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Help Me Understand Mechanical Advantage Please

  1. Jan 28, 2012 #1
    ok, I know that being further away and using a fulcrum/pivot point from an object being moved takes less energy. i.e using a 4 foot crow bar to pry open something. But i can't grasp the concept of why being further away makes it so much easier. thanks
  2. jcsd
  3. Jan 28, 2012 #2


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    welcome to pf!

    hi mechadv44! welcome to pf! :wink:
    no, the energy is the same…

    you can't get extra energy for nothing

    only the force is less
  4. Jan 29, 2012 #3
    same person who started thread, different name, sorry password problem..
    I meant force though, can it be explained in plain english as opposed to just a formula why being further uses less force?thanks
  5. Jan 29, 2012 #4

    The crow bar end you are pushing on, goes further than the other end.

  6. Jan 29, 2012 #5


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    goodness! are there 44 of you? :eek:
    force times distance equals work done (= energy supplied) …

    if the two ends of the lever are at different distances from the fulcrum, so that they move different distances when the lever turns, then different amounts of force will do the same work, and will supply the same energy :wink:
  7. Jan 30, 2012 #6
    I said that i already know that having a longer lever on the force side of the folcrum requires less force. what i'm asking is WHY WHY WHY does it make it easier? why is a longer lever so special if still moving the same object!?Is this just something that exists and can't be explained?
  8. Jan 31, 2012 #7
    I think I asked this question once, too. The answer I got was essentially that yes, that's just the way the universe works. Fortunately it's a very simple thing and you'll see manifestations of it everywhere in everyday life. It quickly starts to just "make sense".

    Climbing stairs for example is easier than going straight up a wall. A door is easier to open if the handle is on the far side of the hinge. A piece of wood is easier to split when hit with the narrow end of an axe, a screw is easy to screw in and yet it holds things together very tightly, gears, levers, pulleys, even a winding road up a mountain....all take advantage of the fact that work is force x distance, and all these mechanisms simply trade distance for more force.

    Unfortunately there are also alot of concepts in physics where the answer is also "that's just the way it is", but they DON'T make any sense. You have to go in pretty deep to start getting to these concepts, though.
  9. Jan 31, 2012 #8


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    Because conservation of energy requires it isn't a good enough answer?
  10. Jan 31, 2012 #9
    "WHY" questions are very hard to answer. Feynman explains just how hard it is. When asked why magnets attract each other, he explains that he can't give a simple answer. If you prefer reading a text instead of watching a video, here's a transcript.

    For your particular "why" question, maybe Archimedes can help.
  11. Jan 31, 2012 #10
    The most important concept is (as already typed by russ_watters in previous post) law of conservation of energy.

    This law states that total energy in the system remains constant , i.e. energy can neither be created nor be destroyed.

    Effort E Newtons upward
    Load ​
    (Axis of rotation)​
    (L Newtons downwards)​

    Now I am not taking in account load arm and effort arm because lever is not in equilibrium.
    Here L >>>> E , so by conservation of energy :
    Work Input = Work output
    L*d = E*x
    (* is multiplication )
    L/E = x/d
    since L>>>>E , so x>>>>d

    x arc >>>>>> d arc covered in circular path with Fulcrum as axis of rotation here.

    So here
    L* d arc = E*x arc

    As work = force * displacement

    By conservation of energy we get this result.

    Note : We talk about like
    Load * Load arm = Effort * Effort arm , when lever is in equilibrium. Longer the effort arm , more the mechanical advantage. This is principle of lever.
    Obviously think logically that one guy sitting at longer distance apply force less to counterbalance because distance being more will dominate the counter force effect !Its centre of gravity will be displaced and will be posed with less friction....
    (And please we neglect friction ! ) Yes ! Centre of gravity will dominate at the side of the guy sitting at longer distance.
  12. Jan 31, 2012 #11


