PROBLEMA 02

Datos
r1 y r5 = 5.0
r2, r3 y r4 = 7.0
A total = 618.9mm^2

X1 = 1.5 Y1 = 10
A1 = ∏r^2
A1= ∏ (5^2)
A1= ∏ (25)
A1 = 78.54mm^2

X2 = 3 Y2 = 7
A2 = ∏ (7^2)
A2= ∏ (49)
A2 = 153.94mm^2

X3 = 7 Y3 =11
A3 = ∏ (7^2)
A3 = ∏ (49)
A3 = 153.94mm^2

X4 = 5 Y4 = 3.5
A4 = ∏ (7^2)
A4 = ∏ (49)
A4 = 153.94mm^2

X5 = 7
Y5 = 5
A5 = ∏ (5^2)
A5 = ∏ (25)
A5 = 78.54mm^2


coordenadas del centroide para x:

Xc = A1(X1) + A2(X2) + A3(X3)+ A4(X4) + A5(X5) / At
Xc = 78.54(1.5)+153.94(3)+153.94(7)+153.94(5)+78.54(7)/ 618.9
Xc = 117.81+461.82+1077.58+769.7+549.78/ 618.9
Xc = 4.81mm

coordenadas del centroide para y:
Yc = A1(Y1) + A2(Y2) + A3(Y3)+ A4(Y4) + A5(Y5) / At
Yc = 78.54(10)+153.94(7)+153.94(11)+153.94(3.5)+78.54(5) / 618.9
Yc = 785.4+1077.58+1693.34+538.79+392.7 / 618.9
Yc = 7.25mm [b]

Area total= At Se me fue la piscucha ingeniero q era en mm.- Gracias

Ejercicio 2
Resolución de la siguiente forma :
r1 y r5 = 5.0
r2, r3 y r4 = 7.0
A total = 618.9 mm^2
A = ∏ (r)2

Áreas de r1 y r5 son iguales por lo tanto 78.54mm^2
Áreas de r2,r3 y r4 son iguales por lo tanto 153.94mm^2


01/ X1 = 1.5 Y1 = 10

02/ X2 = 3 Y2 = 7

03/ X3 = 7 Y3 =11

04/ X4 = 5 Y4 =3.5

05/ X5 = 7 Y5 = 5

Calculando las coordenadas del centroide:

Xc = A1(X1) + A2(X2) + A3(X3)+ A4(X4) + A5(X5) / A total

Xc = 78.54(1.5)+153.94(3)+153.94(7)+153.94(5)+78.54(7)/ 618.9

Xc = 117.81+461.82+1077.58+769.7+549.78/ 618.9

Xc = 4.81mm


Yc = A1(Y1) + A2(Y2) + A3(Y3)+ A4(Y4) + A5(Y5) / A total

Yc = 78.54(10)+153.94(7)+153.94(11)+153.94(3.5)+78.54(5) / 618.9

Yc = 785.4+1077.58+1693.34+538.79+392.7 / 618.9

Yc = 7.25 mm

PROBLEMA 2 (AL FIN)

SOLUCIÓN:

--Nos basaremos en los datos que se dan el la figura y de ello determinaremos primeramente las areas y tendremos que las areas quedarían:

A1=A5=78.54mm²
A2=A3=A4=153.94mm²

Sujetandonos de los puntos de coordenadas determinaremos el centroide respectivamente en “x” e “y” y son:

X1=1.5mm Y1=10mm
X2=3mm Y2=7mm
X3=7mm Y3=11mm
X4=5mm Y4=3.5mm
X5=7mm Y5=5mm

Para Xc:

Xc=(A1X1+A2X2+A3X3+A4X4+A5X5)/Atotal

Xc=[(78.54mm²)(1.5mm)+(153.94mm²)(3mm)+(153.94mm²)(7mm)(153.94mm²)( 5mm)+( 78.54mm²)(7mm)] /618.19mm²

Xc= 2976.69mm³/618.19mm²

Xc=4.81mm

Para Yc:

Yc=(A1Y1+A2Y2+A3Y3+A4Y4+A5Y5)/Atotal

Yc=[(78.54mm²)(10mm)+(153.94mm²)(7mm)+(153.94mm²)(11mm)(153.94mm²)( 3.5mm)+( 78.54mm²)(5mm)] /618.19mm²

Yc= 4487.81mm³/618.19mm²

Yc=7.25mm

ENTONCES EN CONCLUSIÓN EL CENTROIDE DEL SISTEMA DE FIGURAS SE ENCUNETRA EN LOS SIGUIENTES PUNTOS: (4.81,7.25)

A = πr^2
A1 = A5 =78.54
A2 = A3 = A4 = 153.94

X1=1.5 Y1=10
X2=3 Y2=7
X3=7 Y3=11
X4=5 Y4=3.5
X5=7 Y5=5

Xc = (78.54*1.5) + (153.94*3) + (153.94*7) + (153.94*5) + (78.54*7) / (153.94+153.94+153.94+78.54+78.54)
Xc = 2976.69 / 618.9
Xc = 4.81

Yc = (78.54*10) + (153.94*7) + (153.94*11) + (153.94*3.5) + (78.54*5) / (153.94+153.94+153.94+78.54+78.54)
Yc = 4487.81 / 618.9
Yc = 7.25

