Pumping WorkAustin ProbeMath 152Section 202This maplet was built to demonstrate and teach how to calculate the work that is done by pumping water out of various shaped tanks. You have three options for tank shape, a sphere, a cone, or a cylinder, the default is cylinder because it is easy and a good place to start if you're just learning the concept. The maplet also randomly decides whether the tank is full or half full. For a slice of water within the tank at height y and with thickness dy, you have to find the radius of in terms of y, then the area in terms of the radius and also the distance each slice will move in terms of y. Finally you must use all these pieces of information to integrate and find the work done by pumping.# Programer Note;
# Maplet Specific Text =Green
# Procedures =Blue
# The Maplet Itself =Purple################################### Header For All Mapletsrestart:with(Maplets[Elements]):with(Maplets[Tools]):StartEngine();randomize():lightorange:="#FFB300":lightcyan:="#DDFFFF":lightblue:="#CFCFFF":lightgreen:="#CCFFCC":ColorBkgd:=wheat:ColorFooter:=lightcyan:ColorNewButton:=magenta: # or Make, Save, Enter ProblemColorReturnButton:=magenta:ColorCloseButton:=pink: # or Quit, Clear, Reset, CancelColorHintButton:=lightorange: # or SyntaxColorPrevButton:=turquoise: # or UpdateColorEnterButton:=turquoise:ColorSimplifyButton:=turquoise:ColorCheckButton:=green:ColorShowButton:=lightorange:ColorPlotButton:=gold: ColorPlotButtonFrgd:=yellow:ColorTableBkgd:=lightgreen:ColorCalculatorBkgd:=gold:ColorMessage:=white: ColorMessageFrgd:=black:ColorInput:=turquoise: ColorInputFrgd:=black:ColorCorrect:=green: ColorCorrectFrgd:=black:ColorIncorrect:=red: ColorIncorrectFrgd:=white:ColorWarning:=yellow: ColorWarningFrgd:=black:ColorShow:=lightorange: ColorShowFrgd:=black:ColorHint:=lightorange: ColorHintFrgd:=black: # or Info, SyntaxColorDisable:=wheat: ColorDisableFrgd:=black:FontFooter:=Font("helvetica",10):FontSymbol:=Font("symbol",12):FontBig:=Font("times",24):LIBLogo:=cat(libname,"/M4C/M4C.png"):Logo:="M4C.png":#LIBLogo:=cat(libname,"/M4C/WebALT_logo.png"):#Logo:="WebALT_logo.png":# ################################### # Template Translation Table For All MapletsTEXTLprogrammers:="Programmers: D.B. Meade and P.B. Yasskin":TEXTLcopyright:="\302\251 Copyright: Maplets for Calculus 2007":#"\302\251 Copyright: WebALT 2007":TEXTLversion:="M4C v1.0 Nov 2007":TEXTBQuit:="Quit":TEXTBClose:="Close":TEXTBCheck:="Check":TEXTBShow:="Show":TEXTBShowAll:="Show All Steps":TEXTBCheckAns:="Check Answer":TEXTBShowAns:="Show Answer":TEXTBInstructions:="Instructions":TEXTBHint:="Hint":TEXTBHints:="Hints":TEXTBSyntax:="Syntax":TEXTBHintSyntax:="Hints and Syntax":TEXTBPrev:="Preview":TEXTBUpdate:="Update":TEXTBDerivation:="Derivation":TEXTBNewProblem:="New Problem":TEXTBNewFunction:="New Function":TEXTBNewGraph:="New Graph":TEXTBNewEquation:="New Equation":TEXTBNewLimit:="New Limit":TEXTBNewDerivative:="New Derivative":TEXTBNewIntegral:="New Integral":TEXTBNewSequence:="New Sequence":TEXTBNewSeries:="New Series":TEXTBNewDiffEq:="New Differential Equation":TEXTBEnterProblem:="Enter Problem":TEXTBEnterFunction:="Enter Function":TEXTBEnterGraph:="Enter Graph":TEXTBEnterEquation:="Enter Equation":TEXTBEnterLimit:="Enter Limit":TEXTBEnterDerivative:="Enter Derivative":TEXTBEnterIntegral:="Enter Integral":TEXTBEnterSequence:="Enter Sequence":TEXTBEnterSeries:="Enter Series":TEXTBEnterDiffEq:="Enter Differential Equation":TEXTBMake:="Modify or Make Your Own Problem":TEXTBUpdateClose:="Update Problem and Close": #EliminateTEXTBSaveClose:="Save Problem and Close": #Use this oneTEXTBAskQuestion:="Ask Question":TEXTBNextQuestion:="Next Question":TEXTBHowtoAnswer:="How to Answer":TEXTBEnter:="Enter":TEXTBOK:="OK":TEXTBReturn:="Return":TEXTBClear:="Clear":TEXTBClearAll:="Clear All