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{"sheet":"3-Clock+Button","index":3,"n_rows":123,"n_cols":20,"rows_kept":123,"cut":false,"hidden":false,"merged":[]}
[null,null,null,null,null,null,null,null,"Sec. Hand coords"]
[null,"User Controls:",null,null,null,"Frame #","Time","theta","Tipx","Tip y",null,null,"Drawing Data:"]
[null,"Radius",8,"cm",null,0,0,{"$f":"C$8*G3","v":0},{"$f":"C$3*SIN(H3)","v":0},{"$f":"C$3*COS(H3)","v":8}]
[null,"arrow fraction",0.1,"like a %",null,1,{"$f":"G3+C$5","v":0.5},5.2359877559829883E-2,{"$f":"C$3*SIN(H4)","v":0.41868764994355062},{"$f":"C$3*COS(H4)","v":7.9890362780365907},null,null,"Outer Circle",null,null,"Inner Circle",null,null,"Arrow"]
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[null,"Anim. Speed",100,"(10 to 200)",null,3,1.5,0.15707963267948966,1.251475720321847,7.9015067247611022,null,0,{"$f":"($C$3+1)*COS($L6*PI()/180)","v":9},{"$f":"($C$3+1)*SIN($L6*PI()/180)","v":0},null,{"$f":"($C$3/10)*COS($L6*PI()/180)","v":0.8},{"$f":"($C$3/10)*SIN($L6*PI()/180)","v":0},null,0,0]
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[null,"Omega",{"$f":"2*PI()/60","v":0.10471975511965977},"rad/s",null,5,2.5,0.26179938779914941,2.0705523608201659,7.7274066103125465,null,20,8.4572335870731763,3.0781812899310186,null,0.75175409662872683,0.27361611466053498,null,{"$f":"S7-$C$4*$C$3*SIN($C$12-PI()/6)","v":0.39999999999999997},{"$f":"T7-$C$4*$C$3*COS($C$12-PI()/6)","v":7.3071796769724493}]
[null,"Current Index:",0,"From code!",null,6,3,0.31415926535897931,2.4721359549995792,7.6084521303612282,null,30,7.794228634059948,4.4999999999999991,null,0.69282032302755103,0.39999999999999997,null,{"$f":"S7","v":0},{"$f":"T7","v":8}]
[null,"Current \"x\":",{"$f":"VLOOKUP($C$9,$F$3:$J$123,4,1)","v":0},"cm",null,7,3.5,0.36651914291880916,2.8669435963624017,7.4686434119776139,null,40,6.894399988070802,5.7850884871788537,null,0.61283555449518246,0.5142300877492314,null,{"$f":"S9-$C$4*$C$3*SIN($C$12+PI()/6)","v":-0.39999999999999997},{"$f":"T9-$C$4*$C$3*COS($C$12+PI()/6)","v":7.3071796769724493}]
[null,"Current \"y\":",{"$f":"VLOOKUP($C$9,$F$3:$J$123,5,1)","v":8},"cm",null,8,4,0.41887902047863906,3.2538931446064012,7.3083636611408069,null,50,5.7850884871788546,6.894399988070802,null,0.51423008774923151,0.61283555449518246]
[null,"Current angle",{"$f":"VLOOKUP($C$9,$F$3:$J$123,3,1)","v":0},"rad",null,9,4.5,0.47123889803846897,3.631923997916374,7.1280521935069432,null,60,4.5000000000000009,7.7942286340599471,null,0.40000000000000013,0.69282032302755092]
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[null,"Notes: Normally, when you drag cells to",null,null,null,14,7,0.73303828583761832,5.353044850870865,5.9451586038191548,null,110,-3.0781812899310186,8.4572335870731763,null,-0.27361611466053498,0.75175409662872683]
[null,"a new location, all other cells that refer",null,null,null,15,7.5,0.78539816339744828,5.6568542494923797,5.6568542494923806,null,120,-4.4999999999999982,7.794228634059948,null,-0.39999999999999986,0.69282032302755103]
[null,"to them will automatically update along",null,null,null,16,8,0.83775804095727813,5.9451586038191531,5.3530448508708659,null,130,-5.7850884871788546,6.894399988070802,null,-0.51423008774923151,0.61283555449518246]
