.34 1.62 1.89 2.17":5:XX215:YY50:WD$"1 3 5 7 9 11 13 15":L4:5:L45>r)WD$"See the sneaky units on the time column?":YY130:15:100:BACK10520?):WD$"Having these the average speeds happened at odd twentieths of a second.":YY120:15:100:BACK10380>^):WD$"Here is the rest of our data table (after changing units):":YY10:15:WD$" Average Speed (m/s) Time (1/20.0 s)":YYYY10:15:20,40140,40:175,4057,100:1127,100:1198,100<@)YY70:C1:XX5519570:WD$(C)"/20":5:CC2::WD$"This makes it easy to see the midpoints.":YY130:15:100:BACK10380 217 cm/s":5:100:BACK10360:):L45:WD$"So we now have a list of speeds--the average speed for each interval. These average speeds occurred halfway in time through each interval.":YY10:15:300O;")YY50:C0:XX2024070:WD$(C)"/10":X180270:X,20X,140::3:XX175:YY7:WD$"--> 24.7 cm/s":5:YYYYS:WD$"--> 52.1 cm/s":5:YYYYS:WD$"--> 79.5 cm/s":5:YYYYS:WD$"--> 107 cm/s":5(:)YYYYS:WD$"--> 134 cm/s":5:YYYYS:WD$"--> 162 cm/s":5:YYYYS:WD$"--> 189 cm/s":5:YYYYn't already.)":L15:XX180:YY20:5:100:BACK103608(0:X180270:X,20X,150::3:WD$"By dividing these distances by 1/10.0 s we get the average speed for each interval. (Only keep three significant digits.)":XX180:YY20:5:100:BACK103609)043 cm":5:YYYYS:WD$"16.17 cm":5:YYYYS:WD$"18.91 cm":5:YYYYS:WD$"21.65 cm":548(WD$"So these are the distances traveled by the car during each 1/10.0 s interval. You can easily see that the car was speeding up. (Write these down, if you haveYS:WD$"74.83 - 55.92 = 18.91 cm":5:YYYYS:WD$"96.48 - 74.83 = 21.65 cm":5:100:BACK103606(0:X123266:X,5X,155::3:XX125:YY7:WD$"2.47 cm":5:YYYYS:WD$"5.21 cm":5:YYYYS:WD$"7.95 cm":5:YYYYS:WD$"10.69 cm":5W7(YYYYS:WD$"13.XX125:YY7:WD$"2.47 - 0.00 = 2.47 cm":5:YYYYS:WD$"7.68 - 2.47 = 5.21 cm":5:YYYYS:WD$"15.63 - 7.68 = 7.95 cm":5:YYYYS:WD$"26.32 - 15.63 = 10.69 cm":5`6(YYYYS:WD$"39.75 - 26.32 = 13.43 cm":5:YYYYS:WD$"55.92 - 39.75 = 16.17 cm":5:YYYY3090:130,Y270,Y::3:Y2145S:101,Y1120,Y8101,Y16:4(WD$"By subtracting the first number in each pair from the second number we find the distance between dots.":L22:XX130:YY30:5:L45:100:BACK103605(0:Y3090:130,Y270,Y::3:S:WD$"55.92":5:YYYYS:WD$"74.83":5:YYYYS:WD$"96.48"3(5:WD$"Each number is the distance in centimeters from that dot to the first dot. (Write them down.)":L25:XX130:YY30:5:100:BACK10360A4(S20:0:Y::3b2(C4:X110:X220:Y1:3:Y4:3:Y10:3:Y19:3:Y32:3:Y51:3:Y77:3:Y110:3:Y151:3p2(YY0:S19;3(WD$"0.00":XX70:5:YYYYS:WD$"2.47":5:YYYYS:WD$"7.68":5:YYYYS:WD$"15.63":5:YYYYS:WD$"26.32":5:YYYYS:WD$"39.75":5:YYYYtable spark timer set at 10 dots per second. (Note that you can do the same thing with a 60 dot per second paper strip timer by circling every sixth dot and then ignoring the rest.)"1(XX40:L35:YY20:5:L45:100:BACK103602(0:Y2090:40,Y250,. After making a run we measure the distance between dots and make a data table...":YYYY20:15:100:BACK103100(L45::0,1600,010,010,160:X5:X,1:X,4:X,10:X,19:X,32:X,51:X,77:X,110:X,1511(WD$"Here is the tape. We have used an adjusulate from the distance between dots happened half-way in time between the dots.":XX50:YY20:5:40,10230,10230,6840,6840,10:L45/}(WD$"(We are assuming uniform acceleration.)":YYYY30:15:300r0(WD$"Let's try to get some data from a paper tapehe five second mark. So the automobile was moving at 30 mph after accelerating (at 6 mph per second) for 5 seconds.":YYYY10:15.i(43,119240,119:0,129125,129.n(100:BACK10250/x(:L30:WD$"So...":YY10:15:WD$"Each speed value that you calc0-[(WD$"What is the average of 0 seconds and 10 seconds?":YYYY10:15:WD$"Wrong! ":22:"AVERAGE TIME = ";A$:(A$,1)"5"WD$"Right."-_(:T110:B130:200:YY90.d(WD$WD$" The average time is just halfway through the interval, in this case at tn automobile that goes from 0 to 60 mph in 10 seconds of uniform acceleration. What is its average speed?":YY30:15:22:"AVERAGE SPEED = ";A$:WD$"Sorry!":(A$,2)"30"WD$"Correct!"