Calculate the net torque using all the forces

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The discussion focuses on calculating the net torque for a uniform beam supported by a cable and hinge at a 40° angle, with a tension of 600 N. The user initially struggled with the torque equation but realized that in equilibrium, the net torque must equal zero. They correctly identified that the torque due to the weight of the beam (mg) and the tension in the cable must balance out. The final solution involved using the formula mg(l/2)sin(theta) - T*lcos(theta) to find the net torque. The problem is deemed straightforward once the correct approach is applied.
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Homework Statement


In the figure below, a uniform beam of length 12.0 m is supported by a horizontal cable and a hinge at angle θ = 40°. The tension in the cable is 600 N.


Homework Equations



T=F x r

The Attempt at a Solution


I attempted to calculate the net torque using all the forces(mg and tension), so 0=mgsin(40) - Tension.
 

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Nevermind got it. Used mg(l of rod/2)sin(theta)-T*lcos(theta)
 
welcome to forum,
that's an easy problem. As the body is equilibrium net torque should be zero.
 
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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