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Tension in a rope in an accelerating towplane (AP French 7-1)

  1. Oct 4, 2015 #1
    1. The problem statement, all variables and given/known data
    AP French Mechanics Problem 7-1

    Two identical gliders, each of mass m, are being towed through the air in tandem. Initially they are traveling at a constant speed and the tension in the tow rope A is T(sub0). The tow plane then begins to accelerate with an acceleration A. What are the tensions in A and B immediately after this acceleration begins?

    Crude Drawing

    Glider2 (Mass m) ---- rope B ----- Glider1 (Mass m) ----- rope A ------ Tow Plane (Initially at Rest then accelerating)

    2. Relevant equations/ 3. The attempt at a solution

    This is what I tried:

    Initially at constant velocity:

    Forces on Glider1: T(rope A) - T(rope B) = 0

    Since T(ropeA) == T(sub0),
    then T(ropeB) == T(sub0)

    When Tow Plane Starts to Accelerate:

    1) I assumed that entire system accelerated the same

    Forces on Glider1:
    T(ropeA) - T(ropeB) = m * a (1) (where m is mass of Glider 1)

    Forces on Glider2:
    T(ropeB) = m* a (2) (where m is mass of Glider2)

    Therefore,

    substituting, equation (2) into equation (1),

    T(ropeA) = 2*m*a.

    However, in the back of the book the answer states:

    T(ropeA) = T(sub0) + 2ma
    T(ropeB) = .5 * T(sub0) + ma

    I just want to know why the initial condition of T(sub0) is included, though I assume it is because of the constant velocity at the beginning and the plane accelerating in relation to that initial velocity, Also, if it would helpful if someone could point out flaws in my logic.

    Thanks.
     
  2. jcsd
  3. Oct 4, 2015 #2

    andrewkirk

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    If the plane and gliders are initially travelling at constant speed, with tensions in the ropes pulling the gliders forward, there must be an equal force pushing them back. Where does that force come from and what is it called? Does that retarding force disappear when the plane starts to accelerate?

    What does the force in the ropes have to be in order to (1) overcome the retarding force and (2) provide the acceleration.
     
  4. Oct 4, 2015 #3
    I would think the force would come from Drag and that it would equivalent to T(sub0) since the forces must balance out. When the plane accelerates this force does not disappear.

    Therefore initial situation (constant v):

    Forces on Glider 1:

    T(ropeA) - (TropeB) - Force(drag) = 0 (1)

    Forces on Glider 2:

    T(ropeB) - Force(drag) = 0 (2), therefore Force(drag) = T(ropeB)

    Substituting (2) into (1) and substituting T(sub0) for T(ropeA):

    T(sub0) = 2 F(drag)

    F(drag) = .5 * T(sub0)

    Accelerating situation:

    Glider 2)

    T(ropeB) - F(drag) = ma - > T(ropeB) = ma + .5 *T

    Glider 1)

    T(ropeA) - T(ropeB) - F(drag) = ma

    -> T(ropeA) = T(sub0) + 2ma

    Thanks for the help.

    From now on, ill work applicable constant velocity problems in the same way.
     
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