-Z(:WD$WD$" The average of 0 and 60 is 30 mph.":YYYY10:15:30ant?":YYYY10:15:100:BACK10210+F(L45::WD$"What we calculated was the average speed during that particular time interval. The average speed happens at the average time.":YY10:15:230,18250,18:0,28270,28:300,P(WD$"For example, consider ae measure 2.05 cm between these two dots. Dividing by the time interval of 1/60.0 seconds gives us 123 cm/s = 1.23 m/s.":YYYY10:15:300#+<(WD$"But if the speed was constantly changing, it was going at 1.23 m/s for only an instant! When was that inst:WD$"At this point it was really moving!":YYYY10:15:100:BACK10210)((1240,35:T50:B130:200:WD$"Dividing each of the distances between dots by the time interval gives us speed, as before.":YY30:15:300*2(1101,35:1142,35:WD$"Let's say war first started out it was going slowly....":YY40:15:300:10,35:1130,35((WD$"By the time it was here it was going faster and covering more distance during the time interval between dots (1/60.0 second).":YYYY10:15:300H)(1130,35:1240,3530279,130:Y125:1,Y:4,Y:10,Y:19,Y:32,Y:51,Y:77,Y:110,Y:151,Y:202,Y:264,Yi'(100:BACK10170' (:279,00,00,10279,10:Y5:1,Y:4,Y:10,Y:19,Y:32,Y:51,Y:77,Y:110,Y:151,Y:202,Y:264,YN((232,0:233,21:1:48:10,35:WD$"When the cns when the car doesn't keep the same speed?":YY10:15:300&'WD$"If we pull the car with a constant force it accelerates. It keeps going faster and faster.":YYYY10:15:300T''WD$"The dot pattern looks like this:":YYYY10:15:279,1200,1200,18 m/s":XXXX10:YYYY20:5%'300:WD$"Rounding error causes this to differ from our first, correct result of 0.870 m/s.":YY130:15:100:BACK10140=&':WD$"When the car is moving with a constant speed, the dots are uniformly spaced. But what happead substituted 0.0167 s for 1/60.0 s (rounding to three significant digits right away)."l$'YY10:15:300$'WD$"Speed =":XX70:YYYY30:5:120,83170,83%'WD$"1.45 cm":XXXX54:YYYY8:5:WD$"0.0167 s":XXXX3:YYYY15:5:WD$"= 86.8 cm/s = 0.86YY14:5:150,118200,118:WD$"=":XX140:YY115:5:WD$"= 87.0 cm/s = 0.870 m/s":YYYY27:5:100:BACK10120X$':WD$"That last example shows the value of not rounding numbers until the end of the calculation. Consider what would have happened if we hof a second.":YY10:15:300"'WD$"So the speed is given by:":YYYY10:15:WD$"Speed =":XX100:YYYY30:5:WD$"Distance":XX150:YYYY8:5:WD$"Time":XXXX14:YYYY16:5:150,83200,83n#'WD$"1.45 cm":XXXX7:YYYY20:5:WD$" 1/60.0 s":XXXX9:YY you would measure a lot of dots and average the results.":YYYY10:15\!'100:BACK10120"':WD$"Let's say the average distance between dots is 1.45 cm. We also know that the spark timer, regulated by the electrical supply, makes dots every 1/60.0 constant speed, it always traveled the same distance in each time interval.":YY10:15:300G!'WD$"To find the speed of the car all we have to do is measure the distance between the dots and divide by the time between dots. In an actual lab experimentuniform spacing of the dots. This indicates that the car was moving at a constant speed. Do you see why?":YY110:15:100:BACK10050] ':WD$"The dots were placed down every 1/60.0 second. (Your view was in slow motion!) Since the car was moving at aong it has been rolling.":YY10:15:300j'WD$"You give the little car a quick push and turn on the timer. Here is an overhead view.":YYYY8:15:300t'274,905,905,100274,100:Y105114:20,Y40,Y::30,9530,105:16:10:1~'WD$"Notice the ing a Spark Timer, be careful. It operates at 15,000 volts!":YYYY10:15:100:BACK10000)`':WD$"Let's say you have attached a spark timer to a little car that can move along a table top. You are trying to see how the car's position depends on how loth of these timers produce a series of dots on long strips of paper. The dots are placed on the paper at very precise time intervals. (Usually 60 dots are made each second, although some spark timers are adjustable.)"