restart:#"m01_p09"Se dispone de un cilindro horizontal de 15 cm2 de secci\363n y 40 cm de largo, cerrado por un extremo. En el otro extremo se coloca un \351mbolo de hierro de 1 cm de espesor y se empuja hasta conseguir llevarlo a 5 cm del fondo, comprimiendo el aire encerrado. Se pide:a) Trabajo que ser\355a necesario aportar (neto, p.e., desde un dep\363sito mec\341nico reversible) suponiendo que la compresi\363n fuese muy r\341pida.b) Como en a), pero suponiendo que la compresi\363n fuese muy lenta.c) Exerg\355a de la configuraci\363n final (atemperada)d) Sup\363ngase que desde este \372ltimo estado se suelta el \351mbolo; calcular la aceleraci\363n inicial y la posici\363n en la que se alcanzar\355a la velocidad m\341xima.e) Velocidad m\341xima y velocidad a la salida.f) Representar la posici\363n y la velocidad en funci\363n del tiempoDatos:read"../therm_eq.m":read"../therm_proc.m":with(therm_proc):su1:="Aire":su2:="Hierro_fundido":dat:=[A=0.0015*m_^2,L=0.4*m_,e=0.01*m_,x1=0.05*m_]:dat:=[op(dat),x0=subs(dat,L-e*0),mE=subs(dat,rho*A*e)];

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a) Trabajo que ser\355a necesario aportar (neto, p.e., desde un dep\363sito mec\341nico reversible) suponiendo que la compresi\363n fuese muy r\341pida.T1:=T0*(x0/x1)^(gamma-1);T1_:=evalf(subs(dat,T1));p1:=p0*(x0/x1)^gamma;p1_:=evalf(subs(dat,p1)):p1__:=evalf(%/(1e3*Pa_/kPa_));

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W1:=Int((p0*(x0/x)^gamma-p0)*A,x=x0..x1);W1:=int((p0*(x0/x)^gamma-p0)*A,x=x0..x1);W1_:=subs(dat,evalf(subs(dat,W1)));

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b) Como en a), pero suponiendo que la compresi\363n fuese muy lenta.T1:=T0;T1_:=evalf(subs(dat,T1));p1:=p0*(x0/x1);p1_:=evalf(subs(dat,p1)):p1__:=evalf(%/(1e3*Pa_/kPa_));dat:=op([dat]),'p1'=p1_:

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W1:=Int((p0*(x0/x)-p0)*A,x=x0..x1);W1:=int((p0*(x0/x)-p0)*A,x=x0..x1);W1_:=evalf(subs(dat,SI0,W1))*J_;

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NiM+SSRXMV9HNiIsJEkkSl98aXJHRiUkIStdI1xtQSghIik=

c) Exerg\355a de la configuraci\363n final (atemperada).NOTA. Esta pregunta no es del tema 1 (Energ\355a). (Puede pasar al siguiente apartado).DPhi:=W1_;DPhi:=DE+p0*DV-T0*DS;DPhi_:=subs(DE=0,DV=A*x1*(1-p1/p0),DS=-m*R*ln(p1/p0),DPhi);DPhi__:=subs(SI2,SI1,evalf(subs(m=p0*A*x0/R/T0,dat,%)));

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d) Sup\363ngase que desde este \372ltimo estado se suelta el \351mbolo; calcular la aceleraci\363n inicial y la posici\363n en la que se alcanzar\355a la velocidad m\341xima.acel:=A*(p-p0)/mE;acel:=A*(p1*(x1/x)^gamma-p0)/mE;acel0_:=subs(dat,evalf(subs(x=x1,dat,acel)));

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x_velmax:=solve(acel=0,x);x_velmax_:=evalf(subs(dat,x_velmax));

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e) Velocidad m\341xima y velocidad a la salida.deq1:=diff(x(t),t)=xp(t);deq2:=diff(xp(t),t)=subs(x=x(t),acel);deq1_:=deq1:deq2_:=subs(dat,SI0,deq2);ic1:=x(0)=x1;ic2:=xp(0)=0;ic1_:=subs(dat,SI0,ic1);ic2_:=ic2:

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dsol1:=dsolve({deq1_,deq2_,ic1_,ic2_},{x(t),xp(t)},numeric);

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(se ha hecho como si no escapara.)with(plots):odeplot(dsol1,[t,x(t)],0..0.1,numpoints=100,labels=["t(s)","x(m)"],colour=black);odeplot(dsol1,[t,xp(t)],0..0.1,numpoints=100,labels=["t(s)","v(m/s)"],colour=black);odeplot(dsol1,[x(t),xp(t)],0..0.05,numpoints=100,labels=["x(m)","v(m/s)"],colour=black);

Warning, the name changecoords has been redefined

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

Ec:=Int(mE*acel,x=x1..x);Ec:=int(mE*acel,x=x1..x2);vel:=sqrt('2*Ec/mE');

NiM+SSNFY0c2Ii1JJEludEc2JEkqcHJvdGVjdGVkR0YpSShfc3lzbGliR0YlNiQqJkkiQUdGJSIiIiwmKipJI3AwR0YlRi5JI3gwR0YlRi5JI3gxR0YlISIiKSomRjNGLkkieEdGJUY0SSZnYW1tYUdGKUYuRi5GMUY0Ri4vRjc7RjNGNw==

NiM+SSNFY0c2IiwkKixJI3AwR0YlIiIiSSJBR0YlRiksLiomSSN4MUdGJUYpSSN4MEdGJUYpISIiKiRGLSIiI0YpKiZGLUYxSSZnYW1tYUdJKnByb3RlY3RlZEdGNEYpRi8qKEYuRilJI3gyR0YlRiktSSRleHBHNiRGNEkoX3N5c2xpYkdGJTYjKiZGM0YpLUkjbG5HRjk2IyomRi1GKUY2Ri9GKUYpRikqJkY2RilGLUYpRi8qKEY2RilGLUYpRjNGKUYpRilGLUYvLCZGM0YpRi9GKUYvRi8=NiM+SSR2ZWxHNiIqJiIiIyMiIiJGJyomSSNFY0dGJUYpSSNtRUdGJSEiIkYo

vel_:=evalf(subs(dat,SI0,vel));velmax_:=evalf(subs(x2=x_velmax_/m_,vel_))*m_/s_;velsal_:=evalf(subs(x2=subs(dat,x0)/m_,vel_))*m_/s_;

NiM+SSV2ZWxfRzYiLCQqJCwoJCIrdGxaUjkhIiciIiIqJkkjeDJHRiVGLC1JJGV4cEc2JEkqcHJvdGVjdGVkR0YySShfc3lzbGliR0YlNiMsJC1JI2xuR0YxNiMsJCokRi4hIiIkIiImISIjJCIrM0puKlIiISIqRiwkIStXbyc+dSMhIiZGLiQhKzhJJylwOEYrI0YsIiIjJCIraU5AOTlGQQ==NiM+SSh2ZWxtYXhfRzYiLCQqJkkkbV98aXJHRiUiIiJJJHNffGlyR0YlISIiJCIrOj0qZnYjISIpNiM+SSh2ZWxzYWxfRzYiLCQqJkkkbV98aXJHRiUiIiJJJHNffGlyR0YlISIiJCIrMiIpUkVDISIp

f) Representar la posici\363n y la velocidad en funci\363n del tiempoplot([vel_,[[x_velmax_/m_,0],[x_velmax_/m_,30]],[[subs(dat,x0)/m_,0],[subs(dat,x0)/m_,30]]],x2=0..0.7,labels=["t(s)","v(m/s)"],colour=black);

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