[null,"with the drag. However, that's not true",null,null,null,17,8.5,0.89011791851710798,6.2171676916557663,5.0345631283987,null,140,-6.8943999880708011,5.7850884871788555,null,-0.61283555449518234,0.51423008774923162]
[null,"for cell references made in Visual ",null,null,null,18,9,0.94247779607693793,6.4721359549995796,4.7022820183397851,null,150,-7.794228634059948,4.4999999999999991,null,-0.69282032302755103,0.39999999999999997]
[null,"Basic code/macros. The code for this",null,null,null,19,9.5,0.99483767363676778,6.7093645435633915,4.3571122801202176,null,160,-8.4572335870731745,3.0781812899310199,null,-0.75175409662872672,0.27361611466053509]
[null,"\"Start\" button refers to cells C6, C9, and",null,null,null,20,10,1.0471975511965976,6.9282032302755088,4.0000000000000009,null,170,-8.8632697771098723,1.5628335990023725,null,-0.78784620240976644,0.13891854213354424]
[null,"C10. So if you move any of those cells,",null,null,null,21,10.5,1.0995574287564276,7.1280521935069423,3.6319239979163744,null,180,-9,1.102633609417758E-15,null,-0.8,9.8011876392689601E-17]
[null,"you'll need to manually update the code.",null,null,null,22,11,1.1519173063162573,7.3083636611408069,3.253893144606403,null,190,-8.8632697771098723,-1.5628335990023743,null,-0.78784620240976644,-0.13891854213354438]
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{"sheet":"4-Incline+button","index":4,"n_rows":104,"n_cols":21,"rows_kept":104,"cut":false,"hidden":false,"merged":[]}
[]
[null,"User Input Space:",null,null,null,null,null,null,"Simulation Space"]
[null,"Hill Angle q:",39,"deg",null,"User might need to ",null,null,"Frame #","time","z, \"EQ 4\"",null,null,null,null,"Drawings Space",null,"Box: flat at origin",null,"Rotated & Offset"]
[null,"Starting speed v0",4,"m/s \"uphill\"",null,"press \"Reset\" to see",null,null,0,{"$f":"I4*Q$21","v":0},{"$f":"Q$17+C$4*J4+0.5*Q$18*J4^2","v":0.31780314581314995},null,null,null,null,"Hill: x","Hill: y","x","y","x","y"]
[null,"Starting height h0",0.2,"m",null,"impact of changing",null,null,1,1.3722582103512843E-2,0.37211279062847952,null,null,null,null,0,0,0,0,{"$f":"R5*$Q$23-S5*$Q$22+$Q$25*$Q$23","v":0.24697943130701033},{"$f":"R5*$Q$22+S5*$Q$23+$Q$25*$Q$22","v":0.2}]
[null,"Box size w",0.2,"m",null,"these inputs…",null,null,2,2.7445164207025686E-2,0.42526106824636534,null,null,null,null,{"$f":"Q14","v":2},0,{"$f":"C6","v":0.2},0,{"$f":"R6*$Q$23-S6*$Q$22+$Q$25*$Q$23","v":0.40240862359840451},{"$f":"R6*$Q$22+S6*$Q$23+$Q$25*$Q$22","v":0.32586407820996749}]
[null,"g",9.8000000000000007,"m/s2",null,null,null,null,3,4.1167746310538531E-2,0.47724797866680763,null,null,null,null,{"$f":"Q14","v":2},{"$f":"Q15","v":1.619568066390014},{"$f":"C6","v":0.2},{"$f":"R7","v":0.2},{"$f":"R7*$Q$23-S7*$Q$22+$Q$25*$Q$23","v":0.27654454538843704},{"$f":"R7*$Q$22+S7*$Q$23+$Q$25*$Q$22","v":0.48129327050136167}]
[null,"Current Frame?",0,"(0 to 100)",null,null,null,null,4,5.4890328414051372E-2,0.52807352188980616,null,null,null,null,0,0,0,{"$f":"S7","v":0.2},{"$f":"R8*$Q$23-S8*$Q$22+$Q$25*$Q$23","v":0.12111535309704285},{"$f":"R8*$Q$22+S8*$Q$23+$Q$25*$Q$22","v":0.35542919229139419}]
[null,"Animation Speed",50,"(10 to 100)",null,null,null,null,5,6.8612910517564213E-2,0.57773769791536111,null,null,null,null,null,null,0,0,{"$f":"R9*$Q$23-S9*$Q$22+$Q$25*$Q$23","v":0.24697943130701033},{"$f":"R9*$Q$22+S9*$Q$23+$Q$25*$Q$22","v":0.2}]