[V'YYYY10:15:WD$"If you are usather's clock counts the back and forth motion of a long pendulum."d8'YYYY10:15:100:BACK1000B':WD$"Two common laboratory timers are Spark Timers and Paper Strip Timers. Each is regulated by electrical oscillations.":YY10:15:300L'WD$"B timers are regulated by the oscillations in the voltage from a wall electrical socket.":YYYY10C.'15:300:WD$"The Apple computer's timing programs count the vibrations of a crystal inside the computer. Many wrist watches work the same way. A grandf measurement of time. This is not surprising since many of the things you will be studying vary as time goes on.":YY10:15:300a$'WD$"To accurately measure time you must use something that is calibrated to the standard unit of time, the second. Some5)100):((100X.5)100)((10X.05)10)X$X$"0"KX.995X$"0"X$|X(X).995X(X)1X$((X.005))".00"(X(X)).01X$((X.005))".00"X.995X$"1.00"'':L45:0:1:3::WD$"Many physics labs require theXC(J,Q)DIV:YX:4300:B$X$:XTWO(C(J,Q1)DIV)TWO(C(J,Q)DIV):4300C0C(J,Q1)1C(J,Q)1Ė15:A$;:20:" - ";B$;:30:" = ";X$:23:"PRESS A KEY TO CONTINUE. (ESC TO EXIT)":A$:" ":A$""200041105X$((100X.KED-BLOCKED=INTERVAL":::" ALL TIMES IN SECONDS">^C0ZhZ0I1:ADDT4J16ZrC(J,Z)(AD)256(AD1)256256(AD2)256256256(AD3)|XC(J,Z)DIV:CC1H3:Q0C12:C0C(J,Q1)1C(J,Q)1XC(J,Q1)DIV:4300:A$X$:,I"_,10:"PRESS A KEY TO START TIMING. (ESC TO EXIT)":A$:" ":A$""20006:"MONITORING THE SENSORS. (PRESS A KEY TO STOP.)"@STARTJDIV6010483:P1DIV6002087056TJ0P1::"SENSOR(";J1;"): UNBLOCBE ONE INTERVAL EACH TIME A FLAG OR TAB PASSES BY A SENSOR.)":1:"HOW MANY INTERVALS? (1 - 10) ";I:I(I2):I1I20ĺ(7);(7):4080DLAY,3036975,100J0I:TABLEJ2,L(DTJ16):TABLEJ21,H(DTJ16):ZDTDT321:Z,0:ITplugged into the computer!":YY60:15:100:BACK2000;HIT32995XSTART36864ePD32994rDT34048DLAY37068TABLE32768:::"HOW MANY SENSORS? (1 OR 2) ";P:P(P):P1P2ĺ(7);(7):4060PD,P:10:"(THERE WILL DY TO COUNT, NOT FLASHING WHILE TIMING ==>";:H8 768p TIME(848)(849)256(850)65536(851)16777216v  10:XTIME1.40530E6:4300:"ELAPSED TIME = ";X$;" SECONDS" 30205:L45:3::WD$"DO NOT CONTINUE if there are no sensors )10000,3000,4000,50000,1000" ( z 22:"PRESS A KEY TO CLEAR THE TIMER. (ESC TO EXIT)":A$:A$""2000 :5:"PRESS A KEY TO START THE TIMER."::::"PRESS AGAIN TO STOP TIMER."/ V20:H31:V1:H1:"|_|":V:"FLASHING WHEN REAT IS YOUR CHOICE? [ ]"::" (NO NEED TO PRESS 'RETURN')":21:31:A$A$"1"A$"2"A$"3"A$"4"A$"5"ĺ(7);(7):::9:"PRESS ONLY 1,2,3,,4 OR 5!";:2040 " ":" "21:31:A$:22:1:958:23:12:"PLEASE STAND BY..." (A$MERS ":5:" ":7:8:"1. TYPES OF TIMERS"::8:"2. KEYBOARD TRIGGERED TIMER"::8:"3. SENSOR TRIGGERED TIMER"::8:"4. LINE UP PHOTO-SENSORS"::8:"5. RETURN TO EQUIPMENT MENU"J1:21:" WHA37,7,0,53,38,0,54,37,60,46,0,53,39,53,62,5,0Z1023,6:216,0:38400:"RUN MAIN MENU"::10:"I CAN'T FIND THE MENU. INSERT DISK A AND PRESS A KEY.":A$:" ":1020:7:5:" ":5:" LABORATORY TITING THE MENU!":"VERIFY MAIN MENU"a 864,1:865,0:866,4:867,0:868,5:869,0:232,96:233,3z A768830:B:A,B:, 20,0,24,0,27,0,31,0,35,0,39,0,44,0,49,0,52,0,57,0,53,62,36,0,49,38,0,53,55,61,0,53,23,37,0,46,38,52,0,61,46,62,5,0,61,54,)X(X256)256- TWO(X)(X100.5)1008 32760E C(2,20)O &2000Z 1040 ::10:"PUT IN SIDE A OF THE FIRST DISK AND PRESS A KEY. (OR ESC TO CANCEL)":A$:" ":A$""2000$ ::10:10:"PLEASE STAND BY... ...GET":$ m21:1:958:(7);(7):102* n0 V 0:Y0LAST10:0,Y279,Y::3:\ | 0:YTB:0,Y279,Y::3: ,ZZ12000:: ZZ11000:: "BLOAD KEYBD TIME CODE" "BLOAD SENSOR TIME CODE,A$9000" H(X)(X256):L(X:XXXZ:YYYY10:6) XX0:YYYY10:5:/ d: eBACK0 f49168,0:24:958:24::4:"<<< LEFT OR RIGHT ARROW OR ESC >>>";::1:A$:24:1:" "; hA$""ĺ" "::2000 jA$""BACK1:" ": kA$""ĺ" (231):1:XZXXe 100XX,YY:(WD$)LāQ1(WD$):((WD$,Q,1))31:99::232,Q1:233,Q2:Q3:Q4: LTRL11:X$(WD$,LTR,1):X$(32)X$"-"Ă W$(WD$,LTR(X$(32))):100XX,YY:QQ1(W$):((W$,QQ,1))31:99::WD$(WD$,(WD$)LTR):99T:I1002:864,1:865,0:866,4:867,0:868,5:869,0:232,96:233,3:500X30200:1X,95:1X10,105:1X1,95:X,100:1X11,105:X10(X10)ēX,95:X1,YX2,Y65,C:CC19: F(0):Q1(232):Q2(233):232,0:233,8:Q3(249):0:Q4                 " :A$:" ":A$"Y"A$"y"POT1+.