Steps":TEXTBReset:="Reset":TEXTBCancel:="Cancel":TEXTBPlot:="Plot":TEXTBAnimate:="Animate":TEXTBPlay:="Play":TEXTBPause:="Pause":TEXTBForward:="Forward":TEXTBReverse:="Reverse":TEXTBStep:="Step":TEXTBUpdatePlot:="Update Plot":TEXTBZoomIn:="Zoom In":TEXTBZoomOut:="Zoom Out":TEXTBPlotSetup:="Plot Setup":TEXTBRefresh:="Refresh":TEXTBSimplify:="Simplify":TEXTBFactor:="Factor":TEXTBExpand:="Expand":TEXTBNormalize:="Normalize":TEXTBRationalize:="Rationalize":TEXTBSort:="Sort":TEXTBDecimal:="Decimal":TEXTBExact:="Exact":TEXTCorrect:=" correct ":TEXTIncorrect:="incorrect":TEXTWarning:=" warning ":TEXTShown:=" shown ":TEXTSlower:="Slower":TEXTFaster:="Faster":TEXTEnterFormula:=" Enter Formula:":TEXTEvaluate:=" Evaluate:":TEXTApproximate:=" Approximate:":TEXTand:=" and ":TEXTor:=" or ":TEXTThus:=" Thus ":TEXTSo:=" So ":TEXTType:=" Type ":TEXTfor:=" for ":TEXTorcheck:=" or check: ":TEXTCBDNE:="does not exist":TEXTCB11scaling:="1-1 scaling":TEXTCBDoNotShow:="Do not show this window again.":TEXTRBNumeric:="Numeric":TEXTRBSymbolic:="Symbolic":TEXTRBTrue:="True":TEXTRBFalse:="False":TEXTRBT:="T":TEXTRBF:="F":TEXTRBPlot1:="Plot # 1":TEXTRBPlot2:="Plot # 2":TEXTRBPlot3:="Plot # 3":TEXTRBconverge:="converge":TEXTRBdiverge:="diverge":TEXTRBconverges:="converges":TEXTRBdiverges:="diverges":TEXTtitlePROBLEM:="Modify or Make Your Own Problem":TEXTtitlePREVIEW:="Preview":TEXTtitleHINT:="Hint":TEXTCapGoal:="Goal:":TEXTCapProbStat:="Problem Statement:":TEXTCapSyntaxTutorial:="Syntax Tutorial:":TEXTCapEnter:="Enter:":TEXTCapTrueFalse:="True or False?":TEXTCapCalculator:="Calculator":TEXTCapPlot:="Plot":TEXTCapEvaluate:="Evaluate:":TEXTCapDataTable:="Data Table":TEXTCapVis:="Visualization":TEXTCapPreviewer:="Previewer":TEXTCapHorRng:="Horizontal Range:":TEXTCapVertRng:="Vertical Range:":TEXTreplyNoPrev:="You must enter an expression to be previewed.":DNEset:={"", undefined, Undefined, UNDEFINED, divergent, Divergent, DIVERGENT, diverges, Diverges, DIVERGES, dne, DNE, doesnotexist, DoesNotExist}:great:=[" Bullseye."," Right on the mark."," Great."," That's absolutely right."," Awesome. You're unstoppable."," Correct."," WOW, nailed that one."," You got it!"," YES! Right on."," Way to go."," Don't stop now."," I knew you could do it!"," Perfect. You're unstoppable."," Radical Dude."," Power house."," Sweet! Keep on Rockin'."," You rock!"," You got those mad skills."," Awesome!"," Wowzers! That was great!"," Awesome man!"," Good job! You really know what you are doing."," You're awesome kid."," Tearing it up."," Right on the money."," High Five!!!!!"," Cool Beans."," What a nerd!"," You're so money."," You're a genious."," You hit the nail on the head."," Excellent!"," If I had a cookie, I'd give it to you."," You're a winner."," That's a winner."," Whoop! Way to go."," That's the way, ah ha ah ha, I like it."," Oh yeah!"," You're the bomb!"," That was fantastic!"," Oh Snap!"," That's krunk!",NULL]:nextgeneric:=[" Keep it up."," Keep going.",NULL]:nextprob:=[" On to the next problem."," Try another problem."," You're ready for another problem.",NULL]:nextquest:=[" On to the next question."," Try another question."," You're ready for another question.",NULL]:nextpart:=[" On to the next part."," Try another part."," You're ready for another part.",NULL]:nextstep:=[" On to the next step."," Try another step."," You're ready for another step.",NULL]:nexteq:=[" On to the next equation."," Try another equation."," Solve another equation."," You're ready for another equation.",NULL]:nextfn:=[" On to the next function."," Try another function."," You're ready for another function.",NULL]:nextlim:=[" On to the next limit."," Try another limit."," Compute another limit."," You're ready for another limit."," Find another limit.",NULL]:nextderiv:=[" On to the next derivative."," Try another derivative."," Compute another derivative."," You're ready for another derivative."," Differentiate another function",NULL]:nextinteg:=[" On to the next integral."," Try another integral."," Compute another