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[null,null,null,null,null,null,null,null,7,9.6058074724589895E-2,0.67358194837413998,null,null,null,null,"Calculations Space:"]
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[null,"Some Comments:",null,null,null,null,null,null,9,0.12350323893161559,0.76478073004314429,null,null,null,null,"q",{"$f":"Q12*PI()/180","v":0.68067840827778847},"rad"]
[null,"See the handout on the course homepage for more",null,null,null,null,null,null,10,0.13722582103512843,0.80863807008148081,null,null,null,null,"Hill width x",2,"m"]
[null,"info about the physics used here. ",null,null,null,null,null,null,11,0.15094840313864127,0.8513340429223738,null,null,null,null,"Hill peak hmax",{"$f":"Q14*TAN(Q13)","v":1.619568066390014},"m"]
[null,"The position of the box is really just the position",null,null,null,null,null,null,12,0.16467098524215412,0.89286864856582304,null,null,null,null,"h0 true",{"$f":"MIN(C5,Q15)","v":0.2},"m"]
[null,"of its lower left corner. ",null,null,null,null,null,null,13,0.17839356734566697,0.93324188701182864,null,null,null,null,"z0",{"$f":"Q16/SIN(Q13)","v":0.31780314581314995},"m"]
[null,"Unlike the clock, where the user was able to choose",null,null,null,null,null,null,14,0.19211614944917979,0.97245375826039071,null,null,null,null,"az",{"$f":"-C7*SIN(Q13)","v":-6.1673398322884072},"m/s2","EQ 1"]
[null,"the time step between frames, I am instead auto-",null,null,null,null,null,null,15,0.20583873155269264,1.010504262311509,null,null,null,null,"vbottom",{"$f":"-SQRT(C4^2-2*Q18*Q17)","v":-4.46318272088428},"m/s","EQ 3"]
[null,"calculating it here. First, I find the true duration of",null,null,null,null,null,null,16,0.21956131365620549,1.0473933991651838,null,null,null,null,"tbottom",{"$f":"(Q19-C4)/Q18","v":1.3722582103512844},"s; \"duration\"","EQ 2"]
[null,"the simulation. Then, I divide that duration by 100",null,null,null,null,null,null,17,0.23328389575971833,1.0831211688214148,null,null,null,null,"Dt",{"$f":"Q20/100","v":1.3722582103512843E-2},"s"]
[null,"to get the time step between frames. ",null,null,null,null,null,null,18,0.24700647786323118,1.1176875712802021,null,null,null,null,"sinq",{"$f":"SIN(Q13)","v":0.62932039104983739}]
[null,"The drawing of the hill is only 2m \"wide\" at the base.",null,null,null,null,null,null,19,0.260729059966744,1.1510926065415459,null,null,null,null,"cosq",{"$f":"COS(Q13)","v":0.7771459614569709}]
[null,"Since the user might choose some unreasonable",null,null,null,null,null,null,20,0.27445164207025685,1.1833362746054461,null,null,null,null,"Picked out t",{"$f":"VLOOKUP($C$8,$I$4:$K$104,2)","v":0}]
[null,"values, I am using cells (not VB code) to make ",null,null,null,null,null,null,21,0.2881742241737697,1.2144185754719024,null,null,null,null,"Picked out z",{"$f":"VLOOKUP($C$8,$I$4:$K$104,3)","v":0.31780314581314995}]
[null,"sure that if the user enters an angle greater than",null,null,null,null,null,null,22,0.30189680627728255,1.2443395091409153]
[null,"45 degrees, the simulation will only use 45 degrees.",null,null,null,null,null,null,23,0.3156193883807954,1.2730990756124843]
[null,"For reference, the macros use only cells C8 and C9",null,null,null,null,null,null,24,0.32934197048430824,1.3006972748866097,null,null,null,null,null,null,null,null,"EQ 4"]
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