Ejercicios

6.
F1=15KN
F2=20KN
F3=25KN
Fx=Rx=15cos30cos25-20cos35sen40+25cos50cos60=-160.58i
Fy=Ry=-15cos30sen35-20cos35cos40+25cos50sen60=-298.33jFz=Rz=15sen30+20sen35+25sen50=38.12k
=-160.58i-298.33j+38.12k
=Rx 2+ Ry 2+ Rz 2→ = -160.582+-298.332+38.122= 340.93
cosθX=Fx→θx=cos-1Fx=cos-1-160.58340.93=118.09
cosθy=Fy=cos-1Fy=cos-1-298.33340.93=151.05
cosθz= Fz=cos-1Fz=cos-138.12340.93=83.58

4. a
F1=50KN
F2=35KN
F3=20KNFx=Rx=50cos50cos30-35cos26sen30+20cos36sen33=20.91i
Fy=Ry=-50cos50cos30+35cos26cos30+20cos36sen33=24.74j
Fz=Rz=50sen50+35sen26-20sen36=41.88k
=-317.98i-2056.73j+41.88k
=Rx 2+ Ry 2+ Rz 2 → =20.912+24.742+(41.88)2=52.94KN
cosθX=Fxd→θx=cos-1Fxd=cos-120.9152.94=66.73

B
F1=10KN
F2=16KN
F3=24KN
Fx=Rx=10cos26cos42-16cos40sen35+24cos50sen60=7.36iFy=Ry=-10cos26sen42-16cos40cos35+24cos50sen60=-2.69j
Fz=Rz=10sen26+16sen40+24sen50=33.05k
=7.36i-2.69j+33.05k
=Rx 2+ Ry 2+ Rz 2 → = 7.362+-2.692+(33.05)2=33.96cosθX=Fx→θx=cos-1Fx=cos-17.3633.96=77.48

c.
1=20i-37.5j+50kcm
1=202+-37.52+502=65.62cm
1=F111=10KN20i-37.5j+50k56.23=3.04i-5.71j+7.61kN

2=40i-37.5j+50kcm2=402+-37.52+502=74.2cm
2=F222=20KN40i-37.5j+50k74.2=10.78i-10.1j+13.47kN

3=40i-37.5j+12.5kcm
3=402+-37.52+12.52=56.23cm3=F333=20KN40i-37.5j+50k74.2=17.78i-16.67j+5.55kN

Fx=Rx=3.04+10.78+17.78=31.6i
Fy=Ry=-5.71-10.1-16.67=-32.48j
Fz=Rz=7.61+13.47+5.55=133.58k
=31.6i-32.48j+133.58kN
=Rx 2+ Ry 2+ Rz 2→ =31.62+-32.482+133.582=141.05N
cosθX=Fx→θx=cos-1Fx=cos-131.6141.05=118.09
cosθy= Fy=cos-1Fy=cos-1-32.48141.05=103.31
cosθz= Fz=cos-1Fz=cos-1133.58141.05=18.73