# Determine the maximum weight of the flowerpot 14

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

Maximum weight = 76.64 lb

## 14 thoughts on “Determine the maximum weight of the flowerpot”

• Gabriel

Why is FAB being subtracted in the first step?

• questionsolutions Post author

Hi Gabriel. We are only subtracting the x-component of FAB because it’s pointing to the left. You will see that we assumed forces to the right, and forces going up to be positive. So for the x-axis, the x-component of FAB is going left, so it’s negative. Hope that helps 🙂

• Rj

What does it mean by Fac will fail first

• questionsolutions Post author

Cable Fac will break first, like it will snap/tear.

• Rj

Last one, how can we know which cable will fail?

• questionsolutions Post author

Fac would be 1.2 times the force of Fab. In other words, Fac carries a much larger load, so its going to break first.

• Rj

Oh… I get it…. Thank you very much for the clarification and help

• questionsolutions Post author

Excellent! Glad to have helped. Best of luck with your studies 🙂

• Hansel Ong

I think when the summation of x its cos(30) and y is sin(30)

• questionsolutions Post author

No, for F_AC, the x component is from sin and y is from cosine. Don’t always assume that x axis is cosine and y axis is sine.

• Issifu Issah

Confused
How do you get FAC =50lb

• questionsolutions Post author

It’s given in the question. We just plugging in 50 since that’s the max that can be supported.

• Confused

Why didn’t we put Fab=50lb

• questionsolutions Post author

Because FAC will fail first, so we test that first.