ǰ50710:"The distance between grid marks on the screen represents 0.10 meters.":YY130:15fư100:BACK2000pƱ͋Ʋ ASK IF WANT POT OR FORCE/FIELD PLOT4POT0:P$"Y"P$"y"ĉ::22:"DO YOU WANT TO XXXX133:YYYY5:5o\WD$"The distance between grid marks on the screen represents 0.10 meters.":YY130:15fư100:BACK2000pƱƲ ASK IF WANT POT OR FORCE/FIELD PLOTPOT0:P$"Y"P$"y"ĉ::22:"DO YOU WANT TO PLOT EQUIPOTENTIALS?"; Coulombs"=+XX70:YY85:5:WD$"-5":XXXX70:YYYY5:5:5,WD$"Q2 = +5 x 10 Coulombs":(DIPOLE)WD$"Q2 = -5 x 10 Coulombs"-XX70:YY100:5:WD$"-5":XXXX70:YYYY5:5:5/WD$"Test Charge = +6 x 10 Coulombs":XX40:YY120:5:WD$"-5":ess ''RETURN'' to plot or ''C'' to clear the screen."؈ ƭPADDLESWD$"Use the L, R, U, D keys for movement of the test charge. (The arrows also work.) Then press ''RETURN'' to plot or ''C'' to clear the screen."%YYYY6:15 *WD$"Q1 = +5 x 10 Ɨ::WD$"In this part you can place "WO$" on the screen and put a test charge nearby.":YY10:155ƭPADDLESWD$"Use the joystick to roughly position the test charge. Then use the L, R, U, D keys for fine movement. (The arrows also work.) Then prPLOT TX,TY: HCOLOR= 3: GOTO 50020,ū50020lF$"N":POTĢ22:"DO YOU WANT SCALED VECTORS?":5:F$:" "rŗő:Y016010:X027010:X,Y::ƱΆ WO$"two charges":(DIPOLE)WO$"a dipole"WO$"two charges":(DIPOLE)WO$"a dipole"e;" KILOVOLTS"ŭ(POT)(((ALPHA))1.01((ALPHA)).01)Ē0:PX1002(ALPHA),PY1002(ALPHA)PX1002(ALPHA),PY1002(ALPHA):3:PX100,PY100ŭPOTİ100:BACK50020ąŲ ALPHA = 0υū50020!ŲIF TX < 270 AND TY < 160 THEN HCOLOR= 0: H22:13:"EY=";A(FYQP1E6);" MN/C"KŢ21:28:"E=";A(FQP1E6);" MN/C"{Ţ22:28:"THETA=";(THETA):100:BACK50020 ŭPOTēPX1005(ALPHA),PY1005(ALPHA)PX1005(ALPHA),PY1005(ALPHA)::22:"POTENTIAL = ";(KQ1R11000KQ2R21000)Ţ21:13:"FX=";A(FX);" N";vŢ22:13:"FY=";A(FY);" N"XŢ21:28:"F=";A(F);" N"Ţ22:28:"THETA=";(THETA):100:BACK50020ŭFIELD50590ŗ:21:"R1=";A(R1);" M"уŢ22:"R2="A(R2);" M"Ţ21:13:"EX=";A(FXQP1E6);" MN/C"$ŢHETAALPHA1803.14159)Nœ0,159279,159Sŭ(POT)(F$"N"F$"n")ēPX100,PY100PX10010(ALPHA),PY10010(ALPHA):50520Vŭ(POT)ēPX100,PY100PX100FX10,PY100FY10łXŭFR50572]ŗ:21:"R1=";A(R1);" M"bŢ22:"R2="A(R2);" M"l)(PYY1)(PYY1))MR2((PXX2)(PXX2)(PYY2)(PYY2)):R(R1R1R2R2)bF(FXFXFYFY)vALPHA(FYFX)&ŭFX0FY0ALPHA3.14159ALPHAԁ0ŭFX0FY0(ALPHA180ALPHA270)ALPHA3.14159ALPHA:ŭFX0FY0ALPHA23.14159ALPHADTY2LBP1.53.14159.ĭPXX1LAPLAP3.14159bĭPXX2LBP((PYY2)(X2PX)):LBPLBP23.14159FXFAP(LAP)FBP(LBP)FYFAP(LAP)FBP(LBP)ĭTX180FYFYӀĭPXX2FXFAP(LAP)FBP(LBP)F(FXFXFYFY)R1((PXX1)(PXX1XX1)(PYY1)(PYY1))%hFAP(FAP)WrFBPKQ2QP((PXX2)(PXX2)(PYY2)(PYY2))ĭPXX1LAP((PYY1)(PXX1)):50340ĭPYY1LAP3.141592ĭPYY1LAP1.53.14159ĭPXX2LBP((PYY2)(PXX2)):50370ĭPYY2LBP3.141592ĭPYTX2~8ĭTY2TY2'~9ĭTX277TX277:~:ĭTY150TY150~;ĭTXZXTYZYĘ0:1ZX2,ZY:16:1ZX,ZY2:ZXTX:ZYTY:1ZX,ZY2:0:1ZX2,ZY~@ī50160~JPXZX100:PYZY100:X1X1100:X2X2100:Y1Y1100:Y2Y2100~TK9E9^FAPKQ1QP((PXX1)(P)"l"(KEY)""PXPX1:50230T}ĭ(KEY)"R"(KEY)"r"(KEY)""PXPX1:50230}"ĭ(KEY)"C"(KEY)"c"50010: CLEAR},ĭKEY13(49249)128(49250)12850250: PLOT }6P(0)(0):TXP(0)1.1PX5:P(1)(1):TYP(1).6PY~7ĭTX2KEY(49152)128:KEY0(0)P(0)(1)P(1)(49249)128(49250)12850160f|ù49168,0:KEY050230{|í(KEY)""2000|ù49168,0:(KEY)"U"(KEY)"u"KEY11PYPY1:50230|ĭ(KEY)"D"(KEY)"d"(KEY)" "PYPY1:50230}ĭ(KEY)"L"(KEY501426{í(KEY)"C"(KEY)"c"50010: CLEARX{íKEY1350250: PLOT g{íTX2TX2v{íTY2TY2{íTX277TX277{íTY150TY150{íTXZXTYZYĘ0:1ZX2,ZY:16:1ZX,ZY2:ZXTX:ZYTY:1ZX,ZY2:0:1ZX2,ZY{ë50080L|2850080RzKEYKEY128:49168,0:(KEY)"U"(KEY)"u"(KEY)" "TYTY2:50142gzí(KEY)""2000zí(KEY)"D"(KEY)"d"(KEY)" "TYTY2:50142zí(KEY)"L"(KEY)"l"(KEY)""TXTX2:50142{í(KEY)"R"(KEY)"r"(KEY)""TXTX2: yå50640yíPADDLESė:21:"PADDLES, ARROWS, OR L,R,U,D KEYS TO MOVE":23:"PRESS RETURN