integral."," You're ready for another integral."," Integrate another function",NULL]:nextseq:=[" On to the next sequence."," Try another sequence."," Find the limit of another sequence."," You're ready for another sequence.",NULL]:nextser:=[" On to the next series."," Try another series."," Sum another series."," You're ready for another series.",NULL]:sorry:=[" Sorry, that's not right."," Nope, but don't give up."," Not quite, it's a little off."," Bummer, thought you would get it this time."," Close, but no cigar."," Slightly off."," If you need help, please ask a human."," I don't know where you went wrong."," Sorry, killer problem."," No, but don't blow it off."," D'oh!"," That's whack."," Yikes! Really close. You'll get it next time."," Thought you would get it this time."," Nice try, but your answer is wrong."," Ask your neighbor for help."," Brutal kid."," That won't fly."," So close and yet so far."," So, that was just practice."," Ooooh...close."," A swing and a miss."," Better luck next time."," Oops."," Tilt. Play again."," I know you can do better."," Sorry Charlie."," Tisk, tisk. It's a tough one."," It takes a lot of wrongs to make a right."," Even Einstein didn't get everything right."," Oh man, you were so close."," Today's not your lucky day."," Don't quit your day job."," You're colder than a polar bear's toenail.",NULL]:trygeneric:=[" Fix your answer and check it again."," Give it another try."," Try again."," Please try again.",NULL]:tryhint:=[" Try the hints and answer again."," Read the hints and try again."," Study the hints and answer again.",NULL]:tryhelp:=[" Try the Help menu and answer again."," Look at the Help menu and try again.",NULL]:showgeneric:=[" OK That's just practice. But try doing it yourself."," That's fine for practice. Try doing it yourself."," Think about it and enter an answer yourself."," Next time, compute an answer yourself."," So that was practice. Try doing it yourself.",NULL]:showhint:=[" Next time, try the hints."," Read the hints and enter an answer yourself.",NULL]:showhelp:=[" Next time, read the Help menu."," Read the Help and enter an answer yourself.",NULL]:##################################### English Translation Table For PumpingWorkTEXTLasstprogrammer:=
"Assistant Programmer: Austin B. Probe":TEXTtitleMAIN:=
"Work of Pumping a Liquid":TEXTCap1:=
"Enter each of the following for the slice at height y of thickness dy.":TEXTCap2:=
"Set up the integral for the work:":TEXTCap3:=
"Evaluate the integral for the work:":TEXTHint:=
" Work is equal to the force required to move an object times the distance it is moved.\n
For water in a tank, the distance moved depends on the height y in the tank. So, the work done by pumping must be computed using an integral of the weight of the water at height y times the distance it is lifted.\n
The limits of integration run from the lowest point of the tank to the highest point in the tank where there is water.":TEXTHintr:=
" r is the radius of the slice at height y.\n
For a cylinder that is just the radius of the tank.\n
For spherical and conical tanks, it varies with the height.
So you must define r in terms of y using the Pythagorean Theorem
or similar triangles.":TEXTHintA:=
" A is the area of the slice of the water in the tank at height y.\n
In the integral, you need the volume dV of a slice of thickness dy.\n
In formulas: A = Pi r^2 dV = A dy":TEXTHintD:=
" D is the distance that you must lift the slice of water
from height y to the top of the tank.\n
D = Top of the tank - y":TEXTHintWint:=
" Syntax: W = Int( rho * g * D * A, y = min..max).\n
You only need to integrate over the values of y where there is water.":TEXTHintWval:=
" Use paper and pencil to do the integral.\n
Start by expanding the integrand.":TEXTCylinder:=
" Cylinder ":TEXTCone:=
" Cone ":TEXTSphere:=
" Sphere ":TEXTprob1:=
" Compute the work needed to pump the water out of the top of a ":TEXTprob2:=
