In the diagram below a motionless weight is held from the ce

In the diagram below a motionless weight is held from the ceiling by two cables. The weight is 100 lbs. What is the force (weight) pulling on each cable.

Solution

Let F₂be the force in cable 2 and F₁ be the force in cable 1

F_x1=F_x2

F₁cos 45= F₂cos 60

F₁=F₂cos60/cos45

F_y1+F_y2=W

F₁ sin45 + F₂sin 60=100

F₂cos 60 sin 45/cos45 +F₂sin60=100

F₂(cos60+sin60)=100

F₂=100/(cos 60 + sin 60) =73.2 lbs

F₁=F₂cos 60/cos 45 = 73.2 cos 60/cos 45 = 51.8lbs