Determine the tension developed in wires CA and CB required for equilibrium of the 10-kg cylinder. Take ϴ = 40°.
Solution:
The first step is for us to draw a free body diagram like so:
Next we will choose which sides to be positive. We will assume forces going \rightarrow^+ to be positive and \uparrow+ to be positive.
Now, we can write our equations of equilibrium for the x-axis forces and y-axis forces.
F_{CB}\text{cos}\,(40^0)\,-\,F_{CA}\text{cos}\,(30^0)=0 —————–(eq.1)
\sum \text{F}_\text{y}=0
F_{CB}\text{sin}\,(40^0)\,+\,F_{CA}\text{sin}\,(30^0)\,-\,98.1=0 —————–(eq.2)
Next we will solve for F_{CA} and F_{CB}. First we will isolate for F_{CB} in eq.1.
(simplify by getting numerical values for cosine values)
F_{CB}\,=\,1.13F_{CA} —————–(eq.3)
Substitute the value of F_{CB} we found into eq.2.
(Solve for F_{CA})
F_{CA}=80 N
Substitute the value of F_{CA} into eq.3 to find F_{CB}.
F_{CB}\,=\,90.4 N
YOU HAVE SOLVED IT BASED ON FORCE BUT THE QUESTION WAS ABOUT THE TENSION !!!!!!!!!
Well, tension is a type of force. Please read up on it here: https://goo.gl/jvhdjZ
Remember, you can’t push on a rope, so the force on the rope is tension force. Also, not sure what you mean by “solved it based on force?” I think you have a misunderstanding between what type of force a rope can carry, in this case, its always tension force.