"shaped tank with radius ":TEXTheightNotSphere:=
" meters and height ":TEXTprob3:=
" meters. The water level in the tank is ":TEXTfull1:=
"full":TEXTfull2:=
"half full":TEXTprob4:=
".\n The density of water is rho = 1000 kg/m^3 and the acceleration of gravity is g = 9.81 m/sec^2.":TEXTreply1r:=
" You entered the radius of the tank not the variable radius in terms of y.":TEXTreply2a:=
" You need to capitalize the P in your Pi.":TEXTreply2c:=
" You should not have a dy in your formula for area. That is a factor in the volume of the slice.":TEXTreply2b:=
" That is the circumference, not the area.":TEXTreply3a:=
" That is the total height, not the distance lifted from height y.":TEXTreply3b:=
" That is the radius, not the distance lifted from height y.":TEXTreply4a:=
" You do not need the dy. It is automatically generated by the y = min .. max.":TEXTreply4b:=
" You forgot about rho = 1000 kg/m^3 and g = 9.81 m/sec^2.":TEXTreply4c:=
" That integral gives the weight. You forgot the factor of the distance lifted.":TEXTreply4d:=
" You did not account for the tank only being half full.":# ################################### # Customize For Each Mapletswith(plots):with(plottools):nextlocal:=[NULL]:trylocal:=[NULL]:showlocal:=[NULL]:nexts1:=[ #Keep what is appropriate. This is for all but the last check.op(nextgeneric),#op(nextprob),op(nextquest),op(nextpart),op(nextstep),#op(nextlocal),NULL]:nexts2:=[ #Keep what is appropriate. This is for the last check.op(nextgeneric),op(nextprob),#op(nexteq),#op(nextfn),#op(nextlim),#op(nextderiv),#op(nextinteg),#op(nextseq),#op(nextser),#op(nextlocal),NULL]:trys:=[ #Keep what is appropriate.op(trygeneric),op(tryhint),#op(tryhelp),#op(trylocal),NULL]:shows:=[ #Keep what is appropriate.op(showgeneric),op(showhint),#op(showhelp),#op(showlocal),NULL]:randgreat:=rand(1..nops(great)):randnext1:=rand(1..nops(nexts1)):randnext2:=rand(1..nops(nexts2)):randsorry:=rand(1..nops(sorry)):randtry:=rand(1..nops(trys)):randshow:=rand(1..nops(shows)):# #####################################rand0:=rand(1..2):
rand1:=rand(1..5):new_prob:=proc()
global ts, waterlevel, radius, H, TEXThgt, r, A, _D,
ymin, ymax, rhog, Wint, Wval, CorrectA, CorrectD:
local fullness:
options `Copyright 2007, Philip B. Yasskin and Douglas Meade, Maplets for Calculus`:
ts:=Get(tankshape):
waterlevel:=1/rand0():
fullness:=`if`( waterlevel=1, TEXTfull1, TEXTfull2):
radius:=rand1():
H:=2+2*rand1():
TEXThgt:=`if`( ts=TEXTSphere, " ", cat(TEXTheightNotSphere,H)):
r:=piecewise(ts=TEXTCylinder, radius,
ts=TEXTCone, radius/H*y,
ts=TEXTSphere, sqrt(radius^2-y^2));
A:=Pi*r^2;
_D:=`if`( ts=TEXTSphere, radius-y, H-y ):
ymin:=`if`( ts=TEXTSphere, -radius, 0 ):
ymax:=`if`( ts=TEXTSphere, -radius+waterlevel*2*radius, waterlevel*H ):
rhog:=9810:
Wint:=Int(rhog*_D*A, y=ymin..ymax);
Wval:=int(rhog*_D*A, y=ymin..ymax);
CorrectA:=false:
CorrectD:=false:
Set(problem=cat(TEXTprob1, ts, TEXTprob2, radius, TEXThgt, TEXTprob3, fullness, TEXTprob4)):
plot_it();
Set(TFr="");
Set(TFrck="", TFrck(background)=ColorMessage);
Set(TFA=""):
Set(TFAck="", TFAck(background)=ColorMessage);
Set(TFD=""):
Set(TFDck="", TFDck(background)=ColorMessage):
Set(TFWint=""):
Set(TFWintck="", TFWintck(background)=ColorMessage):
Set(TFWval=""):
Set(TFWvalck="", TFWvalck(background)=ColorMessage):
Set(reply="", reply(background)=ColorMessage):
Set(BrCk(enabled)=true, BrCk(background)=ColorCheckButton):
Set(BrSh(enabled)=true, BrSh(background)=ColorShowButton):
Set(BACk(enabled)=false, BACk(background)=ColorDisable):
Set(BASh(enabled)=false, BASh(background)=ColorDisable):
Set(BDCk(enabled)=true, BDCk(background)=ColorCheckButton):
Set(BDSh(enabled)=true, BDSh(background)=ColorShowButton):
Set(BWintCk(enabled)=false, BWintCk(background)=ColorDisable):
Set(BWintSh(enabled)=false, BWintSh(background)=ColorDisable):
Set(BWvalCk(enabled)=false, BWvalCk(background)=ColorDisable):
Set(BWvalSh(enabled)=false, BWvalSh(background)=ColorDisable):