TO PLOT, C TO CLEAR, OR ESC";:50160y×:21:"USE THE L,R,U,D KEYS OR ARROWS TO MOVE":23:"PRESS RETURN TO PLOT, C TO CLEAR, OR ESC";zKEY(49152):KEY1ð50900'xUù232,96:233,3:5:PX0:PY0WxZZX10:ZY170:5:TX50:TY50::::3:50660xdQ15E5:Q25E5:QP6E5:(DIPOLE)Q25E5xnX1090:Y180:X2180:Y280xxÓX13,Y1X13,Y1:X23,Y2X23,Y2xíQ10ēX1,Y13X1,Y13yíQ20ēX2,Y23X2,Y230:15w(x100:BACK2000w2x8wPx POT DISCUSSIONgwx ASK IF WANT POT OR FORCE/FIELD PLOTwxPOT0:P$"Y"P$"y"ĉ::22:"DO YOU WANT TO PLOT EQUIPOTENTIALS?";:A$:" ":A$"Y"A$"y"POT1wy30700:whDIPOLE1:50001wPDIPOLE0xQWD$"Q = -2 x 10 Coulombs"Qv xXX70:YY90:5:WD$"-5":XXXX70:YYYY5:5:5vxWD$"Test Charge = +6 x 10 Coulombs":XX40:YY110:5:WD$"-5":XXXX133:YYYY5:5wxWD$"The distance between grid marks on the screen represents 0.10 meters.":YY12to plot or ''C'' to clear the screen."uxPADDLESWD$"Use the L, R, U, D keys for movement of the test charge. (The arrows also work.) Then press ''RETURN'' to plot or ''C'' to clear the screen."uxYYYY6:15v xWD$"Q = +2 x 10 Coulombs":NEG center of the screen and allows you to place a test charge anywhere else.":YY10:15&uwPADDLESWD$"Use the joystick to roughly position the test charge. Then use the L, R, U, D keys for fine movement. (The arrows also work.) Then press ''RETURN'' BACK30020sw30020sswPOTđ:22:"DO YOU WANT CIRCLES? (Y/N) ";:A$:" "::A$"Y"A$"y"Ĺ0,13:1,144:38263swY016010:X027010:X,Y:::swSIGN$"positive":NEGSIGN$"negative"Vtw::WD$"This program places a "SIGN$" charge at the05(ALPHA)PX1005(ALPHA),PY1005(ALPHA)::22:"POTENTIAL = ";(KQ1R11000);" KILOVOLTS"rw(POT)(((ALPHA))1.01((ALPHA)).01)Ē0:PX1002(ALPHA),PY1002(ALPHA)PX1002(ALPHA),PY1002(ALPHA):3:PX100,PY100 swPOTİ100:30020qtwFIELD306104qww:21:"R=";A(R1);" M"]qyw21:13:"EX=";A(FXQP1E6);" MN/C"q~w22:13:"EY=";A(FYQP1E6);" MN/C"qw21:28:"E=";A(FQP1E6);" MN/C"qw22:28:"THETA=";(THETA):100:BACK30020crwPOTēPX1005(ALPHA),PY101803.14159f0uNEG1If1u30900if5u232,96:233,3:5:PX0:PY0f:uZX10:ZY170:5:TX50:TY50::::3:30650fDuQ12E5:Q20:QP6E5:NEGQ12E5fNuX1140:Y180:X2180:Y280fXuX13,Y1X13,Y1gbuQ10ēXe is to mapping electric fields and forces. Start first with the equipotentials and then draw perpendicular lines.":YYYY10:15:300f(WD$"You should try a variety of electrode arrangements. These represent different charge distributions.":YYYY10:etimes a flat rectangular tank is used to hold a conducting solution. This takes the place of the special paper. You have to be careful not to spill the liquid. Otherwise the experiment works the same way."e(YY10:15:300:WD$"That's about all therlternate arrangement uses a voltmeter to directly measure the potential difference between a probe and the ground on the power supply. This makes it easy to"c(YYYY10:15:WD$"read the voltage and keep it constant.":15:100:BACK10360d(:WD$"Some power supply sends a small current through the special paper. One probe is touched to the paper. The hand-held probe is then used to find all locations at the same potential.":YY10c(15:300:WD$"The galvanometer reads zero when this occurs. An asets up the equipotentials on the paper.":YY10:15:3:WD$"The galvanometer helps you trace out the equipotential lines.":YY10:15a(WD$"Galvanometer":XX100a(YY25:5:180,30197,30:100:BACK10330b(:WD$"The apparatus is pretty simple. Th Notice the difference between them.":0:YY10:15:3:WD$"Battery":XX10:YY140:5:WD$"The battery (or a power supply) sets up the equipotentials on the paper.":YY10:15`(60,14375,130:100:BACK10330a(0:WD$"The battery (or a power supply) inted on it.":YY10:15:3:WD$"These are the probes. Notice the difference between them.":YY10:15:WD$"Probe (on stand)":XX40:YY40:5_(142,43150,43:WD$"Hand Probe":XX210:YY90:5:205,93180,61:100:BACK10330`(WD$"These are the probes.144:38263:"BLOAD CIRCLES,A$900D"^(WD$"Here is the special paper. It usually has electrodes painted on it.":YY10:15:WD$"Paper":XX20:YY50:5:58,56100,80^(100:BACK10330_(0:WD$"Here is the special paper. It usually has electrodes pa108:WD$"voltage. (There is no potential difference pushing a current through the meter.)":15:300]n(WD$"Let's take a look at the set up....":YYYY20:15:100:BACK10290#^x(::10:15:"HOLD ON...":"BLOAD FIELD MAPPER,A$900D":230,32::0,13:1, paper causes a small electrical current to flow."