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What does this value represent in this work question?

  1. Jun 23, 2011 #1
    Answered this myself as I wrote it.

    1. The problem statement, all variables and given/known data

    Eight bricks, each 6.0 cm thick with a mass of 1.5 kg, lie flat on a table. How much work is required to stack them one on top of another?

    hbrick = 0.060 m
    m = 1.5 kg


    2. Relevant equations

    W = Fd
    Fg = m*g


    3. The attempt at a solution

    I tried the following, and was correct. Please read the fourth point for my question.

    Fg = 1.5*9.8 = 14.7 N

    Wt = W1+W2+W3+W4+W5+W6+W7+W8

    Wt = 14.7*0 + 14.7*.06 + . . . + 14.7*0.42 = 25 J


    4. My question

    The answer to the question goes a little something exactly like this:

    Where did that 3.5 come from?

    7 bricks lifted divided by 2? Oh . . . Probably. Yeah. Averages and what not.

    Writing this helped. Might as well post it.
     
  2. jcsd
  3. Jun 25, 2011 #2

    CompuChip

    User Avatar
    Science Advisor
    Homework Helper

    Yep. Your calculation is
    [tex]W_t = 1.5 \times 9.81 \times (0.06 \times 0 + 0.06 \times 1 + \cdots + 0.06 \times 7)[/tex]
    Since (1 + 2 + ... + n) = 1/2 * n * (n + 1), you get (note that n = 7 in your case):
    [tex]W_t = 1.5 \times 9.81 \times \frac{1}{2} \times 8 \times 7[/tex]
    which you can re-order to give the expression you had.
     
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