end proc:plot_it:=proc()
global radius, H, waterlevel, ts, CorrectA, CorrectD, TEXThgt;
local p1, p2, p3;
options `Copyright 2007, Philip B. Yasskin and Douglas Meade, Maplets for Calculus`;
if ts=TEXTCylinder then
p1:=cylinderplot(radius, theta=0..2*Pi, z=0..H, transparency=1, grid=[25,5]),
cylinderplot([R, theta, 0], R=0..radius, theta=0..2*Pi, transparency=1, grid=[5, 25]):
p2:=cylinder([0,0,0], radius, waterlevel*H,
color=turquoise, style=patchnogrid):
p3:=display([p1,p2], scaling=constrained, orientation=[20, 80],
axes=framed, labels=[z, x, y],
tickmarks=[[-radius, 0, radius], [-radius, 0, radius], [0, H/2, H]]);
elif ts=TEXTCone then
p1:=cylinderplot(radius/H*z, theta=0..2*Pi, z=0..H, transparency=1, grid=[25,5]):
p2:=cone([0, 0, 0], waterlevel*radius, waterlevel*H,
color=turquoise, style=patchnogrid):
p3:=display([p1,p2], scaling=constrained, orientation=[20, 80],
axes=framed, labels=[z, x, y],
tickmarks=[[-radius, 0, radius], [-radius, 0, radius], [0, H/2, H]]);
elif ts=TEXTSphere then
p1:=sphereplot(radius, theta=0..2*Pi, phi=0..Pi, transparency=1, grid=[25,13]):
p2:=`if`(waterlevel=1, sphere, hemisphere)([0, 0, 0], radius,
color=turquoise, style=patchnogrid):
p3:=display([p1,p2], scaling=constrained, orientation=[20, 80],
axes=framed, labels=[z, x, y],
tickmarks=[[-radius, 0, radius], [-radius, 0, radius], [-radius, 0, radius]]);
end if:
Set(myplot=p3);
end proc:check_r:=proc()
global r, ts, radius;
local user_r;
options `Copyright 2007, Philip B. Yasskin and Douglas Meade, Maplets for Calculus`;
user_r:=Get(TFr::algebraic);
if simplify(normal(user_r - r))=0 then
Set(TFrck=TEXTCorrect,
TFrck(background)=ColorCorrect, TFrck(foreground)=ColorCorrectFrgd);
Set(reply=cat(great[randgreat()], nexts1[randnext1()]),
reply(background)=ColorCorrect, reply(foreground)=ColorCorrectFrgd);
Set(BACk(enabled)=true, BACk(background)=ColorCheckButton);
Set(BASh(enabled)=true, BASh(background)=ColorShowButton);
elif ts<>TEXTCylinder and
simplify(normal(user_r - radius))=0 then
Set(TFrck=TEXTIncorrect,
TFrck(background)=ColorIncorrect, TFrck(foreground)=ColorIncorrectFrgd);
Set(reply=cat(TEXTreply1r, trys[randtry()]),
reply(background)=ColorIncorrect, reply(foreground)=ColorIncorrectFrgd);
else
Set(TFrck=TEXTIncorrect,
TFrck(background)=ColorIncorrect, TFrck(foreground)=ColorIncorrectFrgd);
Set(reply=cat(sorry[randsorry()], trys[randtry()]),
reply(background)=ColorIncorrect, reply(foreground)=ColorIncorrectFrgd);
end if;
end proc:show_r:=proc()
global r;
options `Copyright 2007, Philip B. Yasskin and Douglas Meade, Maplets for Calculus`;
Set(TFr=r);
Set(TFrck=TEXTShown,
TFrck(background)=ColorShow, TFrck(foreground)=ColorShowFrgd);
Set(reply=shows[randshow()],
reply(background)=ColorShow, reply(foreground)=ColorShowFrgd);
Set(BACk(enabled)=true, BACk(background)=ColorCheckButton);
Set(BASh(enabled)=true, BASh(background)=ColorShowButton);
end proc:check_A:=proc()
global r, A, CorrectA, CorrectD;
local user_A, notAcirc;
options `Copyright 2007, Philip B. Yasskin and Douglas Meade, Maplets for Calculus`;
notAcirc:=2*Pi*r;
user_A:=Get(TFA::algebraic);
if simplify(normal(user_A - A))=0 then
Set(TFAck=TEXTCorrect,
TFAck(background)=ColorCorrect, TFAck(foreground)=ColorCorrectFrgd);
Set(reply=cat(great[randgreat()], nexts1[randnext1()]),
reply(background)=ColorCorrect, reply(foreground)=ColorCorrectFrgd);
CorrectA:=true;
if CorrectD then
Set(BWintCk(enabled)=true, BWintCk(background)=ColorCheckButton);
Set(BWintSh(enabled)=true, BWintSh(background)=ColorShowButton);
end if;
elif has(user_A,pi) then
Set(TFAck=TEXTWarning,
TFAck(background)=ColorWarning, TFAck(foreground)=ColorWarningFrgd);
Set(reply=cat(TEXTreply2a, trys[randtry()]),
reply(background)=ColorWarning, reply(foreground)=ColorWarningFrgd);
elif has(user_A,dy) then
Set(TFAck=TEXTWarning,
TFAck(background)=ColorWarning, TFAck(foreground)=ColorWarningFrgd);
Set(reply=cat(TEXTreply2c, trys[randtry()]),
