Determine the maximum weight of the flowerpot 10


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.

Determine the maximum weight of the flowerpot

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 answerโ†“

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

Determine the maximum weight of the flowerpot

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

 

This question can be found in Engineering Mechanics: Statics, 13th edition, chapter 3, question 3-9.

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