Vectores Fuerza physicsleninac@hotmail.com JSFH

- Saber la los temas principales de vectores en el plano y el espacio. Vectores con Components Embedded link: http://mobius.maplesoft.com/maplenet/mobius/application.jsp?appId=190415020 Operaciones con Vectores link: http://mobius.maplesoft.com/maplenet/mobius/application.jsp?appId=120375001 Descomposici\303\263n Vectorial link: http://www.mapleprimes.com/posts/201240-Vector-Decomposition-In-Two-Dimensions Proyecciones Vectoriales link: http://mobius.maplesoft.com/maplenet/mobius/application.jsp?appId=5663865996050432

01.- Saber aplicar bien la teoria fundamental. 02.- Interpretar el gr\303\241fico e identificar las variables intervinientes. 03.- Primero observa que los campos esten vacios si no es asi presiona el bot\303\263n reset en cada tema. 04.- Presiona la tecla Enter en restart y with(VectorCalculus). 05.- Para ingresar los vectores fuerza usa: <x,y,z>. Ejm: <4,-2,3> con doble click en cada campo. 06.- Si te equivocaste de ingresar el vector fuerza; doble click en el campo elegido e ingrese nuevamente. 07.- Finalemente presione el bot\303\263n que calcula lo que se pide.

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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= JSFH Ingrese los vectores F[1] y F[2]: F[1] = N F[2] = N use DocumentTools in #with(VectorCalculus): F1:=Do(%F1): F2:=Do(%F2): angulor:=Do(arccos((DotProduct(F1,F2))/(Norm(F1)*Norm(F2)))); angulo:=Do(evalf(convert(angulor,degrees)),5); Do(%alfa=angulo); end use; = \302\260 use DocumentTools in Do(%F1=NULL): Do(%F2=NULL): Do(%alfa=NULL): end use; LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= Vector Unitario de F 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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= Ingrese F = N LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= use DocumentTools in F:=Do(%F): U_EFE:=Do(<F[1]/Norm(F),F[2]/Norm(F),F[3]/Norm(F)>); Do(%UF=U_EFE); Do(%UFn=evalf(U_EFE),5); end use; = = N LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= use DocumentTools in Do(%F=NULL): Do(%UF=NULL): Do(%UFn=NULL): end use; Proyecciones de T[1] sobre T[2] y viceversa 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JSFH Ingrese las Tensiones: T[1] = N T[2] = N use DocumentTools in T1:=Do(%T[1]): T2:=Do(%T[2]): cmp_es:=Do(DotProduct(T1,T2)/Norm(T2)): Do(%T1sT2=(cmp_es)*(T2/(Norm(T2)))); Do(%T1sT2n=evalf((cmp_es)*(T2/(Norm(T2)))),5); end use; = = N use DocumentTools in T1:=Do(%T[1]): T2:=Do(%T[2]): cmp_es:=Do(DotProduct(T1,T2)/Norm(T1)): Do(%T2sT1=cmp_es*T1/(Norm(T1))); Do(%T2sT1n=evalf(cmp_es*T1/(Norm(T1))),5); end use; = = N use DocumentTools in Do(%T[1]=NULL): Do(%T[2]=NULL): Do(%T1sT2=NULL): Do(%T1sT2n=NULL): Do(%T2sT1=NULL): Do(%T2sT1n=NULL): end use; LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= Fuerza dirigida a lo largo de