reply(background)=ColorWarning, reply(foreground)=ColorWarningFrgd);
elif simplify(normal(user_A - notAcirc))=0 then
Set(TFAck=TEXTIncorrect,
TFAck(background)=ColorIncorrect, TFAck(foreground)=ColorIncorrectFrgd);
Set(reply=cat(TEXTreply2b, trys[randtry()]),
reply(background)=ColorIncorrect, reply(foreground)=ColorIncorrectFrgd);
else
Set(TFAck=TEXTIncorrect,
TFAck(background)=ColorIncorrect, TFAck(foreground)=ColorIncorrectFrgd);
Set(reply=cat(sorry[randsorry()], trys[randtry()]),
reply(background)=ColorIncorrect, reply(foreground)=ColorIncorrectFrgd);
end if;
end proc:show_A:=proc()
global A, CorrectA, CorrectD;
options `Copyright 2007, Philip B. Yasskin and Douglas Meade, Maplets for Calculus`;
Set(TFA=A);
Set(TFAck=TEXTShown,
TFAck(background)=ColorShow, TFAck(foreground)=ColorShowFrgd);
Set(reply=shows[randshow()],
reply(background)=ColorShow, reply(foreground)=ColorShowFrgd);
CorrectA:=true;
if CorrectD then
Set(BWintCk(enabled)=true, BWintCk(background)=ColorCheckButton);
Set(BWintSh(enabled)=true, BWintSh(background)=ColorShowButton);
end if;
end proc:check_D:=proc()
global _D, ts, radius, CorrectA, CorrectD;
local user_D;
options `Copyright 2007, Philip B. Yasskin and Douglas Meade, Maplets for Calculus`;
user_D:=Get(TFD::algebraic);
if simplify(normal(user_D - _D))=0 then
Set(TFDck=TEXTCorrect,
TFDck(background)=ColorCorrect, TFDck(foreground)=ColorCorrectFrgd);
Set(reply=cat(great[randgreat()], nexts1[randnext1()]),
reply(background)=ColorCorrect, reply(foreground)=ColorCorrectFrgd);
CorrectD:=true:
if CorrectA then
Set(BWintCk(enabled)=true, BWintCk(background)=ColorCheckButton);
Set(BWintSh(enabled)=true, BWintSh(background)=ColorShowButton);
end if;
elif simplify(normal(user_D - `if`(ts=TEXTSphere,2*radius,H)))=0 then
Set(TFDck=TEXTIncorrect,
TFDck(background)=ColorIncorrect, TFDck(foreground)=ColorIncorrectFrgd);
Set(reply=cat(TEXTreply3a, trys[randtry()]),
reply(background)=ColorIncorrect, reply(foreground)=ColorIncorrectFrgd);
elif simplify(normal(user_D - radius))=0 then
Set(TFDck=TEXTIncorrect,
TFDck(background)=ColorIncorrect, TFDck(foreground)=ColorIncorrectFrgd);
Set(reply=cat(TEXTreply3b, trys[randtry()]),
reply(background)=ColorIncorrect, reply(foreground)=ColorIncorrectFrgd);
else
Set(TFDck=TEXTIncorrect,
TFDck(background)=ColorIncorrect, TFDck(foreground)=ColorIncorrectFrgd);
Set(reply=cat(sorry[randsorry()], trys[randtry()]),
reply(background)=ColorIncorrect, reply(foreground)=ColorIncorrectFrgd);
end if;
end proc:show_D:=proc()
global _D, CorrectA, CorrectD;
options `Copyright 2007, Philip B. Yasskin and Douglas Meade, Maplets for Calculus`;
Set(TFD=_D);
Set(TFDck=TEXTShown,
TFDck(background)=ColorShow, TFDck(foreground)=ColorShowFrgd);
Set(reply=shows[randshow()],
reply(background)=ColorShow, reply(foreground)=ColorShowFrgd);
CorrectD:=true:
if CorrectA then
Set(BWintCk(enabled)=true, BWintCk(background)=ColorCheckButton);
Set(BWintSh(enabled)=true, BWintSh(background)=ColorShowButton);
end if;
end proc:check_Wint:=proc()
global Wint, _D, A, ymin, ymax, waterlevel, ts, rhog, H, radius;
local user_Wint;
options `Copyright 2007, Philip B. Yasskin and Douglas Meade, Maplets for Calculus`;
user_Wint:=Get(TFWint::algebraic);
if simplify(normal(user_Wint - Wint))=0 then
Set(TFWintck=TEXTCorrect,
TFWintck(background)=ColorCorrect, TFWintck(foreground)=ColorCorrectFrgd);
Set(reply=cat(great[randgreat()], nexts1[randnext1()]),
reply(background)=ColorCorrect, reply(foreground)=ColorCorrectFrgd);
Set(BWvalCk(enabled)=true, BWvalCk(background)=ColorCheckButton);
Set(BWvalSh(enabled)=true, BWvalSh(background)=ColorShowButton);
elif has(user_Wint,pi) then
Set(TFWintck=TEXTWarning,
TFWintck(background)=ColorWarning, TFWintck(foreground)=ColorWarningFrgd);
Set(reply=cat(TEXTreply2a, trys[randtry()]),
reply(background)=ColorWarning, reply(foreground)=ColorWarningFrgd);
elif has(user_Wint,dy) then
Set(TFWintck=TEXTWarning,
