HP 35S Calculator Programs - pgccphy.net

1 HP 35S Calculator of Physical Sciences and EngineeringPrince George s Community CollegeMay 3, 2014 Programs in this appendix are written for the Hewlett-Packard HP 35s scientificcalculators, and can be easily modified to run on other HP calculators that use Projectile Problem2. Kepler s Equation3. Hyperbolic Kepler s Equation4. Barker s Equation5. Reduction of an Angle6. Helmert s Equation7. Pendulum Period8. 1D Perfectly Elastic Collisions11 Projectile ProblemThis program solves the projectile problem: given a target sitting on a hill at ;yt/and a cannon with muzzle velocityv0, at what angle should the cannonbe aimed to hit the target? The solution is found numerically using Newton s run the program, enter:v0 ENTERxtENTERytENTER 0 XEQ J ENTERH erev0,xt,andytmay be in any consistent set of units, and the angle 0(theinitial estimate of the answer) is in degrees. The program returns the angle needed tohit the target in running the program, the Calculator will be set to degrees ListingJ001 LBL JJ002 RADJ003!

2 RADJ004 STO TJ005 R#J006 STO YJ007 R#J008 STO XJ009 R#J010 STO VJ011 STO NJ013 RCL TJ014 2J015 J016 SINJ017 RCL XJ018 J019 RCL TJ020 COSJ021x2J022 RCL YJ023 J024 2J025 J026 J027 RCL XJ028 RCL VJ029 J030x22J031 J033 J034 RCL TJ035 2J036 J037 COSJ038 RCL XJ039 J040 2J041 J042 RCL TJ043 2J044 J045 SINJ046 RCL YJ047 J048 2J049 J050CJ051 J052 RCL TJ053x<>yJ054 J055 STO TJ056 ISG NJ057 GTO J014J058!DEGJ059 DEGJ060 RTNP rogram:LN=194 CK= ,.xt; ;20m/,and 0D30 .Entertheabove program, then type:30 ENTER 50 ENTER 20 ENTER 30 XEQ J ENTERThe program returns D41:5357 .32 Kepler s EquationGiven the mean anomalyM(in degrees) and the orbit eccentricitye, this programsolves Kepler s equationMDE esinEtofind the eccentric anomalyE. This is a very simple implementation it includes noconvergence test, and simply solves Kepler s equation by performing 15 iterations ofNewton s run the program, enter:MENTEReXEQ K ENTER whereMis in degrees.

3 The program returns the eccentric anomalyEin running the program, the Calculator will be set to degrees ListingK001 LBL KK002 STO EK003x<>yK004!RADK005 STO MK006 STO AK007 RADK008 STO KK010 RCL AK011 RCL MK012 RCL AK013 -K014 RCL AK015 SINK016 RCL EK017 K018 +K019 RCL AK020 COSK021 RCL EK022 K023 1K024 -K025 K026 -K027 STO A4K028 ISG KK029 GTO K011K030!DEGK031 DEGK032 RTNP rogram:LN=102 CK= ,eD0:15. Enter the above program, then type:60 ENTER .15 XEQ K ENTER (HP 35s)The program returnsED67:9667 .53 Hyperbolic Kepler s EquationGiven the mean anomalyM(in degrees) and the orbit eccentricitye, this programsolves the hyperbolic Kepler equationMDesinhF Ftofind the variableF. This is a very simple implementation it includes no conver-gence test, and simply solves the hyperbolic Kepler equation by performing 15 itera-tions of Newton s run the program, enter:MENTEReXEQ Y ENTER whereMis in degrees. The program returns the ListingY001 LBL YY002 STO EY003x<>yY004!

4 RADY005 STO MY006 STO AY007 STO KY009 RCL AY010 RCL MY011 RCL AY012 +Y013 RCL AY014 SINHY015 RCL EY016 Y017 -Y018 RCL AY019 COSHY020 RCL EY021 Y022 1Y023x<>yY024 -Y025 Y026 -Y027 STO AY028 ISG K6Y029 GTO Y010Y030 RTNP rogram:LN=96 CK= ,eD1:15. Enter the above program, then type:60 ENTER XEQ Y ENTERThe program returnsFD1 Barker s EquationGiven the constantKDpGM=.2 q3/.t Tp/, this program solves Barker s equationtan f2 C13tan3 f2 Tp/tofind the true run the program, enter the dimensionless Tp/as follows:KXEQ B ENTER (HP 35s)The program returns the program will work in either Degrees or Radians ListingB001 LBL BB002 STO KB003 ABSB004 B006 ENTERB007 ENTERB008 B009 1B010 +B011pxB012 +B013 3B0141=xB015yxB016 ENTERB017 ENTERB018 B019 1B020 -B021x<>yB022 B023 RCL K8B024 ENTERB025 ABSB026 B027 B028 ATANB029 2B030 B031 RTNP rogram:LN=100 CK= :38and set the Calculator s angle mode to degrees.