\d(YY10:15:300:WD$"A galvanometer is used to locate the equipotentials on the paper. It will read zero if both of its probes are at the same.":YYYY10:15d]i(180,88250,88:0,98260,98:0,10845,the direction of the electrical vectors."K[P(YYYY10:15:100:BACK102502\Z(:WD$"The equipment used to make the measurements is pretty simple. A special type of paper is used which has a uniform resistance. A battery or power supply attached to thee lines of the electric field and electric force.":15:300)[F(WD$"To find the direction of these lines place an imaginary positive charge on them. Figuring out which way it will move (toward negative charges and away from other positives) will give you BACK10220Y2(:WD$"All you do is mark out the lines where the voltage doesn't change. These are the equipotentials. Then by drawing lines that are perpendicular to these equipotentials, you will have determined the location of":YY10;Z<(15:WD$"thWD$"Knowing this allows us to plot the electric field and electric force in a region just by mapping out the equipotentials. It is generally much easier to measure voltages than forces on charges or the amount of force per charge." Y((YYYY10:15:100: that the electric force which moves the charge is perpendicular to the equipotentials. It also means that the lines of the electric field (which is just force per charge) are also at right angles"W(YY10:15:WD$"to the equipotentials.":15:300X(o roll down a hill will move at right angles to the elevation lines.":YYYY6V(15:WD$"In a similar manner, a charge will move along a path that is perpendicular to the electrical equipotential lines.":YYYY6:15:100:BACK10180W (:WD$"This means lines of constant voltage) are at right angles to the lines of electric field strength.":YY10:15:300MV'WD$"Sometimes it helps to think about gravity equipotentials, lines of constant elevation, like the lines on a topographic map. A ball allowed te rules for vector addition. If you want a little practice, run the computer lesson on the force table.":YYYY10:15T'100:BACK10140iU':WD$"In class you learned that the lines of constant potential energy per charge (called ''EQUIPOTENTIALS'' orrces and fields. They are vectors. To add them up you have to keep track of their directions too. Both point in the direction a positive test charge would go."vT'YYYY10:15:95,98253,98:0,108195,108:WD$"Look in your book if you need to review thng with the POTENTIAL is that it is not a vector. To find the potential at a point due to a bunch of charges, simply add the effects of each of the charges. That's all there is to it!":YY10S'15:300:WD$"Things aren't quite so easy with electric fonergy per charge relative to a charge infinitely far away. It is simply called POTENTIAL and has units of Joules per Coulomb. This combination of units is given a familiar name--Volts.":YY90Q'15:100:BACK10090R':WD$"The nice thing about worki70:5:WD$"Q":XXXX37:YYYY8:5:WD$"r":XXXX:YYYY15:5jP'142,73160,73:232,0:233,3:2:2155,75P'300:0:Y7490:150,Y165,Y::Y7080:110,Y115,Y::3:WD$"r":XX147:YY76:5:WD$"V":XX110:YY70:5Q'WD$"This gives us the potential eou probably remember from earlier classes, it is often easier to deal with energy considerations than with forces. To find the energy per charge we just end up multiplying our electric field by distance."O'YY10:15:300J.'300:WD$"Force in Newtons":XX10:YY50:5:30,60105,83:300OULOMB