Coordenadas del Centroide: (4.81, 7.25)

carlos cristales
Primero hallamos las areas individuale y la total

A1=A5=3.14(52)=78.53mm

A2=A3=A4=3.14(72)=153.93mm

area total=618.85mm


Ahora procedemos al calculo de las coordenadas del centroide de la siguiente manera:


Xc = 78.54(1.5)+153.94(3)+153.94(7)+153.94(5)+78.54(7)/ 618.9
Xc = 117.81 + 461.82 + 1077.58 + 769.7 + 549.78 / 618.9
Xc = 4.81



Yc = 78.54(10)+153.94(7)+153.94(11)+153.94(3.5)+78.54(5) / 618.9
Yc = 785.4+1077.58+1693.34+538.79+392.7 / 618.9
Yc = 7.25

Luciano Alberto Calderón Crespín

DATOS:
r1 y r5 = 5.0 r2, r3 y r4 = 7.0 A total = 618.9 u^2

X1 = 1.5 Y1 = 10
A1 = ∏r^2
A1 = ∏ (5^2)
A1 = ∏ (25)
A1 = 78.54 u^2

X2 = 3 Y2 = 7
A2 = ∏ (7^2)
A2 = ∏ (49)
A2 = 153.94 u^2

X3 = 7
Y3 =11
A3 = 153.94 u^2

X4 = 5
Y4 = 3.5
A4 = 153.94 u^2

X5 = 7
Y5 = 5
A5 = 78.54 u^2

calculo de las coordenadas del centroide:

Xc = A1*X1 + A2*X2 + A3*X3+ A4*X4 + A5*X5 / A total
Xc = 78.54(1.5) + 153.94(3) + 153.94(7) + 153.94(5) + 78.54(7) / 618.9
Xc = 117.81 + 461.82 + 1077.58 + 769.7 + 549.78 / 618.9
Xc = 4.81

Yc = A1*Y1 + A2*Y2 + A3*Y3+ A4*Y4 + A5*Y5 / A total
Yc = 78.54(10) + 153.94(7) + 153.94(11) + 153.94(3.5) + 78.54(5) / 618.9
Yc = 785.4 + 1077.58 + 1693.34 + 538.79 + 392.7 / 618.9
Yc = 7.25

Las áreas de cada uno son las siguientes:

A1=78.54mm²
A5=78.54mm²
A2=153.94mm²
A3=153.94mm²
A4=153.94mm²
Area total =A1+A2+A3+A4+A5 = 618.19
Los puntos coordenados para cada circulo respectivamente son los siguientes:

X1=1.5mm Y1=10mm
X2=3mm Y2=7mm
X3=7mm Y3=11mm
X4=5mm Y4=3.5mm
X5=7mm Y5=5mm
Xc=[(78.54mm²)(1.5mm)+(153.94mm²)(3mm)+(153.94mm²)(7mm)(153.94mm²)(5mm)+(78.54mm²)(7mm)] /618.19mm²
Xc= 2976.69mm³/618.19mm²
Xc=4.81mm

Yc=[(78.54mm²)(10mm)+(153.94mm²)(7mm)+(153.94mm²)(11mm)(153.94mm²)(3.5mm)+( 78.54mm²)(5mm)] /618.19mm²
Yc= 4487.81mm³/618.19mm²
Yc=7.25mm

Luis Mario Aberegop Hernández

Áreas
Πr²

A01 = Π(5.0)² = 78.54 mm²
A02 = Π(7.0)² = 153.94 mm²
A03 = Π(7.0)² = 153.94 mm²
A04 = Π(7.0)² = 153.94 mm²
A05 = Π(5.0)² = 78.54 mm²

Coordenadas:

x1 = 1.5 mm y1 = 10 mm
x2 = 3 mm y2 = 7 mm
x3 = 7 mm y3 = 11 mm
x4 = 5 mm y4 = 3.5 mm
x5 = 7mm y5 = 5 mm

Coordenada X centroidal:

Xc=(A01*x1 A02*2 A03*x3 A04*x4 A05*x5) / (Área total x)

Xc=((78.54mm²*1.5mm) (153.94mm²*3mm) (153.94mm²*7mm)(153.94mm²*5mm) (78.54mm²*7mm)) / 618.9mm²

Xc= 2976.69 mm³ / 618.9 mm²

Xc = 4.81 mm

Coordenada Y centroidal :

Yc =(A01*y1 A02*y2 A03*y3 A04*y4 A05*y5)/ (Área total y)

Yc =((78.54mm²*10mm) (153.94mm²*7mm) (153.94mm²*11mm) (153.94mm²*3.5mm) (
78.54mm*5mm)) / 618.9mm²

Yc = 4487.81mm³/ 618.9mm²

Yc = 7.25 mm

Centroide (4.81 , 7.25)

X1= 1.5mm Y1= 10mm R1= 5
X2= 3mm Y2= 7mm R2= 7
X3= 7mm Y3= 11mm R3= 7
X4= 5mm Y4= 3.5mm R4= 7
X5= 7mm Y5= 5mm R5= 5

Para encontrar Xc= A1X1+A2X2+A3X3+A4X4+A5X5/Atotal

Entonces: 78.54(1.5)+153.94(3)+153.94(7)+153.94(5)+78.54(7)/618.9

Xc= 4.81

Yc= A1Y1+A2Y2+A3Y3+A4Y4+A5Y5/Atotal

Entonces: 78.54(10)+153.94(7)+153.94(11)+153.94(3.5)+78.54(5)/618.9

Yc= 7.25

Las coordenadas respectivas son: X= 4.81
Y= 7.25