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Homework Help: The law of the machine

  1. Jun 21, 2008 #1
    1. The problem statement, all variables and given/known data

    A screw jack has a single start thread of pitch 7mm and a operating handle 800mm long.when raising a load of 750kg the effort required on thev end of the handle is 26N.
    determine for these operating conditions the following :
    (a) the mechanical advantage
    (b) the velocity ratio
    (c) the efficiency of the machine
    (d) the law of the machine

    2. Relevant equations
    ma = load/effort
    vr = 2 x pie x r/p
    effiency of the machine = ma/vr x 100%
    law of the machine = E = aw+b

    3. The attempt at a solution

    (a) mechanical advantage = 750 x 9.81/26N = 282.98

    (b) the velocity ratio = 2 x pie x 800mm/7mm = 718.07

    (c) the effiency of the machine = 282.98/718.07 x 100% = 39.40%

    (d) the law of the machine this is where i am struggling i no the formula is E = aw+b

    where a is the velocity ratio and w is the load however what does the b stand for and if i need to caculate this how do i do this please help ......
  2. jcsd
  3. Jun 21, 2008 #2
    Substitute the values of E,a,w in the law of machines to obtain the value of b (it is a constant).
  4. Jun 21, 2008 #3
    so i have transposed correctly i think and have came up with this :

    b = E-a/w

    therefore b = 26n - 718.07/750 x 9.81 = 16.60

    thanks for the quick reply
  5. Jun 21, 2008 #4
    sorry to reply again as i have misread part (e) in the question

    it says if the effort needed to raise a load of 400kg is 17N determine :

    the law of the machine.

    also should the law of the machine when calculated total 17N

    thanks again mark
  6. Jun 22, 2008 #5
    I don't understand what you mean by this.

    However, you have been provided with two sets of values for E and W. Substitute these in the law of machines, and obtain the values of 'a' and 'b' by solving the system of linear equations that you get.
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