SET-UP":HA(A$)*H" ":" "eH21:31:A$:22:1:958:23:12:"PLEASE STAND BY..."H(A$)10000,29000,30000,49000,50000,1000H' INSTRUCTIONS|I'::WD$"As you know, electrical charges exert forces on each other. That force is dURN TO EQUIPMENT MENU"yG1:21:" WHAT IS YOUR CHOICE? [ ]"::" (NO NEED TO PRESS 'RETURN')":21:31:A$GA$""(A$)1(A$)6((A$))(A$)ĺ(7):2030HA$""ė:"SET-UP COMMAND RECOGNIZED.":10:10:"STAND BY....":" RUN C:" ELECTRIC FIELD MAPPING ":5:" ":F7:10:"1. INTRODUCTION"::10:"2. SINGLE POSITIVE CHARGE"::10:"3. SINGLE NEGATIVE CHARGE"::10:"4. DIPOLE"::10:"5. TWO POSITIVE CHARGES"G:10:"6. RET..GETTING THE MENU!":1023,1:"VERIFY MAIN MENU"XE1023,6:216,0:"RUN MAIN MENU":E:10:"I CAN'T FIND THE MENU. INSERT DISK A AND PRESS A KEY.":A$:" ":1010E:: MENUE3:0:1:L45OF:5:" ":5RASE WORDS 1D0:Y0LAST10:0,Y279,Y::3:DD,ZZ12000::WDZZ11000::bD1500D::10:"PUT IN SIDE A OF THE FIRST DISK AND PRESS A KEY. (ESC TO CANCEL)":A$:" ":A$""20001E::10:10:"PLEASE STAND BY... .eBACK0Cf49168,0:24:958:24::4:"<<< LEFT OR RIGHT ARROW OR ESC >>>";::1:A$:24:1:" ";ChA$""ĺ" "::2000CjA$""BACK1:" ":CkA$""ĺ" ":Cm21:1:958:(7);(7):102Cn D EX0:YYYY10:5:B"OPEN COULOMB INFO":"READ COULOMB INFO":K$:FR$:FIELD$:P$:"CLOSE COULOMB INFO":PADDLES0:K$"Y"K$"y"PADDLES1BFR0:FR$"Y"FR$"y"FR1BFIELD0:FIELD$"Y"FIELD$"y"FIELD1B2000Bd ARROWS AND ESCCXX,YY:(WD$)LāQ1(WD$):((WD$,Q,1))31:99::232,Q1:233,Q2:Q3:Q4:ALTRL11:X$(WD$,LTR,1):X$(32)X$"-"ĂAW$(WD$,LTR(X$(32))):100XX,YY:QQ1(W$):((W$,QQ,1))31:99::WD$(WD$,(WD$)LTR):99:XXXZ:YYYY10:6BX,KE@1002:36875:"BLOAD SQUEEZE,A$9577":"BLOAD CIRCLES,A$900D":@864,1:865,0:866,4:867,0:868,5:869,0:232,96:233,3:5:@A(X)(X100.5)100@20@F(0):Q1(232):Q2(233):232,0:233,8:Q3(249):0:Q4(231):1:XZXXMA100                         " yK@?M M OMJH @@G55U555D7?!; ;HH|?; 7x @`08 0 ;@0p ;~8@@@ H8 ? ?7Dյ~ |2,2,2,2,2,2 @ @  2 2,2? ` p 6h@ ;@ @`>>":XX40:YY182:5:3[!N230,64:Y180190:30,Y260,Y::0:WD$"<<< LEFT OR RIGHT ARROW OR ESC >>>":XX40:YY182:5:3["NBACK0:A$\#NA$""ĺ" "::2000X(10(X))10:^ZN*X1X1OFFSET2:X2X1OFFSET1:SC64Ĺ230,64:S1X1,Y:S2X2,Y:49237,0ZX*SC32Ĺ230,32:S1X1,Y:S2X2,Y:49236,0Zb*20000:BACK2000Zg*10380Zl*V(M1V1M2V2)(M1M2)Zv*XV1:10770:V1X[*XV2:10770:V2X:XV:10770:V(PBM1VA)M2#Y)XVA:10770:VAX8Y)XVB:10770:VBXCY)10005bY* ROUNDING SUBROUTINE vY*(X)((X))ıY&*(X0)((10X)((10X)).5)XA(X):Y0*(X0)(10(X)(10(X)).5)XA(X).1:Y:*X0XX.05:XA(X):ZD*X0XX.05:LASTIC10860XJ)PBM1V1M2V2>XT)EB.5M1V1V1.5M2V2V2VX^)AM12M1M1(2M2)fXh)BM1PBM2|Xr)CPBPB(2M2)EBX|)VA(B(BB4AC))(2A)X)VB(PBM1VA)M2X)XVA:10770:VAXX)XVB:10770:VBXX)VA(B(BB4AC))(2A)Y)VB$):V2100V2100ĺ(7);(7):10518W)V10V20Ģ20:(7);(7):21:27:"|":WD$"That's kind of boring, isn't it?":YY10:15:I14000::10510W6)V10V20Ģ20:(7);(7):21:27:"|":WD$"NO COLLISION POSSIBLE!":YY10:15:I14000::10510 X@)E16087,150185,150185,160:136,150136,160aV)21:13:"| | |":13:"|______|______|"V)21:13:"| | |";:15:"";V1$:21:20:"|":V1(V1$):V1100V1100ĺ(7);(7):10516$W)21:20:"| |";:22:"";V2$:21:27:"|":V2(V2D$"Pick reasonable speeds for the carts before they collide. (Something between 0 and 100 cm/s. Use negative speeds for carts moving from right to left).":YY50:15U)WD$"Speeds in cm/s":XX93:YY130:5:WD$"Cart #1 Cart #2":XX87:YY140:5+V)87,13:"|______|______|"yT(21:13:"| | |";:15:"";M1$:21:20:"|":M1(M1$):M110M11000ĺ(7);(7):10464T(21:20:"| |";:22:"";M2$:21:27:"|":M2(M2$):M210M21000ĺ(7);(7):10466T(M1M2S22T)M1M2S12U)::W between 10 and 1000 grams. Pick values within this range for the simulated carts.":YY50:15:WD$"Masses in grams":XX89:YY130:5:WD$"Cart #1 Cart #2":XX87:YY140:5S(87,16087,150185,150185,160:136,150136,160T(21:13:"| | |":stic. (No need to press the RETURN key.)":YY110:15iR(10:A$:" ":ELASTIC1:A$"I"A$"i"ELASTIC0R(A$"I"A$"i"A$"E"A$"e"ĺ(7);(7):10410R(L100R(OFFSET16R(5R(S11:S21S(L45:::WD$"Real air track carts have massess a ''perfect bounce''. No energy is lost during the collision process. During