una cuerda LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= 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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUklbXN1YkdGJDYlLUkjbWlHRiQ2KlEickYnLyUlc2l6ZUdRIzI2RicvJSVib2xkR1EldHJ1ZUYnLyUnaXRhbGljR0Y3LyUrZm9yZWdyb3VuZEdRLlsyNTUsMjU1LDI1NV1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSxib2xkLWl0YWxpY0YnLyUrZm9udHdlaWdodEdRJWJvbGRGJy1GIzYnLUYvNihRI09BRidGMkY4RjpGPS9GQVEnaXRhbGljRidGMkY6Rj0vRkFRJ25vcm1hbEYnLyUvc3Vic2NyaXB0c2hpZnRHUSIwRictRi82I1EhRidGMkY6Rj1GTQ== = unidades de longitud (m) LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUklbXN1YkdGJDYlLUkjbWlHRiQ2KlEickYnLyUlc2l6ZUdRIzI2RicvJSVib2xkR1EldHJ1ZUYnLyUnaXRhbGljR0Y3LyUrZm9yZWdyb3VuZEdRLlsyNTUsMjU1LDI1NV1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSxib2xkLWl0YWxpY0YnLyUrZm9udHdlaWdodEdRJWJvbGRGJy1GIzYnLUYvNihRI09CRidGMkY4RjpGPS9GQVEnaXRhbGljRidGMkY6Rj0vRkFRJ25vcm1hbEYnLyUvc3Vic2NyaXB0c2hpZnRHUSIwRictRi82I1EhRidGMkY6Rj1GTQ== = unidades de longitud (m) use DocumentTools in rOA:=Do(%r[OA]): rOB:=Do(%r[OB]): Do(%r[BA]=rOA-rOB); end use; = m y use DocumentTools in mFBA:=Do(%m_FBA): rOA:=Do(%r[OA]): rOB:=Do(%r[OB]): r_BA:=Do(rOA-rOB): UrBA:=Do(<r_BA[1]/Norm(r_BA),r_BA[2]/Norm(r_BA),r_BA[3]/Norm(r_BA)>): FBA:=Do(evalf(mFBA*UrBA),5): Do(%F[BA]=FBA); end use; = N use DocumentTools in Do(%m_FBA=NULL): Do(%r[OA]=NULL): Do(%r[OB]=NULL): Do(%r[BA]=NULL): Do(%F[BA]=NULL): end use; JSFH Caracter\303\255sticas entre F[1] y F[2] 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Ingrese los vectores F[1] y F[2]: F[1] = N F[2] = N Seleccione el tipo de operaci\303\263n vectorial: use DocumentTools in p_e:=Do(DotProduct(%F[1],%F[2])): Do(%R=p_e); ang:=Do(arccos(p_e/(Norm(%F[1])*(Norm(%F[2]))))); Do(%anf1f2=evalf(convert(ang,degrees)),5); Do(%an1=NULL): Do(%an2=NULL): Do(%an3=NULL): Do(%mg=NULL): Do(%vecunit=NULL): end use; use DocumentTools in pv:=Do(CrossProduct(%F[1],%F[2])): Do(%R=pv); mag:=Do(Norm(pv)): Do(%mg=evalf(mag),5); direcc1:=Do(arccos(pv[1]/Norm(pv))): Do(%an1=evalf(convert(direcc1,degrees)),5); direcc2:=Do(arccos(pv[2]/Norm(pv))): Do(%an2=evalf(convert(direcc2,degrees)),5); direcc3:=Do(arccos(pv[3]/Norm(pv))): Do(%an3=evalf(convert(direcc3,degrees)),5); Do(%vecunit=evalf(<pv[1]/Norm(pv),pv[2]/Norm(pv),pv[3]/Norm(pv)>),5); Do(%anf1f2=NULL); end use; use DocumentTools in s_m:=Do((%F[1]+%F[2])): Do(%R=s_m); mag:=Do(Norm(s_m)): Do(%mg=evalf(mag),5); direcc1:=Do(arccos(s_m[1]/Norm(s_m))): Do(%an1=evalf(convert(direcc1,degrees)),5); direcc2:=Do(arccos(s_m[2]/Norm(s_m))): Do(%an2=evalf(convert(direcc2,degrees)),5); direcc3:=Do(arccos(s_m[3]/Norm(s_m))): Do(%an3=evalf(convert(direcc3,degrees)),5); Do(%vecunit=evalf(<s_m[1]/Norm(s_m),s_m[2]/Norm(s_m),s_m[3]/Norm(s_m)>),5); Do(%anf1f2=NULL); end use; use DocumentTools in