Finding Static Equilibrium: Solving a Rod and Cable System

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The discussion focuses on solving a static equilibrium problem involving a rod and cable system. Key equations include the resultant force being zero and the sum of all forces and torques also equating to zero. The initial analysis concluded that the tension in the cable equals the weight, but further exploration of the forces at the strut was necessary for a complete solution. Participants emphasized the importance of a Free-Body Diagram to visualize all force contributions and aid in resolving the system. The conversation highlights the need for thorough analysis beyond initial assumptions to achieve equilibrium.
RodriRego
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Homework Statement


problem.png


Homework Equations


Fr (resultante force) = 0
Sum of all forces aplied at the strut = 0
Sum of the torque of all forces = 0

The Attempt at a Solution


I started by analysing the torque, since the strut is on static equilibrium and I ended up having C (tension on the cable) = W. However, when I applied that relation to the system of equations that studies the sum of all forces applied at the strut, I ended up having no conclusion.
 
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Hi RodiRego, :welcome:

Can you show your work ? C = W says little about the strut staying in place !
 
A good start. Because the angles are equal the ##\Sigma \tau## with the foot of the strut as axis of rotation didn't bring you any further.
But you can do a lot with the force balance at the foot ! Make sure you don't forget any force contributions.
 
A Free-Body-Diagram for the rod should let you finish the solutionm.

upload_2016-4-11_12-41-25.png
 
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The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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