an INELASTIC COLLISION there is energy lost.":YY50:15Q(FIRST05R(WD$"Which type of collision do you want to simulate? Press an ''E'' for elastic or an ''I'' for inelaF1023,6:216,0:"RUN MAIN MENU":zF|:10:"I CAN'T FIND THE MENU. INSERT DISK A AND PRESS A KEY.":A$:" ":5010A0end.":YYYY6:15:100:BACK30170n v:WD$"That's about all there is to using an air track. You should now go back to the menu. For fun why don't you try the simulated collision experiment?":YY70:15:100:BACK30220n*v2000ttself or it will warp. If that happens it is almost impossible to make sense out of a cart's motion!""nvYYYY6:15:300:WD$"You must also be sure that the track is as level as possible. Even a very slight tilt will cause the cart to coast toward one ily":YY10:15lvWD$"damaged. If the base is bent or dirty it can drag on the track. Don't slide the carts along the track without the blower running either. You will scratch the cart and the track.!"lv15:300fmvWD$"Do not lean on the track ie springs it is (nearly) elastic, if they stick together it is an inelastic collision.":YY10wk v15:100:BACK30130l v:WD$"An air track and carts can make it easy and fun to examine many fundamental physical laws, but be careful. The carts are easthem together. Magnets or Velcro are also used to do this.":YY10:15:32jjv1223,97:100:BACK30130xjv1223,97^k vLAST47:150:WD$"By using the proper ends of two carts you can set up an elastic or an inelastic collision. If they bounce off thspring. Very little energy is lost in that type of collision.":YY10:15:232,0:233,21:140,81wiu100:BACK30130Kjv140,81:LAST40:150:WD$"The other end of the cart has a lump of clay which will stick to another cart when they collide, holding X140:YYYY6:5:WD$"Time Blocking Sensor":XX110:YYYY13:5:110,143230,143dhu100:BACK30130hu0:Y130156:60,Y230,Y::3biuLAST47:150:WD$"The spring on one end of the cart allows it to collide and bounce off another cart with a similar 35,0guWD$"Here is a cart with a tab used to block a photocell. Knowing the size of the tab and how long it blocks the photocell allows you to find the speed by dividing distance by time.":YY10:15OhuWD$"Speed = ":XX60:YY140:5:WD$"Tab Width":Xn's laws of motion or the conservation of momentum and energy. In the ''real world'' friction complicates things too much!":YYYY6:15fu100:BACK30070gu::10:10:"HOLD ON...":"BLOAD BIG CART,A$920A":0,10:1,146:38263:49232,0:49236,0:4925:300euWD$"Regardless of the style of top you will be using in lab, its purpose is to allow you to keep track of the position of the cart as it moves.":YYYY6:15:300fuWD$"Since frictional forces are nearly eliminated, you can easily study NewtoBACK30020du:WD$"The top of the cart can be several things. Quite often it is a tab which can be followed in a strobe photograph or used to block a photocell timer. Sometimes a blinking light source or a spark timer is mounted on top."euYY10:13:30,8943,7557,89:31,9043,7757,90:T150::0:30,8943,7557,89:31,9043,7757,90:T150:::3cu100:BACK30020 duLAST27:150:WD$"There is a very slight drag due to the air itself, but it can almost always be ignored.":YY10:15:100::YY120:5Hbu50,5595,55:65,8395,83:60,11065,123:100:BACK30020buLAST25:150:WD$"This air ''cushion'' keeps the cart from touching the track. Since there is no contact between the surfaces, there is no friction.":YY10:15:300jcuI120: attached to the base.":YY10:15:40,7040,4046,4046,7061,8558,8843,7329,8825,8540,69 buWD$"Here is an end view.":XX150:YY60:5:43,7963,10043,12123,10043,79:WD$"Top":XX100:YY50:5:WD$"Base":YY80:5:WD$"Section through track":XX70PLOT EQUIPOTENTIALS?";:A$:" ":A$"Y"A$"y"POT1A.ǰ50710:L" IS ":50019 |aâ12:22:"NOT"+|cë50005( D? U@? ``?NTVCT0`@@NA6y x OD 8~8 | F F F Ap@@@ A``` Aqu B F F FaY@0 $`U8<T`@@p@@Nb _=0<<0 ___:@@@"<":";"___= << O` `0|N~ T@`H0@T`f""" "