restart:with(Maplets[Tools]): with(Maplets[Elements]): with(plots): with(plottools):
StartEngine();rand10:=rand(1..10):
rand5:=rand(1..5):
rand25:=rand(1..25):ask:=proc()
global rand10, rand5, rand25, hgt, wgt, dens, Wwgt,Wdrope,Wrope,Wtotal;
local building,pulley,rope1,rope2, rope3,mass,tplot,plotlist,t,workplot;
hgt:=10*rand10();
Set('high'=hgt);
dens:=rand5();
Set('density'=dens);
wgt:=rand25();
Set('weigh'=wgt);
Wwgt:=wgt*hgt;
Wdrope:=dens*(hgt-y)*dy;
Wrope:=1/2*dens*hgt^2;
Wtotal:=Wwgt+Wrope;
Set(answer_w="");
Set(answer_r="");
Set(answer_t="");
Set(answer_rt="");
Set(reply="");
Set('LW'(caption)=" W =");
Set('LdR'(caption)="dW =");
Set('LR'(caption)=" W =");
Set('LT'(caption)=" W =");
building:=rectangle([0,0], [hgt/10,hgt], color=red):pulley:=circle([hgt/10+hgt/40,hgt+hgt/10],hgt/40, color=grey):rope1:=plot([[0,hgt+1.25*hgt/10],[hgt/10+hgt/40,hgt+1.25*hgt/10]], color=black):rope2:=arc([hgt/10+hgt/40,hgt+hgt/10],hgt/40, 0..Pi/2, color=black):plotlist:=NULL;
for t from 0 by hgt/20 to hgt dorope3:=plot([[hgt/10+hgt/20,t+hgt/20],[hgt/10+hgt/20,hgt+hgt/10]], color=black):mass:=rectangle([hgt/10+hgt/40,t], [hgt/10+3*hgt/40,t+hgt/20], color=yellow):tplot:=textplot([hgt/10+3*hgt/20,t+hgt/40,convert(wgt,string)]);
plotlist:=plotlist, display([building,pulley,rope1,rope2, rope3,mass,tplot]);
end do:workplot:=display([plotlist], scaling=constrained, insequence=true, xtickmarks=0, ytickmarks=[0,hgt]);
Set('WorkPlot'=workplot);
end proc:LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yncheck_w:=proc()
global Wwgt;
local userWwgt;
userWwgt:=Get('answer_w'::anything):
if simplify(userWwgt-Wwgt=0)
then Set('reply'="Correct work for lifting the weight! Now do the rope.")
else Set('reply'="Incorrect. Try again.")
end if;
end proc:show_w:=proc()
global Wwgt;
Set('answer_w'=Wwgt);
end proc:LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yncheck_dr:=proc()
global Wdrope;
local userWdrope;
userWdrope:=Get('answer_r'::anything):
if simplify(userWdrope-Wdrope=0)
then Set('reply'="Correct work for lifting a piece of the rope! Now integrate over the rope.")
else Set('reply'="Incorrect. Try again.")
end if;
end proc:show_dr:=proc()
global Wdrope;
Set('answer_r'=Wdrope);
end proc:LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yncheck_r:=proc()
global Wrope;
local userWrope;
userWrope:=Get('answer_t'::anything):
if simplify(userWrope-Wrope=0)
then Set('reply'="Correct work for lifting the whole rope! Now total the rope and weight.")
else Set('reply'="Incorrect. Try again.")
end if;
end proc:show_r:=proc()
global Wrope;
Set('answer_t'=Wrope);
end proc:LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yncheck_t:=proc()
global Wtotal;
local userWtotal;
userWtotal:=Get('answer_rt'::anything):
if simplify(userWtotal-Wtotal=0)
then Set('reply'="Super! Try another problem.")
else Set('reply'="Incorrect. Try again.")
end if;
end proc:show_t:=proc()
global Wtotal;
Set('answer_rt'=Wtotal);
end proc:
hint_w:=proc()
Set('LW'(caption)="W = FD =")
end proc;hint_dr:=proc()
Set('LdR'(caption)="dW = Density * (Height-y) * dy =")
end proc;hint_r:=proc()
Set('LR'(caption)="W = Integral of Previous Answer =")
end proc;hint_t:=proc()
Set('LT'(caption)="W = W(entire rope) + W(weight) =")
end proc;
WorkRope:=Maplet(onstartup = RunWindow(MAIN),
Font[helv10]("helvetica",10),
Window[MAIN]('title'="Work of a Rope",
[ [ Button("New Problem", Evaluate('function' = "ask")), Button("Quit",Shutdown())
],
[ [ BoxColumn( border=true,
[ "Find the work needed to lift a",
TextField['weigh']('width'=3, 'editable'='false'),
"lb object by",
TextField['high']('width'=3, 'editable'='false'),
"ft"
],
[ "up a building using a rope whose density is",
TextField['density']('width'=3, 'editable'='false'),
"lb/ft."
],
[ "Note: y is measured from the base of the building."
]
),
[ border = true,
caption="Find the work to lift the weight alone:",
Label[LW](" W ="), TextField['answer_w']('width'=25),
HorizontalGlue(),
Button("Check", Evaluate('function' = "check_w")),
Button("Show", Evaluate('function' = "show_w")),
Button("Hint", Evaluate('function' = "hint_w"))
],
[ border = true,
caption="Find the work to lift the piece of rope of length dy which is a distance y from the bottom:",
Label[LdR] ("dW ="), TextField['answer_r']('width'=25),
HorizontalGlue(),
Button("Check", Evaluate('function' = "check_dr")),
Button("Show", Evaluate('function' = "show_dr")),
Button("Hint", Evaluate('function' = "hint_dr"))
],
[ border = true,
caption="Find the work to lift the entire rope:",
Label[LR] (" W ="), TextField['answer_t']('width'=25),
HorizontalGlue(),
Button("Check", Evaluate('function' = "check_r")),
Button("Show", Evaluate('function' = "show_r")),
Button("Hint", Evaluate('function' = "hint_r"))
],
[ border=true,
caption="Find the work to lift the entire rope with the weight attached:",
Label[LT](" W ="), TextField['answer_rt']('width'=25),
HorizontalGlue(),
Button("Check", Evaluate('function' = "check_t")),
Button("Show", Evaluate('function' = "show_t")),
Button("Hint", Evaluate('function' = "hint_t"))
]
],
[ [ Button[BPlay]("Play", onclick=SetOption('WorkPlot'(play)=true) ),
Button[BStop]("Stop", onclick=SetOption('WorkPlot'(pause)=true) )
],
[ Button[BForward]("Forward", onclick= Action(SetOption('WorkPlot'(pause)=true),
SetOption('WorkPlot'(frame_forward)=true)) ),
Button[BReverse]("Reverse", onclick= Action(SetOption('WorkPlot'(pause)=true),
SetOption('WorkPlot'(frame_backwards)=true)) )
],
[ Plotter[WorkPlot](width=150, height=300)
]
]
],
[ TextField['reply']('width'=70)
],
BoxRow('background'="#DDFFFF", 'inset'=0, 'spacing'=0,
Label("Programmers: Calderon and Davidson", 'font'=helv10),
HorizontalGlue(),
Label("Copyright 2006, D.B. Meade and P.B. Yasskin", 'font'=helv10),
HorizontalGlue(),
Label("v. 1.2a May 2006", 'font'=helv10)
)
]
)
):Maplets[Display]( WorkRope );