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:
Show me the final answer↓
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
Final Answer:
Maximum weight = 76.64 lb
Why is FAB being subtracted in the first step?
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 🙂
What does it mean by Fac will fail first
Cable Fac will break first, like it will snap/tear.
Last one, how can we know which cable will fail?
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.
Oh… I get it…. Thank you very much for the clarification and help
Excellent! Glad to have helped. Best of luck with your studies 🙂
I think when the summation of x its cos(30) and y is sin(30)
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.
Confused
How do you get FAC =50lb
It’s given in the question. We just plugging in 50 since that’s the max that can be supported.
Why didn’t we put Fab=50lb
Because FAC will fail first, so we test that first.