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Work Question (Pulling a chain on the Moon)

  1. Feb 1, 2017 #1
    1. The problem statement, all variables and given/known data
    At a lunar base,a uniform chain hangs over the edge of a horizontal platform.A machine does ##1.0J## of work in pulling the rest of the chain onto the platform.The chain has a mass of ##2.0 kg## and a length of ##3.0m##.What lenght was initally hanging over the edge ? On the moon,the gravitational acceleraiton is ##\frac 1 6## of ##9,8 \frac {m} {s^2}##
    2. Relevant equations
    ##ρ_{chain}=M/L##
    ##W_g=-ΔU_g##

    3. The attempt at a solution
    Lets suppose ##L_1## lenght is needed to pull.
    So chain density will be ##ρ=\frac {2kg} {3m}=0.66\frac {kg} {m}##
    The mass of ##L_1## is## L_1ρ=M_1##

    The gravitational work on ##M_1## is ##W_g## which its ##-M_1gL_1=1J##
    ##(L_!)^2ρg=6J##

    which ##L_1=1.05m## but the answer is ##1.4m##

    Theres a "-" sign which makes me uncomfortable.Also I am making wrong at some point
     
  2. jcsd
  3. Feb 1, 2017 #2

    Doc Al

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    Staff: Mentor

    Hint: If the length hanging over the edge is L, does every bit of the mass have to pulled up a height L?

    Also, the work is done by some force pulling the chain up, so its sign would be +. (It's work against gravity, not by gravity.)
     
  4. Feb 1, 2017 #3
    Here what I did

    ##(M_1dm)g(L1-dl)=W-dw## dw is zero and ##(M_1-dm)=(L_1-dl)p##
    Is this true ?
    yeah thats right but the work done by gravity on the chain is negative .The work done by machine to the chain is positive.Thats why I confused
     
  5. Feb 2, 2017 #4

    Doc Al

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    Staff: Mentor

    Not quite sure what you're doing here. Are you trying to set up an integral?

    Hint: If some extended object changed height, what point on the object would you track to compute its change in gravitational PE?

    The work done by the machine equals the change in gravitational PE; both are positive.
     
  6. Feb 2, 2017 #5
    yep I see now
    I was...If the lengh decreases a bit what would be happen
    Ok let me try again
     
  7. Feb 2, 2017 #6
    I found 1.36m by usig this equation
    ##(L_1)^2ρg=12J##
    Is it true ?
     
  8. Feb 2, 2017 #7

    Doc Al

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    Staff: Mentor

    Don't just toss out an equation; show how you got the equation.

    Consider a mass element dm of the hanging section of the chain. If the length hanging is L, what is the average distance that each mass element must be lifted to get to the platform?
     
  9. Feb 2, 2017 #8
    ##M_1a_gH=1J##

    ##H=\frac {L_1} {2}##; The center of mass of ##M_1## moves this much.
    ##M_1=L_1ρ##
    so,
    ##(L_1)ρ\frac {g} {6}\frac {L_1} {2}=1J##
     
  10. Feb 2, 2017 #9

    Doc Al

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    Staff: Mentor

    Perfect!
     
  11. Feb 2, 2017 #10
    Average distance will be ##\frac {L_1} {2}##

    ##∫\frac {L_1} {2}dmg=1J## from 0 to M and so This is true I am sure but If I wanted to convert it to ##dl## ,

    ##dm=dlρ## so ;
    ##∫\frac {L_1} {2}gρdl## from 0 to ##L_1p## ?
     
    Last edited: Feb 2, 2017
  12. Feb 2, 2017 #11

    Doc Al

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    Staff: Mentor

    Once you use the center of mass there's no need to integrate. But if you do, you'll get the same answer.
     
  13. Feb 2, 2017 #12
    Oh ok thank you
     
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