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Falling object

  1. Jan 31, 2008 #1
    1. The problem statement, all variables and given/known data
    a block 20% moe massive than yo uhangs from a rope. the other end of hte rpe goes over a massless frictionless pulley and dangles freely, with what acceleration must you climb th rope to keep the block from falling.


    2. Relevant equations

    possible w = mg
    f = ma
    p = mv

    3. The attempt at a solution
    mass of the body = 1 kg (easy to work with)
    mass of block = 1.2 kg

    the block falls w/ -g

    if i want to keep the block from falling i haev to counter the block falling at

    g * mass of block = 11.76 m/s^2 * kg



    i feel like the answer is wrong because of units...
     

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  3. Feb 1, 2008 #2
  4. Feb 1, 2008 #3
    You have the (almost) correct answer, but I would suggest you change your process a bit.

    You're looking for the acceleration of 'you' so that the block does not move. So, you're main goal is:

    [tex] \Sigma F = ma = 0 [/tex]

    We can use [tex]m_1[/tex] for the person, and [tex]m_2[/tex] for the block. And we know
    [tex]m_2 = 1.2 m_1[/tex]
    and the weight of the block is [tex]m_2 g[/tex]

    The equation will look like:
    [tex]m_1a + m_2g = 0[/tex]
    [tex]m_1a = -m_2g[/tex]

    Substituting for [tex]m_2[/tex] we get:
    [tex]m_1a = -1.2 m_1 g [/tex]
    divide by [tex]m_1[/tex] to get
    [tex]a = -1.2g [/tex]
    Then solve using -9.8 for g
    [tex]a = 11.76 m/s^2[/tex]

    Even though it may seem more complicated, it is generally easier and cleaner just to leave unknown quantities as the variables, i.e. don't substitute some random amount such as the 1 you used for m.
     
  5. Feb 1, 2008 #4
    ah that makes sense how you got the units to end up correct, i like how you set it up, thanks!
     
  6. Feb 1, 2008 #5
    You're welcome!
     
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