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Extension of spring pulled at both ends

  1. May 11, 2016 #1
    1. The problem statement, all variables and given/known data

    A spring with spring constant 50 N/m is pulled with 10 N force at both ends of the spring.
    So, the extension of spring length is..
    A. 0.0 m
    B. 0.1 m
    C. 0.2 m
    D. 0.3 m
    E. 0.4 m

    2. Relevant equations

    F = k Δx

    3. The attempt at a solution

    F = 10 N <--- 0000000000000000000000 ----> F = 10 N

    I think the Δx should be 20/50 = 0.4 m

    But, the teacher said that it should be 0.2 m.
    He said that it's like a common problem where the spring is attached to the wall, and we pull it.
    The wall exerts the reaction force which magnitude is the same as the pulling force, but in opposite direction (reaction force).

    But, then I think, if the reaction force given by the wall is the same magnitude as the action, the spring won't get stretched, right?
    I think the reaction force must be less than the one I exert on the spring..

    Which one is correct?? Please help me...
    I somehow don't get the insight.
  2. jcsd
  3. May 11, 2016 #2

    rude man

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    The force is the same in magnitude but opposite in direction. That makes all the difference ...
  4. May 11, 2016 #3
    So, you agree that the extension is 0.2 m ??

    So, if the spring is attached to wall and then get pulled out, the wall gives a reaction which magnitude is the same as the pull force??

    How come the spring get stretched if the net force working on it is zero?
    Or, does it mean the spring get double-stretched since the force pulls both ends of the spring??
    Please explain me the concept ._.
  5. May 11, 2016 #4

    rude man

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    The net force on the spring is not zero. Force has magnitude AND DIRECTION. Force is pulling equally on both ends or it would accelerate per F = ma.
    This is a matter of definition. We say the spring constant is the force applied equal in magnitude but opposite in direction divided by the stretch of the spring.
  6. May 11, 2016 #5
    Why the net force is not zero?? I know the force has direction too -_-
    The Free Body Diagram for the spring is like this, right?

    (Assume 000000000 is a spring figure hahaha)

    10 N (the reaction force) <-------- 0000000000000 -------> 10 N (The pulling force)

    Because the direction is opposite, so the force cancels out, so net force is zero... So, the extension is zero

    But, we can also make separate Free Body Diagram for both ends

    000 -------> 10 N

    Which means that the extension is 0.2 m at one end

    10 N <-----000

    That means the extension is 0.2 at the other end.
    So, the extension is 0.2 + 0.2 = 0.4 m

    So, which one is correct??? Please help me
  7. May 12, 2016 #6


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    It is a common pitfall to think of a tension or compression as a force. It is more like a pair of opposite forces, or maybe a continuous chain of pairs of opposite forces. If a body is under tension but not accelerating, it is necessarily subject to a pair of equal and opposite pulls.
    Since the object under tension exerts a force at each end, we describe the magnitude of the tension as the magnitude of the force exerted at each end. Perhaps the convention could have been that the magnitude of the tension is the sum of the magnitudes of the forces at the end, but it isn't. So when we say the spring is under tension of 10N it is a matter of definition that it is pulling with a force of 10N at each end.
    (Things do get a bit more complicated when the tension varies along the spring, of course.)
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