In anticipation of part B I am going to take moments about the cable A attachment
I will do it all in Kg instead of Newtons because g will cancel except at the end.
m positive down
cable A x = 0 m = A
Man x = 1.5 m = 75
beam x = 4 m = 68.8
cable B x = 6 m = B
cat x = 8 m = 3.5
total m = 0 = A + B + 75 + 68.8 + 3.5
A + B = -147.3
now moments or torques about A
0 = 75*1.5+68.8*4+B*6+3.5*8
-6B = 415.7
B = - 69.3 Kg * 9.8 = 679 Newtons up tension
A -69.3 = -147.3
A = -78 * 9.8 = 764 Newtons up tension
Now with no cat and the man at the right
A + B = -143.8
0 =75*9 +68.8*4+B*6
B = -158.4
Oh my, that means that A will have to be positive (force down) to make the A+B=-143.3
The cable A will be under negative tension. Cables do not so well under negative tension, they collapse and the left end goes up and the man falls off.
Could you explain the meaning of your symbols you use. for example the "m positive down" Ok i know what you mean, but this is extremely confusing if you don t state what each symbol means beforehand.
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