d_f:=Do((%F[1]-%F[2])): Do(%R=d_f); mag:=Do(Norm(d_f)): Do(%mg=evalf(mag),5); direcc1:=Do(arccos(d_f[1]/Norm(d_f))): Do(%an1=evalf(convert(direcc1,degrees)),5); direcc2:=Do(arccos(d_f[2]/Norm(d_f))): Do(%an2=evalf(convert(direcc2,degrees)),5); direcc3:=Do(arccos(d_f[3]/Norm(d_f))): Do(%an3=evalf(convert(direcc3,degrees)),5); Do(%vecunit=evalf(<d_f[1]/Norm(d_f),d_f[2]/Norm(d_f),d_f[3]/Norm(d_f)>),5); Do(%anf1f2=NULL); end use; Resultante = Magnitud = Vector Unitario = Direcci\303\263n = , , Angulo entre F[1] y F[2] = \302\260 use DocumentTools in Do(%F[1]=NULL): Do(%F[2]=NULL): Do(%R=NULL): Do(%mg=NULL): Do(%vecunit=NULL): Do(%an1=NULL): Do(%an2=NULL): Do(%an3=NULL): end use; LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

JSFH 1.- An elastic rubber band is attached to points A and B as shown in Figure. Determine its length and its direction measured from A toward B . 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JSFH LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= Soluci\303\263n: 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 y LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUkjbWlHRiQ2J1EickYnLyUlc2l6ZUdRIzE2RicvJSdpdGFsaWNHUSV0cnVlRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNigtRiM2Ji1GLDYnUSNPQkYnRi9GMkY1RjhGL0Y1L0Y5USdub3JtYWxGJ0YvRjVGQy8lJW9wZW5HUSJbRicvJSZjbG9zZUdRIl1GJy1JI21vR0YkNi9RIj1GJ0YvRjVGQy8lJmZlbmNlR0Y3LyUqc2VwYXJhdG9yR0Y3LyUpc3RyZXRjaHlHRjcvJSpzeW1tZXRyaWNHRjcvJShsYXJnZW9wR0Y3LyUubW92YWJsZWxpbWl0c0dGNy8lJ2FjY2VudEdGNy8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRmluLUY8NigtRiM2Ky1GTDYvUSomdW1pbnVzMDtGJ0YvRjVGQ0ZPRlFGU0ZVRldGWUZlbi9GaG5RLDAuMjIyMjIyMmVtRicvRltvRmRvLUkjbW5HRiQ2JlEiMkYnRi9GNUZDLUZMNi9RIixGJ0YvRjVGQ0ZPL0ZSRjRGU0ZVRldGWUZlbi9GaG5RJjAuMGVtRicvRltvUSwwLjMzMzMzMzNlbUYnRmZvRmpvLUZnbzYmUSIzRidGL0Y1RkNGL0Y1RkNGL0Y1RkMvRkZRJyZsYW5nO0YnL0ZJUScmcmFuZztGJ0YvRjVGQw== Usamos la Aplicaci\303\263n: Vector Posici\303\263n r[AB] = <-3,2,6>m Tip: Saber la ubicaci\303\263n del punto inicial y final Usamos la Aplicaci\303\263n: Caracter\303\255sticas entre F[1] y F[2] Longitud = 7m Tip: Digite <0,0,0> para el segundo vector y elija suma Direcci\303\263n : 115.3769\302\260 , 73.3984\302\260 y 31.0027\302\260 2.- If FB = 700 N, and FC = 560 N, determine the magnitude and coordinate direction angles of the resultant force acting on the flag pole. 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Soluci\303\263n: 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 , 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 y 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 Usamos la Aplicaci\303\263n: Vector Posici\303\263n F[AB] = <200,-300,-600>N F[AC] = <240,160,-480>N Usamos la Aplicaci\303\263n: Caracter\303\255sticas entre F[1] y F[2] Magnitud = 1174.5637N Direcci\303\263n : 68\302\260 , 96.8455\302\260 y 156.8516\302\260 JSFH JSFH JSFH JSFHLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= JSFH