5 Enter theabove program, then XEQ B ENTERThe program returnsfD149:0847 .95 Reduction of an AngleThis program reduces a given angle to the range 0; 360 /in degrees mode, or 0;2 /in radians mode. It will work correctly whether the Calculator is set for degrees orradians run the program: XEQ R ENTERThe program will return the equivalent reduced ListingR001 LBL RR002 STO TR003 -1R004 ACOSR005 2R006 R007 STO ZR008 RCL TR009x 0?R010 GTO R022R011 RCL ZR012 R013 +/-R014 IPR015 1R016 +R017 RCL ZR018 R019 RCL TR020 +R021 RTNR022 RCL ZR023x<>yR024x<y?R025 RTNR026x<>yR027 R028 IPR029 RCL ZR030 R031 RCL TR032x<>yR033 -10R034 RTNP rogram:LN=106 CK= D5000 and set the Calculator s angle mode to degrees. Enter theabove program, then type:5000 XEQ R ENTER (HP 35s)The program returns320 .116 Helmert s EquationGiven the latitude (in degrees) and the elevationH(in meters), this program usesHelmert s equation tofind the acceleration due to run the program, enter: ENTERHXEQ H ENTER where is in degrees andHis in meters.

6 The program returns the acceleration dueto gravitygin running the program, the Calculator will be set to degrees ListingH001 LBL HH002 DEGH003x<>yH004 2H005 H006 STO GH007 COSH008 H010 <>yH012 -H013 RCL GH014 COSH015x2H016 H018 +H019x<>yH020 H022 -H023 RTNP rogram:LN=99 CK= D38:898 ,HD53m. Enter the above program, then ENTER 53 XEQ H ENTER (HP 35s)The program returnsgD9:80052 Pendulum PeriodGiven the lengthLand amplitude of a simple plane pendulum, this programfindsthe periodT, using the arithmetic-geometric mean run the program, enter:LENTER XEQ P ENTER whereLis in meters and is in degrees. The program returns the running the program, the Calculator will be set to degrees ListingP001 LBL PP002 DEGP003 STO QP004x<>yP005 STO LP006 1P007 RCL QP008 2P009 P010 COSP011 +P012 2P013 P014 STO AP015 RCL QP016 2P017 P018 COSP019pxP020 STO GP021 STO KP023 RCL AP024 ENTERP025 ENTERP026 RCL GP027 +P028 2P029 P030 STO AP031 R#P032 RCL G13P033 P034pxP035 STO GP036 ISG KP037 GTO P023P038 RCL LP039 P041pxP042 2P043 P044 P045 P046 RCL AP047 P048 RTNP rogram:LN=158 CK= :2mand D65.

7 Enter the above program, then ENTER 65 XEQ P ENTER (HP 35S)The program returnsTD2 1D Perfectly Elastic CollisionsGiven the massesm1andm2of two bodies and their initial velocitiesv1iandv2i,thisprogramfinds the post-collision velocitiesv1fandv2f,usingv1fD m1 m2m1Cm2 v1iC 2m2m1Cm2 v2iv2fD 2m1m1Cm2 v1iC m2 m1m1Cm2 v2iTo run the program, enter:m1 ENTERm2 ENTERv1iENTERv2iXEQ E ENTERThe program will return the post-collisionvelocitiesv1f(in theXregister) andv2f(in theYregister), in the same ListingE001 LBL EE002 STO WE003 R#E004 STO VE005 R#E006 STO NE007 R#E008 STO ME009 RCL NE010 E011 RCL ME012 RCL NE013 +E014 STO ZE015 E016 RCL VE017 E018 2E019 RCL NE020 E021 RCL WE022 E023 RCL ZE024 E025 +E026 STO XE027 215E028 RCL ME029 E030 RCL VE031 E032 RCL ZE033 E034 RCL NE035 RCL ME036 E037 RCL ZE038 E039 RCL WE040 E041 +E042 RCL XE043 RTNP rogram:LN=131 CK= :0kg,m2D7:0kg,v1iD4:0m/s, andv2iD 5 the above program, then type:2 ENTER7 ENTER4 ENTER5+/- XEQ E ENTERThe program returnsv1fD 10m/s in theXregister, andv2fD 1m/s in