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Homework Help: Some wacky spring/hinge problem

  1. Aug 16, 2004 #1
    hey everybody,
    i've been having some trouble figuring out the forces involved in a hypothetical set-up im working on for an interface:

    an object is attached to the end of a spring which is hanging from a hinge-like joint. when in equilibrium the object and spring hang down and left at an angle from the hinge. the spring is stretched to about say, 125% of its normal length.

    im trying to figure out what kind of forces are involved here, so that it can be animated by applying an external force to the system, or increasing the object's mass. when i plotted it out i came up with the downward force of gravity on the object, the spring force to the upper-right, as well as what seemed some sort of normal force to the upper-left. yet it still doesnt seem quite right, is there anything missing? is torque in play here too?

    any help would be greatly appreciated.
  2. jcsd
  3. Aug 17, 2004 #2
    At the point of contact of the spring and the joint (which can be visualized as a lever one end of which is pivoted at another fixed point), there is a normal force--rather two, one on the lever due to the spring and its reaction on the spring. At the point of contact of the spring and the mass, there is a -ky force on the mass and a +ky force on the spring (or more generally, a force of magnitude ky and direction depending on the datums/conventions you chose).

    The torque is always in play..depends on whether you analyze it or not. The torque here can be taken about the pivot of the lever. In that case, the spring+mass can be visualized as a system which is compositely responsible for the force that provides this torque...

    I am uncertain about the assistance that this explanation provides you, since I am not sure if I have understood the situation properly........
  4. Aug 17, 2004 #3
    thanks, it did help.

    i realized my description may have been a bit fuzzy, so heres a diagram i drew up of the system in equilibrium with the mass on it with my original conception of the forces acting on it (the normal force was basically what i added to balance out the other two), and also a diagram of the system without the mass (the spring is massless for simplicity's sake).

    what i gather from what you said there is also a force going in the opposite direction of the springs force towards the mass, transitioning some of the weight to the anchor? and the normal forces are an upward one as well as one to the direction of the spring compensating for its horizontal direction. is that an accurate description based on your info?

    thanks again.

    Attached Files:

  5. Aug 17, 2004 #4
    I am sorry but to help you out further I need a diagram of the actual arrangement (preferably without the forces drawn). I think it looks similar to the one on the right in your attachment, but it is not very clear. From what I gather you have a lever pivoted at one end, the other end of which is attached to one end of a spring. The other end of the spring is attached to the mass.

    So essentially I gather that you have a spring mass system, the other end of the spring being attached to a lever that can rotate. Am I right? If so, the forces are:

    1. Two on the mass:
    (a) its weight acting vertically downwards
    (b) spring force acting upwards

    2. Two on the spring
    (a) one due to the mass acting vertically downwards
    (b) normal force of contact due to the lever

    3. On the lever
    (a) normal force at the point of pivot
    (b) force due to spring acting down (inclination as in your diagram)

    Now take another look at your diagram and lemme know if I am right or wrong :-)
  6. Aug 17, 2004 #5
    my apologies, i just realized that my diagram was rather misleading, though the forces you listed made things a lot more clear.

    so i did a new one, that line at the top of the old diagram wasnt supposed to be a lever, just a mass that the spring was attached to. i figured the spring was attached to that mass and acted similar to a hinge joint when force was applied, though i guess i could very well be completely off there.

    i also included a free body diagram of the forces you listed to check if im understanding you clearly.

    while doing these diagrams i realized exactly what it was im looking for in this system, something that balances out the forces and torques according to the mass of the object, so that when the mass of the object is increased or an outside force is applied the object will drop, stretching and rotating the spring until equilibrium is found.

    Attached Files:

  7. Aug 18, 2004 #6

    Okay I get it now...the spring can rotate too. Interesting...

    But there is one small mistake that you have made drawing the forces on the spring. The force acting on the spring (due to the mass) is in a direction opposite to the force acting on the mass due to the spring, not vertically downwards as you have shown.

    Think about it and we will proceed after that.

    For the rotation of the spring, you have to assume that it always compresses or elongates longitudinally and not transversely...that is the spring behaves as a rigid rod whose length can change dynamically due to the longitudinal forces on it. If you consider the transverse displacement of individual links of a spring, it will make the analysis impossible using Newtonian methods.
  8. Aug 18, 2004 #7
    ok, that gave me an idea, hopefully its not too far fetched. i decided to eliminate all forces but those that are directly on the object, because for the animation all that will be necessary to calculate are those forces directly affecting the objects movement.

    if you take a look at the new sketch i did, i rotated the spring so that its force would be directed vertically, so that it could be seen as stretching only one way, with the force of gravity on the object thrown off at an angle. it seemed to me that the y-component of the gravity vector would counter-balance the upward force of the spring, while the x-component accounted for the rightward torque that rotated the spring.

    to balance this out there had to be another force in the opposite direction as the x-component of gravity, balancing out the torques as well as forces. this additional force i assumed was due to friction in the hinge-like connection of the spring. now im hoping that the force of the spring could be treated as a normal force, so that a coeficient of friction could be found that will help in balancing out the system in the case that the mass of the object is increased. but i've had no luck in finding any info. on how friction in a hinge works.

    whadya think?

    Attached Files:

  9. Aug 19, 2004 #8
    Gravity always acts downwards. So if Fg is the force due to gravity, you cannot make it at an angle with the vertical. It must always be acting down along the vertical. However, if Fg is a component of the force of gravity along your chosen axes, its okay.

    A normal force treatment of hinges can be found in elementary text on Statics/Dynamics. See for example, Irving Shames, Hibbeler or Beer/Johnston.

    Hope that helps...

  10. Aug 19, 2004 #9

    the force of gravity was still acting downward, just down became more towards the right when the forces were rotated for a different vantage point :)

    ill give this a shot when i write up the code and see if its succesful, and ill check out one of those books for the hinge stuff.

    thanks a ton for helping me out!
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