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Tug-of-war paradox

  1. Jan 15, 2012 #1
    1. The problem statement, all variables and given/known data

    Imagine a tug-of-war contest between red and blue teams.

    (a) Early on in the proceedings, the two teams are equally matched and so there
    is no movement of the rope at all.

    (b) Having been more moderate over lunch, the blue team begins to pull the red
    team along at an increasing speed in a straight line.

    (c) The red team steady themselves but only to the point where they are being
    pulled at constant speed in a straight line.

    Describe each of the stages (a)–(c) in this contest in terms of the forces exerted
    by the teams on the rope, and whether or not the forces are balanced.



    2. Relevant equations



    3. The attempt at a solution

    I'm interested in scenario (b). The answer given in the book I took the quiz from says that the blue team are pulling with greater force on the rope than the red team. I can see why the book says that: since the rope is accelerating, an unbalanced force must be acting on the rope. The two forces acting on the rope are the pull from the blue team and the pull from the red team. In order for the rope to accelerate, the pull from the blue team must be larger. But I must confess I'm a bit confused. This topic's already been discussed on this forum (e.g. https://www.physicsforums.com/showthread.php?t=522448) and other sources I checked also assume that the tension in the rope is constant (because its mass is negligible and the accelerations involved are also low). This then implies that the pull from both teams is actually the same, which contradicts the book's answer. The only way I can make sense of the contradiction is as follows: in theory the rope accelerates because an unbalanced force is exerted on it but in practice (since the mass of the rope is negligible and the acceleration low) the two teams are exerting the same pull on the rope and the rope accelerates because the blue team, by pushing harder on the ground, accelerate. This means that in a real-life scenario the reason why the rope accelerates is because one of the teams push harder on the ground not because one of the teams push harder on the rope (since in a real-life scenario the tension in the rope is constant). Is this correct?

    Many thanks in advance for your help!

    Cris
     
    Last edited: Jan 15, 2012
  2. jcsd
  3. Jan 15, 2012 #2

    Doc Al

    User Avatar

    Staff: Mentor

    Yes, that is correct.
     
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