Lever with discs

Classical Mechanics Level pending

With an angled metal bar I want to balance the weight W=40kg in point B. The bar has an angle of 60° on the left side and can pivot around O. I have 4 discs with weight 5kg, 10kg, 15kg, 20kg and thickness 36mm, 68mm, 96mm, 120mm respectively that have a hole in the middle and can be loaded on the top left part of the bar. In blue I added the measures, OA=700mm, OB=475mm

What is the sequence of disc I should load on the bar to balance exactly the weight W.

Ignore the weight of the bar and assume that each disc is symmetrical. In the solution append the weights you will load in the order chosen, for example if you think 5kg, 10kg, 20kg should be loaded in this order type 51020


The answer is 151020.

Meneghin Mauro by Meneghin Mauro , 42, United Kingdom

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1 solution

Meneghin Mauro
Jan 19, 2018

After loading a disc the arm of the next disc increases, so the order of the weights affects the momentum. There are 40 possible choices of load, quite a few to calculate manually. So I thought a script would be the easiest way to find the solution

The solution is 15kg, 10kg, 20kg in this order 

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import itertools

class Weight:
  def __init__(self, weight, width):
    self.weight = weight
    self.width = width

if __name__ == '__main__':
  stick_base = 700
  weights = [ Weight(5, 36), Weight(10, 68), Weight(15, 96), Weight(20, 120) ]
  for i in range(1, len(weights)):
    for p in itertools.permutations(weights, i):
      l = stick_base
      M = 0
      wlist = ''
      for w in p:
        M += w.weight * (l+w.width/2)/2
        l += w.width
        wlist += str(w.weight) + '-'
      wlist = wlist.rstrip('-')
      if M == (475*40):
        print(wlist, M)

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