Center of Mass of a BarJonathan Campoverde and Emily Slackrestart:with(Maplets[Tools]): with(Maplets[Elements]): with(plots): with(plottools):
StartEngine();randomize():lightorange:="#FFB300":rand10:=rand(1..10):
rand5:=rand(1..5):
rand01:=rand(0..1):
rand4:=rand(0..4):
Phis:=[0, Pi, Pi/2, 3*Pi/2, Pi/4, 3*Pi/4, 5*Pi/4, 7*Pi/4, Pi/6, Pi/3, 2*Pi/3, 5*Pi/6, 7*Pi/6, 4*Pi/3, 5*Pi/3, 11*Pi/6]:
randPhi:=rand(1..16):ask:=proc()
global L, rho, Mass, Moment, xbar;
local f, Phi1, barplot;
L:=rand10();
Phi1:=Phis[randPhi()]:
f:=rand4();
Mass:=0;
while evalf(Mass)<=0 do
if f<2 then
rho:=randpoly(x, degree=3, terms=2, coeffs=rand(0..9));
elif f=2 then
rho:=rand5()*Pi*(1+sin(Phi1*x));
elif f=3 then
rho:=rand5()*Pi*(1+cos(Phi1*x));
elif f=4 then
rho:=rand5()*exp((-1)^rand01()*rand5()*x);
end if:
Mass:=int(rho,x=0..L);
end do;
Moment:=int(rho*x,x=0..L);
xbar:=Moment/Mass;
Set(length=L);
Set(density=rho);
Set(TFM="");
Set(TFM1="");
Set(TFxbar="");
Set(reply="");
Set(LM(caption)="M = ");
Set(LM1(caption)="M_1 = ");
Set(LXbar(caption)="x_cm =");
barplot:=display(densityplot(-rho, x=0..L, y=0..L/10, style=patchnogrid, color=yellow),
scaling=constrained, tickmarks=[[0,L],0]);
Set(BarPlot=barplot);
end proc:check_m:=proc()
global Mass;
local userMass;
userMass:=Get(TFM::realcons):
if simplify(userMass-Mass=0) then
Set(reply="Correct value of the Mass! Now do the Moment.")
else
Set(reply="Incorrect Mass. Try again.")
end if;
end proc:show_m:=proc()
global Mass;
Set(TFM=Mass);
Set(reply="Next time try it yourself.")
end proc:LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yncheck_m1:=proc()
global Moment;
local userMoment;
userMoment:=Get(TFM1::realcons):
if simplify(userMoment-Moment=0) then
Set(reply="Correct value of the Moment! Now do x_cm.")
else
Set(reply="Incorrect Moment. Try again.")
end if;
end proc:show_m1:=proc()
global Moment;
Set(TFM1=Moment);
Set(reply="Next time try it yourself.")
end proc:LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yncheck_xbar:=proc()
global xbar;
local userxbar;
userxbar:=Get(TFxbar::realcons):
if simplify(userxbar-xbar=0) then
Set(reply="Correct value of x_cm!")
else
Set(reply="Incorrect x_cm. Try again.")
end if;
end proc:show_xbar:=proc()
global xbar;
Set(TFxbar=xbar);
Set(reply="Next time try it yourself.")
end proc:LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Ynhint_m:=proc()
Set(LM(caption)="M = Int( rho, x=0..L ) =")
end proc:hint_m1:=proc()
Set(LM1(caption)="M_1 = Int( rho * x, x=0..L ) =")
end proc:hint_xbar:=proc()
Set(LXbar(caption)="x_cm = M_1 / M =")
end proc:CenterBar:=Maplet(onstartup=RunWindow(MAIN),
Font[helv10]("helvetica",10),
Window[MAIN](title="Center of Mass of a Bar",
[ halign=none, valign=none, inset=0, spacing=0,
[ halign=none,
Button("New Problem", Evaluate(function="ask"), background=magenta),
HorizontalGlue(),
Button("Quit",Shutdown(), background=pink)
],
[ halign=none, inset=0, spacing=0,
[ valign=none, inset=0, spacing=0, border=true,
caption="Problem Statement",
[ halign=none,
"Find the mass and center of mass of a bar with length",
TextField[length](width=3, editable=false, background=white),
"cm ",
HorizontalGlue()
],
[ halign=none,
"and with linear density rho =",
TextField[density](width=15, editable=false, background=white),
"g/cm",
HorizontalGlue()
],
[ halign=none,
"where x is measured from the left end.",
HorizontalGlue()
]
],
[ border=true,
caption="Density Plot of the Bar",
Plotter[BarPlot](width=150, height=100)
]
],
[ halign=none, border=true,
caption="Find the mass of the bar:",
Label[LM]("M = "),
TextField[TFM](width=25),
HorizontalGlue(),
Button("Hint", Evaluate(function="hint_m"), background=lightorange),
Button("Check", Evaluate(function="check_m"), background=green),
Button("Show", Evaluate(function="show_m"), background=lightorange)
],
[ halign=none, border=true,
caption="Find the moment of the bar:",
Label[LM1] ("M_1 = "),
TextField[TFM1](width=25),
HorizontalGlue(),
Button("Hint", Evaluate(function="hint_m1"), background=lightorange),
Button("Check", Evaluate(function="check_m1"), background=green),
Button("Show", Evaluate(function="show_m1"), background=lightorange)
],
[ halign=none, border=true,
caption="Find the center of mass of the bar:",
Label[LXbar]("x_cm ="),
TextField[TFxbar](width=25),
HorizontalGlue(),
Button("Hint", Evaluate(function="hint_xbar"), background=lightorange),
Button("Check", Evaluate(function="check_xbar"), background=green),
Button("Show", Evaluate(function="show_xbar"), background=lightorange)
],
[ halign=none,
TextField[reply](width=40)
],
BoxRow(background="#DDFFFF", inset=0, spacing=0,
Label("Programmers: Jonathan Campoverde and Emily Slack", font=helv10),
HorizontalGlue(),
Label("@ Copyright P Yasskin 2007", font=helv10)
)
]
)
):Maplets[Display]( CenterBar );