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Why does a Lever arm magnify force?

  1. Jan 3, 2012 #1
    Hey, I'm looking for an explanation of the why we observe T = F * d
    In the sense of two people applying a force to a lever arm and the person closer to the pivot point requiring more force to keep the torque in equilibrium.

    I can only find explanations in the sense of work and energy conservation. I know the lever must be observed as conserving energy but how does the lever mechanically magnify the force? Maybe I'm in need of a microscopic understanding? Any in-depth reading on it?
  2. jcsd
  3. Jan 3, 2012 #2
    You could try thinking of it like this, if you have a lever on a hinge and you grab it close to the hinge and move it a tiny bit then you end up moving all of the atoms a lot more than if you grab the very end and move it a tiny bit, so for each microscopic movement you're actually having to "do" more when you push from closer to the fulcrum.
  4. Jan 3, 2012 #3
    If Force is equal to Mass times Acceleration, and the end of a longer end on an arm must move further in the same time as the shorter end of that arm, you have to evaluate the balance.

    Imagine a see saw...except we offset the fulcrum point to make it near the seat of one side instead of in the middle.

    So, one side of the see saw is longer, and one side is shorter.

    If we lower the long end, it moves through a large arc...and, makes the short end go through a small arc, but, in the same total time. So the long and short ends cover different travel distances, but in the same time.

    So, we apply a given MASS, over a given time period, so each side gets a particular mass times acceleration, but, the longer side's acceleration is higher, and, therefore, its FORCE is greater.

    If you add more mass, you get more force, if you add more acceleration you get more force, and a lever adds acceleration to the longer side, so the longer side applies more force.

    IE: The longer lever arm applies more force because whatever mass is used to push it down is moving downward at a higher acceleration, due to the longer arm's travel.
  5. Jan 3, 2012 #4
    Thanks for your replies. Very helpful.
  6. Jan 3, 2012 #5
    hmmm, So in the sense of loosening a nut with a wrench. The same force being applied with a greater lever arm is a lot easier. How would you explain this? Maybe without using torque? just in terms of linear motion equations would be helpful.
  7. Jan 3, 2012 #6
    I like to think of it in terms of energy conservation.Ignoring energy losses we can say that the loss of gravitational potential energy on one side is equal to the gain of gravitational potential energy on the other side.Expressing it differently for your first scenario,the force times the change of height on one side equals the force times the change of height on the opposite side.This raises another question;
    Why is energy conserved?

    ANS (I don't know)

    For the wrench substitute the more general "force times distance moved in direction of force" for the "force times height change".
    Last edited: Jan 3, 2012
  8. Jan 3, 2012 #7
    actually, I think I've been able to clarify it as the larger lever arm allowing a greater acceleration with less force.
  9. Jan 3, 2012 #8
    Well, if work(energy) is force x distance. We know that every force has an equal and opposite counterpart so the opposite of this work always exists. Where a force is doing work, energy is conserved. I hope
  10. Jan 3, 2012 #9
    The longer lever can have the same force applied to it, but, the mass at either end of the fulcrum point will move at a different speed.

    The shorter arm will move a smaller distance in the same time...and the larger arm will move a longer distance in the same time.

    F = MA

    As for any given mass in this equation, the higher the acceleration, the higher the force applied.

    This is also why other lever types exert more or less mechanical advantage...you simply look at the amount of mass and the distance it was moved, on each side of the fulcrum point.

    The side that moves the furthest will exert the higher force/require less force to move the same mass, etc.
  11. Jan 3, 2012 #10


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    If A does positive work on B, then B does equal negative work on A?
    Not necessarily; if the forces are conservative forces like gravity or spring forces, then mechanical energy is conserved. When non-conservative forces (like friction) act, mechanical energy is not conserved; total energy (in a closed system) is always conserved. Just don't confuse Newton 3 with work-energy concepts.
  12. May 23, 2013 #11


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    Work and energy are not involved because at equilibrium nothing moves. If the system is rotationally stationary, the total moment must be zero. Then Force1 / Force 2 = Distance 1 / Distance 2, and you can obtain any desired step up or down in effort.
  13. Jan 25, 2016 #12
    A lever gives capability of moving a bigger force with a smaller force. Archemedese had claimed lifting of earth with a lever and this additional force comes from within the mechanical properties of the material of lever.
  14. Jan 25, 2016 #13


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    Please do not revive old threads. The OP has been answered, and hasn't been on PF for 4 years.

    Thread closed.
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