Calculating Toolbox Mass in Horizontal Pulley System

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SUMMARY

The discussion focuses on calculating the mass of a toolbox in a horizontal pulley system where a bundle of bricks weighing 1400 kg is lowered. The coefficient of kinetic friction between the toolbox and the floor is 0.690, and the acceleration of the bricks is 4.56 m/s². The correct formula to determine the mass of the toolbox (mA) is derived from the equations of motion and friction, specifically mA = ((g * uk * mB) - (a * mB)) / (a + g). Participants noted the importance of correctly identifying the variables and ensuring proper sign conventions in the equations.

PREREQUISITES
  • Understanding of Newton's laws of motion
  • Knowledge of friction coefficients and their application
  • Familiarity with pulley systems and tension calculations
  • Basic algebra for rearranging equations
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  • Study the principles of Newton's second law in detail
  • Learn about the effects of friction in mechanical systems
  • Explore advanced pulley system mechanics
  • Practice solving problems involving multiple bodies and forces
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This discussion is beneficial for physics students, engineering students, and professionals involved in mechanics, particularly those working with pulley systems and friction analysis.

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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