TFWintck(background)=ColorWarning, TFWintck(foreground)=ColorWarningFrgd);
Set(reply=cat(TEXTreply4a, trys[randtry()]),
reply(background)=ColorWarning, reply(foreground)=ColorWarningFrgd);
elif simplify(user_Wint=Int(_D*A, y=ymin..ymax)) then
Set(TFWintck=TEXTIncorrect,
TFWintck(background)=ColorIncorrect, TFWintck(foreground)=ColorIncorrectFrgd);
Set(reply=cat(TEXTreply4b, trys[randtry()]),
reply(background)=ColorIncorrect, reply(foreground)=ColorIncorrectFrgd);
elif simplify(user_Wint=Int(rhog*A, y=ymin..ymax)) then
Set(TFWintck=TEXTIncorrect,
TFWintck(background)=ColorIncorrect, TFWintck(foreground)=ColorIncorrectFrgd);
Set(reply=cat(TEXTreply4c, trys[randtry()]),
reply(background)=ColorIncorrect, reply(foreground)=ColorIncorrectFrgd);
elif waterlevel=1/2 and (
( ts<>TEXTSphere and
simplify(user_Wint=Int(rhog*_D*A, y=0..H))) or
( ts=TEXTSphere and
simplify(user_Wint=Int(rhog*_D*A, y=-radius..radius)))
) then
Set(TFWintck=TEXTIncorrect,
TFWintck(background)=ColorIncorrect, TFWintck(foreground)=ColorIncorrectFrgd);
Set(reply=cat(TEXTreply4d, trys[randtry()]),
reply(background)=ColorIncorrect, reply(foreground)=ColorIncorrectFrgd);
else
Set(TFWintck=TEXTIncorrect,
TFWintck(background)=ColorIncorrect, TFWintck(foreground)=ColorIncorrectFrgd);
Set(reply=cat(sorry[randsorry()], trys[randtry()]),
reply(background)=ColorIncorrect, reply(foreground)=ColorIncorrectFrgd);
end if;
end proc:show_Wint:=proc()
global Wint;
options `Copyright 2007, Philip B. Yasskin and Douglas Meade, Maplets for Calculus`;
Set(TFWint=Wint);
Set(TFWintck=TEXTShown,
TFWintck(background)=ColorShow, TFWintck(foreground)=ColorShowFrgd);
Set(reply=shows[randshow()],
reply(background)=ColorShow, reply(foreground)=ColorShowFrgd);
Set(BWvalCk(enabled)=true, BWvalCk(background)=ColorCheckButton);
Set(BWvalSh(enabled)=true, BWvalSh(background)=ColorShowButton);
end proc:check_Wval:=proc()
global Wval;
local user_Wval;
options `Copyright 2007, Philip B. Yasskin and Douglas Meade, Maplets for Calculus`;
user_Wval:=Get(TFWval::algebraic);
if simplify(normal(user_Wval - Wval))=0 then
Set(TFWvalck=TEXTCorrect,
TFWvalck(background)=ColorCorrect, TFWvalck(foreground)=ColorCorrectFrgd);
Set(reply=cat(great[randgreat()], nexts2[randnext2()]),
reply(background)=ColorCorrect, reply(foreground)=ColorCorrectFrgd);
elif has(user_Wval,pi) then
Set(TFWvalck=TEXTWarning,
TFWvalck(background)=ColorWarning, TFWvalck(foreground)=ColorWarningFrgd);
Set(reply=cat(TEXTreply2a, trys[randtry()]),
reply(background)=ColorWarning, reply(foreground)=ColorWarningFrgd);
else
Set(TFWvalck=TEXTIncorrect,
TFWvalck(background)=ColorIncorrect, TFWvalck(foreground)=ColorIncorrectFrgd);
Set(reply=cat(sorry[randsorry()], trys[randtry()]),
reply(background)=ColorIncorrect, reply(foreground)=ColorIncorrectFrgd);
end if;
end proc:show_Wval:=proc()
global Wval;
options `Copyright 2007, Philip B. Yasskin and Douglas Meade, Maplets for Calculus`;
Set(TFWval=Wval);
Set(TFWvalck=TEXTShown,
TFWvalck(background)=ColorShow, TFWvalck(foreground)=ColorShowFrgd);
Set(reply=shows[randshow()],
reply(background)=ColorShow, reply(foreground)=ColorShowFrgd);
end proc:Pumping_Work:=Maplet(onstartup=RunWindow(MAIN),
Window[MAIN](title=TEXTtitleMAIN, defaultbutton=BHint0,
[ halign=none, valign=none, inset=0, spacing=0, background=ColorBkgd,
[ halign=none, background=ColorBkgd,
"Tank Shape",
DropDownBox[tankshape](TEXTCylinder, [TEXTCylinder, TEXTCone, TEXTSphere], width=100),
Button(TEXTBNewProblem, Evaluate(function="new_prob"), background=ColorNewButton),
HorizontalGlue(),
Button[BHint0](TEXTBHint, onclick=AH, background=ColorHintButton),
Button(TEXTBQuit, Shutdown(), background=ColorCloseButton)
],
[ halign=none, background=ColorBkgd,
TextBox[problem](width=70, height=3)
],
[ halign=none, inset=0, spacing=0, background=ColorBkgd,
[ background=ColorBkgd, border=true,
caption=TEXTCapPlot,
Plotter[myplot](width=250, height=250),
"To rotate the plot, click in the plot and drag the mouse."
