# Determine the tension developed in wires CA and CB 2

Determine the tension developed in wires CA and CB required for equilibrium of the 10-kg cylinder. Take ϴ = 40°. Image from: Hibbeler, R. C., S. C. Fan, Kai Beng. Yap, and Peter Schiavone. Statics: Mechanics for Engineers. Singapore: Pearson, 2013.

#### 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.

$\sum \text{F}_\text{x}=0$

$F_{CB}\text{cos}\,(40^0)\,-\,F_{CA}\text{cos}\,(30^0)=0$ —————–(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)

Show me the free body diagram again

Next we will solve for $F_{CA}$ and $F_{CB}$. First we will isolate for $F_{CB}$ in eq.1.

$F_{CB}=\frac{F_{CA}\text{cos}\,(30^0)}{\text{cos}\,(40^0)}$

(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.

$1.13F_{CA}\text{sin}\,(40^0)\,+\,F_{CA}\text{sin}\,(30^0)\,-\,98.1=0$

(Solve for $F_{CA}$)

$F_{CA}=80$ N

Substitute the value of $F_{CA}$ into eq.3 to find $F_{CB}$.

$F_{CB}\,=\,(1.13)(80)$

$F_{CB}\,=\,90.4$ N

## 2 thoughts on “Determine the tension developed in wires CA and CB”

• GHAITH

YOU HAVE SOLVED IT BASED ON FORCE BUT THE QUESTION WAS ABOUT THE TENSION !!!!!!!!!

• questionsolutions Post author

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.