Work done to pull the entire chain

AI Thread Summary
To calculate the work done to pull a chain entirely onto a table, one must consider the mass distribution of the hanging portion. The chain has a mass of 4 kg and a length of 2 m, with 60 cm hanging off the edge. The mass of the hanging section is 1.2 kg, but not all of it is at the same height; the center of mass of the hanging part is 0.3 m below the table. Therefore, the work done against gravity is calculated using this height, resulting in 3.6 J, which aligns with the given answer. Understanding the center of mass is crucial for accurately determining the work required.
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Homework Statement


A chain of mass 4Kg and length 2m is lying on a table, such that 60 cm of one end is hanging from one edge off the table. Find the work done to pull the entire chain on the table.

Homework Equations


(anything that'll work i suppose)

The Attempt at a Solution


I thought that the work done to do this is simply the work done against gravity to lift the hanging mass.
The mass per unit length of the chain is λ=m/l=2Kg/m
So the mass of the hanging portion is λ*60cm=2*0.6Kg=1.2Kg
So the work done to lift it 0.6m up is 1.2*9.8*0.6J=7.056J

But the given answer is 3.6J.
What am I doing wrong?
 
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You assumed that the entire mass of the portion of the chain that needs to be lifted is 0.6 m below that table. But that is not correct. Most of the portion is above that. And those parts need less work. How could you take this into account?
 
I don't get that! The mass that's on the table is on the table! So shouldn't I lift only the part that's hanging?
 
The part that is hanging is contiguous. Only its end is 0.6 m below the table. The other bits of the hanging part are still below the table, but HIGHER than 0.6 m.
 
Oh yeah! of course! so if I assume lifting the centre of mass of the hanging portions, then I lift 1.2Kg by 0.3m! the answer then comes! thanks.
 
Correct.
 

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