Finding moment, relative to a different axis

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To find the moment relative to the x, y, and z axes for the given system with tensions TCB and TCA, the moments are calculated as M = MTCA + MTCB, with MTCA determined by A × TCA and MTCB by B × TCB. The challenge arises when calculating the moment relative to the axis OB, which requires establishing a new axis system where OB is the y-axis. The angle α between the new y-axis and OB is found to be 26.565°, leading to the realization that the moment around OB should only involve components My and Mz, as OB lies in the y-z plane. The proposed formula for the moment around OB is expressed as (My/cos(26.565))j + (Mz/sin(26.565))k, which needs verification for correctness.
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given the following system:
2 cords are attached to point C,
http://picasaweb.google.com/devanlevin/DropBox?authkey=Gv1sRgCL_4l4PpvP_YsQE&pli=1&gsessionid=oBksCECRwcHSRoX-oRPaRA#5329455433140212770

and knowing that
|TCB|=380N
|TCA|=450N

find:
1) the moment relative to x,y,z
2) the moment relative to the axis 'OB'

for the 1st part, what i did was
M=MTCA+MTCB
and i found that
MTCA=A×TCA
MTCB=B×TCB


now comes the problem, how do i find the momentum relative to OB, i know that i need to make a new axis system, where OB is my "y" axis, and an axis 90degrees to it(63.43° from z axis) will be my new "z" axis, while x will stay the same,
i found the angle of my new axis relative to the original system

α=angle between 'y' and OB
α=26.565°

to find the moment, i need

1) force Tx (which is the same force Tx i used before)
2) the shortest distance dz between Tx and my new z axis
3) force Tz
4) the shortest distance dx between Tz and my new x axis

i am not at all sure that this is correct, if you can see a better way let me know.
 
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am i right in saying:

since the axis OB passes through the origin O, the moment relative to axis OB will be the same as the moment relative to O ?
BUT THAT DOESNT LOOK RIGHT TO ME,
i don't think that Mob should have any magnitude on the X axis since the line OB is on the y-z plane:

i thought that maybe i could do this:

since i can find the angle of OB, (comes to 26.565 degrees) i can say that since OB is on the YZ plane, the moment can only be My and Mz, so the moment around OB is:

(My/cos(26.565))j + (Mz/sin(26.565))k

is this correct??
 
Last edited:
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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