Calculating Toolbox Mass in Horizontal Pulley System

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In a horizontal pulley system, a group of construction workers is attempting to calculate the mass of a toolbox connected to a bundle of 1400 kg bricks. The toolbox experiences a coefficient of kinetic friction of 0.690, while the bricks accelerate at 4.56 m/s². The equations of motion are provided, but the initial attempt at solving for the toolbox's mass was incorrect. A suggestion was made to verify the assignment of variables A and B, as well as to check the signs in the equations used. The discussion emphasizes the importance of correctly applying the physics principles to arrive at the right solution.
Haniah
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Homework Statement


A group of construction workers are building a house and want to lower down an excess bundle of 1400 kg bricks to ground. They tie one end of a rope to the bundle of bricks, loop it through a pulley, and tie the other end of the rope to a toolbox. If the coefficient of kinetic friction between the toolbox and the floor is 0.690 and the acceleration of the bundle of bricks is 4.56 m/s2, what is the mass of the toolbox?
where A=toolbox
and B=bricks

Homework Equations


T-ukmBg=-mBaA
T-mAg=mAaA
(mA-ukmB)g=-(mA+mB)aA

The Attempt at a Solution


mA = ((gukmB)-(amB))/(a+g)
I tried to solve by using this rearranged formula but did not get the right answer. I'm not quite sure what I'm doing wrong or what I'm missing. I am also assuming that acceleration (4.56 m/s2) is uniform, is this a correct assumption.
 
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Haniah said:
T-ukmBg=-mBaA
T-mAg=mAaA
I think you have your A and B reversed. Also, check your signs. (Let "a" be the magnitude of the acceleration.)
 
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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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