Determine the force in cables AB and AC necessary

Determine the force in cables AB and AC necessary to support the 12-kg traffic light.

Image from: Hibbeler, R. C., S. C. Fan, Kai Beng. Yap, and Peter Schiavone. Statics: Mechanics for Engineers. Singapore: Pearson, 2013.

We will first draw the free body diagram representing the forces at point A (the traffic light).

We will assume forces going $\rightarrow^+$ to be positive and $\uparrow+$ to be positive and write our equations of equilibrium.

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

$F_{AB}\text{cos}\,(12^0)\,-\,\frac{24}{25}F_{AC}=0$ ——————(eq.1)

\sum \text{F}_\text{y}=0

$F_{AB}\text{sin}\,(12^0)\,+\,\frac{7}{25}F_{AC}\,-\,117.72=0$ ——————(eq.2)

To solve for $F_{AB}$ and $F_{AC}$ , we will isolate for $F_{AB}$ in eq.1.

F_{AB}=\frac{24\,F_{AC}}{25\,\text{cos}\,(12^0)}

(Simplify)

$F_{AB}\,=\,0.9814F_{AC}$ ——————(eq.3)

We will now substitute this value into eq.2.

0.9814F_{AC}\text{sin}\,(12^0)\,+\,\frac{7}{25}F_{AC}\,-\,117.72=0

(solve for $F_{AC}$ )

$F_{AC}=243.2$ N

We can now substitute the value of $F_{AC}$ into eq.3 to figure out $F_{AB}$ .

F_{AB}\,=\,(0.9814)(243.2)

$F_{AB}\,=\,238.7$ N

3 thoughts on “Determine the force in cables AB and AC necessary”

good

How did it come up with an answer 243.2N? How did you solve it?

Reply ↓

questionsolutions Post author September 27, 2024 at 7:13 am

You can directly solve for FAC, it’s a single variable. If you think of FAC as “x” it will make it easier for you to see. You can directly plug it into your calculator.

Determine the force in cables AB and AC necessary 3