# Determine the maximum weight of the flowerpot 12

Determine the maximum weight of the flowerpot that can be supported without exceeding a cable tension of 50 lb in either cable AB or AC.

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

#### Solution:

We will first draw a free body diagram, depicting the forces around ring A.

We can now write equations of equilibrium for the x and y-axis forces.

$\rightarrow ^+\sum \text{F}_\text{x}\,=\,0$

$F_{AC}\sin30^0-F_{AB}\dfrac{3}{5}=0$

(Isolate for $F_{AC}$)

$F_{AC}=1.2F_{AB}$ (eq.1)

Notice how the force of $F_{AC}$ would be 1.2 times the force of $F_{AB}$, which means $F_{AC}$ will fail first.

$+\uparrow \sum \text{F}_\text{y}\,=\,0$

$F_{AB}\dfrac{4}{5}+F_{AC}\cos30^0-W=0$ (eq.2)

We will now equate $F_{AC}=50$ lb into eq.1.

$F_{AC}=1.2F_{AB}$

$50=1.2F_{AB}$

$F_{AB}=41.67$ lb

Substitute this value into eq.2.

$(41.67)\dfrac{4}{5}+50\cos30^0-W=0$

$W=76.64$ lb