Determine the tension developed in wires CA and CB

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.

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)

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”

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

Determine the tension developed in wires CA and CB 2