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    Let's say you have a lever of length 6 m and the pivot is 2 m from the object being moved so that your end of the lever is 4 m from the pivot. As you move the lever through angle [itex]\theta[/itex] radians, you will have moved your end of the lever a distance [itex]4\theta[/itex] meters. At the same time the object will have moved a distance of [itex]2\theta[/itex] meters. Since work (energy) is "force times distance" and energy is conserved, the work you do, the force you apply to the lever times [itex]4\theta[/itex] must be equal to the force applied to the object by the lever times [itex]2\theta[/itex]:
    [tex]F_{object}(2\theta)= F_{you}(4\theta)[/tex]
    which reduces to
    [tex]F_{object}= 2F_{you}[/tex]
    Showing a mechanical advantage of 2 to 1- the force applied to the object is twice the force you apply to the lever.
  13. Jan 31, 2012 #12
    I'm suprised no one has mentioned the link from mechanical advantage to velocity ratio and mechanical efficiency.
  14. Jan 31, 2012 #13


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    Here's a way to understand mechanical advantage in general terms. Energy is always conserved. [edit: as mentioned by Tiny-Tim]

    When using any kind of pulleys or gears or levers, the power transferred through (work per unit time) is constant and so the work done over an interval is constant.

    So, for example if you have a lever, applying a force F on one side and moving a distance [itex]\Delta x[/itex], it yields an amount of work [itex]\Delta W = F\Delta x[/itex]
    That must be equal to the work done on the other side of the lever so you get:
    [itex]F_1 \Delta x_1 = F_2 \Delta x_2[/itex]
    You can thus use mechanical advantage to double the force but it will halve the motion.
    (classic lever with fulcrum 2/3 at 2/3 the length so the two sides has a 2/3 : 1/3 or 2:1 ratio.

    Apply 10 Newtons to one side and you'll get 20 Newtons on the other... however move the one side 5 cm and the other side will only move 2.5 cm.

    10*5 = 20 * 2.5 = 50 newton cm = .5 newton m = 0.5 joules.

    You can also generalize to pressures and change of volume torques and angles of rotation and also to voltage and flow of charge.

    Work = force times [itex]\Delta[/itex]distance = pressure times [itex]\Delta[/itex]volume = torque times [itex]\Delta[/itex]radian angle = voltage

    likewise time rate of change of work which is power is:
    power = force times speed= pressure times volumetric flow rate = torque times angular speed = voltage times current.

    This assumes the ideal case with 100% transmission efficiency. Friction and other loss effects will suck up some of the energy or power in an actual example.

    So assume you want to lift an engine block which masses 1/2 a metric ton=500kg.
    It thus weighs 500kg x 9.8m/s^2 = 500 x 9.8=4900 newtons. (Multiply mass times gravitational acceleration to get weight as a force)

    You wish to lift it 2 meters. That means you want to do 9800 Joules of work. (Joule = Newton Meter)

    You can do this with a 5:1 pulley system where you pull on the rope with a 100kg lifting force (980 newtons=1/5 the force) by pulling with that force 5 times as far (10 meters).

    You can also do this with a pneumatic lift applying say 1 torr = (100,000 Pa = 100,000N/m^2 = 100,000 Joules / meter^3)
    by displacing .098 cubic meters= 98000cc's.
    (or use 100 torr displacing 980cc's that's a bit under 1 atmosphere pressure)

    Or use a 240V electric wench which will require 9800/240 ~ 40.83Coulombs. (at 10Amps that will lift it in 4.083 seconds.)

    Mechanical advantage is a matter of spreading the work out over a greater amount of motion so it requires less force. In the end though work input = work output.

    Archimedes said “Give me a place to stand and with a lever I will move the whole world.” what he neglected to say was “but not very far ; ) ”
    Last edited: Jan 31, 2012
  15. Feb 9, 2012 #14
    Sorry if the answer’s already posted and I’m just not bright enough to see it. But, what I’m really asking is can a person (the smartest person ever for argument’s sake) move a lever with mechanical advantage and actually understand/feel it in their mind how it‘s requiring less force, or is it ‘just how the universe works?’ Is it how sankalpmittal said, center of gravity will dominated at the longer side of the lever?

  16. Feb 9, 2012 #15
    See the post of Michael C i.e. post 9 , it has link to a good site which has your answer I think.