],
[ background=ColorBkgd, inset=0, spacing=0,
BoxColumn( halign=none, valign=none, background=ColorBkgd, border=true,
caption=TEXTCap1,
[ halign=none, background=ColorBkgd, inset=0,
"r =",
TextField[TFr](width=30, background=ColorInput),
Button(TEXTBHint, onclick=Ar, background=ColorHintButton),
Button[BrCk](TEXTBCheck, Evaluate(function="check_r"),
enabled=false, background=ColorDisable),#ColorCheckButton),
TextField[TFrck](width=6, editable=false, background=ColorMessage),
Button[BrSh](TEXTBShow, Evaluate(function="show_r"),
enabled=false, background=ColorDisable)#ColorShowButton)
],
[ halign=none, background=ColorBkgd, inset=0,
"A =",
TextField[TFA](width=30, background=ColorInput),
Button(TEXTBHint, onclick=AA, background=ColorHintButton),
Button[BACk](TEXTBCheck, Evaluate(function="check_A"),
enabled=false, background=ColorDisable),#ColorCheckButton),
TextField[TFAck](width=6, editable=false, background=ColorMessage),
Button[BASh](TEXTBShow, Evaluate(function="show_A"),
enabled=false, background=ColorDisable)#ColorShowButton)
],
[ halign=none, background=ColorBkgd, inset=0,
"D =",
TextField[TFD](width=30, background=ColorInput),
Button(TEXTBHint, onclick=AD, background=ColorHintButton),
Button[BDCk](TEXTBCheck, Evaluate(function="check_D"),
enabled=false, background=ColorDisable),#ColorCheckButton),
TextField[TFDck](width=6, editable=false, background=ColorMessage),
Button[BDSh](TEXTBShow, Evaluate(function="show_D"),
enabled=false, background=ColorDisable)#ColorShowButton)
]
),
[ halign=none, background=ColorBkgd, border=true,
caption=TEXTCap2,
"W =",
TextField[TFWint](width=30, background=ColorInput),
Button(TEXTBHint, onclick=AWint, background=ColorHintButton),
Button[BWintCk](TEXTBCheck, Evaluate(function="check_Wint"),
enabled=false, background=ColorDisable),#ColorCheckButton),
TextField[TFWintck](width=6, editable=false, background=ColorMessage),
Button[BWintSh](TEXTBShow, Evaluate(function="show_Wint"),
enabled=false, background=ColorDisable)#ColorShowButton)
],
[ halign=none, background=ColorBkgd, border=true,
caption=TEXTCap3,
"W =",
TextField[TFWval](width=30, background=ColorInput),
Button(TEXTBHint, onclick=AWval, background=ColorHintButton),
Button[BWvalCk](TEXTBCheck, Evaluate(function="check_Wval"),
enabled=false, background=ColorDisable),#ColorCheckButton),
TextField[TFWvalck](width=6, editable=false, background=ColorMessage),
Button[BWvalSh](TEXTBShow, Evaluate(function="show_Wval"),
enabled=false, background=ColorDisable)#ColorShowButton)
]
]
],
[ background=ColorBkgd,
TextField[reply](width=70, editable=false, background=ColorMessage),
Label(Image(Logo)),
Label(Image(LIBLogo))
],
[ halign=none, background=ColorFooter, inset=0, spacing=0,
Label("Programmer: Austin B. Probe", font=FontFooter),
HorizontalGlue(),
Label("\302\251 Copyright P Yasskin 2007", font=FontFooter)
]
]),#End Column, End Window
Window[Hint](title=TEXTtitleHINT,
[ halign=none, background=ColorBkgd,
[ halign=none, background=ColorBkgd,
MathMLViewer(value=MathML[Export](W=Int('rho'*'g'*`D `*'A','y'='a'..'b')),
width=250, height=75),
HorizontalGlue(),
Button(TEXTBClose, CloseWindow(Hint), background=ColorCloseButton)
],
TextBox(TEXTHint, width=61, height=11)
]),
Action[AH](RunWindow(Hint)),
Window[Hintr](title=TEXTtitleHINT,
[ halign=none, background=ColorBkgd,
[ halign=none, background=ColorBkgd,
HorizontalGlue(),
Button(TEXTBClose, CloseWindow(Hintr), background=ColorCloseButton)
],
TextBox(TEXTHintr, width=70, height=8)
]),
Action[Ar](RunWindow(Hintr)),
Window[HintA](title=TEXTtitleHINT,
[ halign=none, background=ColorBkgd,
[ halign=none, background=ColorBkgd,
HorizontalGlue(),
Button(TEXTBClose, CloseWindow(HintA), background=ColorCloseButton)
],
TextBox(TEXTHintA, width=72, height=6)
]),
Action[AA](RunWindow(HintA)),
Window[HintD](title=TEXTtitleHINT,
[ halign=none, background=ColorBkgd,
[ halign=none, background=ColorBkgd,
HorizontalGlue(),
Button(TEXTBClose, CloseWindow(HintD), background=ColorCloseButton)
],
TextBox(TEXTHintD, width=58, height=5)
]),
Action[AD](RunWindow(HintD)),
Window[HintWint](title=TEXTtitleHINT,
[ halign=none, background=ColorBkgd,
[ halign=none, background=ColorBkgd,
HorizontalGlue(),
Button(TEXTBClose, CloseWindow(HintWint), background=ColorCloseButton)
],
TextBox(TEXTHintWint, width=72, height=4)
]),
Action[AWint](
RunWindow(HintWint),
SetOption(TFWint=" Int( rho * g * D * A, y = min..max) ")
),
Window[HintWval](title=TEXTtitleHINT,
[ halign=none, background=ColorBkgd,
[ halign=none, background=ColorBkgd,
HorizontalGlue(),
Button(TEXTBClose, CloseWindow(HintWval), background=ColorCloseButton)
],
TextBox(TEXTHintWval, width=50, height=4)
]),
Action[AWval](RunWindow(HintWval))
):Maplets[Display](Pumping_Work);