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Finding the change in length of the rope

  1. Nov 26, 2016 #1
    1. The problem statement, all variables and given/known data
    a= 0.3 m / s2
    k = 10 000 N / m
    m = 1800 kg ( of the car that is being pulled)
    Ignore friction.

    A car is being pulled by another car by a rope ( stiffness = 10 000 N/m) with acceleration of 0.3 m/s2.. Find the change in length of the rope.
    2. Relevant equations
    F = ma
    F = kx (x is the change in length)

    3. The attempt at a solution
    x = F / k
    I am having trouble at finding F. I have made a graph, which I have uploaded here, of the car that is being pulled in this situation and I don't know if it's correct. A hint would be appreciated.
     

    Attached Files:

  2. jcsd
  3. Nov 26, 2016 #2
    Welcome to Physics Forums.

    Here is a hint: There is only one horizontal force acting on the car being towed and that force is what is causing it to accelerate. The weight of the car is a downward force and the normal force is upward. So use one of the "relevant equations" that you listed.
     
  4. Nov 26, 2016 #3
    So F should be 540 N ( since there is only one horizontal force, got it simply by F = ma) , or is there something else I'm not noticing ? Because I'm not getting a correct answer. It's supposed to be 0.011 m, but I get 0.0054 m, so F should be approximately 1100 N.
     
  5. Nov 26, 2016 #4
    Well, unless there's something I'm not noticing also, I don't see how you did anything wrong. But I got 0.054 m, instead of 0.0054 that you got. That may have just been a typo. Sometimes the "correct answers" are wrong.
     
  6. Nov 26, 2016 #5
    You may just want to check that you copied down all of the information from the problem correctly.
     
  7. Nov 26, 2016 #6
    I forgot one 0 for k: it's supposed to be 105, my bad. And it seems I lost one bit of information while translating this exercise, so I will re-do it:

    Car A is being towed by car B with a rope ( k = 105) and acceleration of 0.3 m/s2. Car A has a mass of 1800 kg. Ignore friction. Find the change in length of the rope.
     
  8. Nov 26, 2016 #7

    haruspex

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    It's definitely 0.0054m, unless you forgot to mention it is going uphill.
     
  9. Nov 26, 2016 #8
    No, it's going horizontal. Maybe car B has something to do with it ? If I imagine right, car B has 2 horizontal forces: one in direction of the rope, and another one to the front of the car B.

    Edit : Although, nevermind. That still got me back to F = ma. I guess the answer is 0.054 m then. Thanks for help !
     
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