    Here is my answer :
    I think you are confusing principle of lever with law of conservation of energy.

    http://www.astarmathsandphysics.com/o_level_physics_notes/o_level_physics_notes_moments_the_lever_principle_html_210ae596.gif [Broken]

    Now see , in above image that lever is balanced at fulcrum with distance d > distance D
    Now since lever is balanced , then anticlockwise moments equals clockwise moments.

    Then ,
    w*d = W*D
    since w<W and d>D
    W/w = d/D
    Now see that resultant force will act on the point which divides the ratio of distance "d+D" in d:D.
    As we know that d> D so the resultant force will dominate at the side of distance d.
    Hint : Here centre of gravity will be at midpoint of distance "d+D" that is at the side left of fulcrum in this system ! Also think about section formula of coordinate geometry.
    W/w = mechanical advantage as well
    M.A. = d/D
    Hence the mechanical advantage will be with the small stone of weight w.

    Does this help ?:smile:

    Edit : Tiny-Tim thought that you were asking about law of conservation of energy in which work input equals work output. That's different matter although here it applies as its a universal law. Halls Of Ivy too answered your question in different way. jambaugh too had a great explanation.
    Last edited by a moderator: May 5, 2017
  17. Feb 9, 2012 #16


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    Meditate on the idea that Force is a Rate of work per distance. Say it out loud, "Force is work per distance!"

    As I move a lever I am doing a given amount of work, since the lever transforms distance traveled it "dilutes" or "concentrates" the work per distance i.e. the force.
  18. Feb 10, 2012 #17
    Refer this image : http://postimage.org/image/51wfdnhwn/ [Broken]

    Mathematical reason :

    Kinetic energy of load arm = Kinetic energy of effort arm
    By this we get :\
    Mass of load/Mass of effort =Inverse Ratio of square of velocities
    By image we get
    Mass of load = 4 times mass of effort
    As velocity of effort is twice the velocity of load
    So Velocity ratio = 2
    For an ideal machine
    Mechanical advantage = Velocity ratio
    Load = twice of effort
    From this we can get that acceleration in effort is twice of load.

    Also power input = power output
    or work input equals work output
    So greater the arm less is required force for lever to be in equilibrium.

    Theoretical reason : Since angle θ is same in both triangles (see image) and base of effort side is double of base of load side then its obvious that effort arm will cover greater arc distance than load arm. Since work input equals work output , we have to say that effort must be half of load for same work distance. Less mass more acceleration. Also note arc distance by effort is twice of that of load ,as ratio has to be maintained. Also note that initially both arms are at rest.
    Last edited by a moderator: May 5, 2017
  19. Feb 10, 2012 #18
    I think the OP is asking, not for a way to prove that levers supply a mechanical advantage, but for how the atoms in a lever interact so that the forces at one end are different to the forces at the other.
    i.e. what is the cause of mechanical advantage?
  20. Feb 10, 2012 #19


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    Ahhhh, yes that's a different question. For that it is important to understand (if I'm lifting you with an off center see-saw) that it is not my downward force which lifts you but rather the force the fulcrum is pushing upward to both lift you and oppose my downward force.

    It is the same force that keeps us from falling to the center of the Earth though gravity is trying to make us do just that.

    It is also an important consideration when setting up a mechanical advantage system. You can have a strong lever and good advantage but if you use a weak fulcrum it will break before you lift your load.

    Ultimately to get a full understanding I think one should study vectors and understand how the various directed forces add up and cancel.
  21. Feb 10, 2012 #20


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    I think that is taking things much too far in one go. All in one breath you're supposed to have a grasp of inter-atomic forces / quantum mechanics AND the Principle of Moments. Moments are soooo much easier to cotton on to that they are taught to 13yr old kids. QM is seldom grasped until Degree level.

    'Looking back' one can often see a link between elementary and advanced stuff but only when 'you know the answer anyway'.

    Also, I am not at all happy about the term "Kinetic energy of the Load arm" in the first post. Moments have nothing at all to do with MASS or Kinetic energy. They relate FORCES and DISTANCES. If you consider Power, then you should be discussing Force times Speed - which is measured in Watts, in the end.
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