October 4th, 2012, 12:00 PM
Everyone knows about the law of the lever, in order for a see-saw to balance the torques must cancel each other.
The question is, how fundamental is it? Can the Law of the Lever be derived from Newton's three laws or is it a fundamental law in its own regard?
Some may say it stems from consv. of energy, but it still holds when no work is being done.
No laws are fundamental, doggy. A "law" is where some guy says "it's the law, it just is" instead of explaining why it is. A variant on that is "a symmetry of nature". That said, the law of the lever is a variant of Newton's third law, which can be paraphrased as "for every action there is a reaction". Note that the wikipedia article on action(physics) says this:
"Action has the dimensions of [energy]•[time], and its SI unit is joule•second. This is the same units as angular momentum."
i can see how it relates to the 3rd law, but how is the equation F1d1 = F2d2 derived? From consv. of energy, or is that just the way it is?Originally Posted by Farsight
Wherever there is a force, work is being done, in some frame of reference.
Yes, from conservation of energy, but from direct experience too. It's to do with the way force is an aspect of interaction, and interaction is a two-sided coin. If we interact and I push you on a playground swing, I exert a force on you for a distance. I just can't do this without you exerting a force on me for a distance too. When we interact on a seesaw, the lever that is the seesaw serves as a primitive gear, changing the ratios. If ever you see some expression involving force, such as F=ma, always remember that this is only half of a two-sided coin.
well that still doesn't bring me closer to a rigorous derivation.Yes, from conservation of energy, but from direct experience too. It's to do with the way force is an aspect of interaction, and interaction is a two-sided coin. If we interact and I push you on a playground swing, I exert a force on you for a distance. I just can't do this without you exerting a force on me for a distance too. When we interact on a seesaw, the lever that is the seesaw serves as a primitive gear, changing the ratios. If ever you see some expression involving force, such as F=ma, always remember that this is only half of a two-sided coin.
maybe its just the way it is, no derivation involved.
I don't think the law of the lever is some "just the way it is" thing. See this for something about it.
but all that was empirically determined.
Naggy, could you explain what you mean by "fundamental"?
From a seesaw, let's go back one step of complication to tug-of-war. A tug-of-war is one-dimensional, involves positive and negative forces, works by summing the forces, and can be zeroed.
Now let's move up to a seesaw. A seesaw is two-dimensional, involves positive and negative (helium balloons?) forces, involves positive and negative radii, works by summing the products of each force times its radius, and can be zeroed.
You could make the seesaw more complicated than that by solving its zeroed position using more complicated method*, and you can do the same thing for a tug-of-war, but that's not really saying anything remarkable because it seems we can always add on some mathematical bells and whistles.
So, I'm just wondering now what you mean by "fundamental".
Apart from pure mathematics, isn't everything based on observation and evidence? That is one of the things that makes science, science.
I second that, Naggy. Mathematics is a vital tool for physics, but empirical evidence is what makes physics what it is. It's like we're sitting round a green baize table, and you play your trump card called mathematical proof. Only then I lay my hard scientific evidence card on top of yours. It trumps your mathematical proof. It's more important.
Please don't call me Naggy or Doggy. You have to call me by my full name, Naggy Doggy.
Apart from pure mathematics, isn't everything based on observation and evidence? That is one of the things that makes science, science.
But the KE formulacan be derived from newton's 2nd law and integration techniques. So not everything may have a purely empirical underpinning. but i suppose the law of the lever was straight up from empirical evidence.
But where does Newton's second law come from: observation of how the world works.But the KE formula
Newton's second hypothesis is borrowed from Galileo's works.
It does, you just have to be able to see through the maths to understand what lies beneath. Imagine a 1kg cannonball is travelling at 1000m/s, and you apply some constant braking force to slow it down to a halt in say 5 seconds. Kinetic energy KE=½mv² is statement of its energy-momentum in terms of force x distance, whilst momentum p=mv is a statement of its energy-momentum in terms force x time. Draw out lines of different lengths to represent how far the cannonball travels for each second you're slowing it down, and you end up with something like this:But the KE formula
____________________
________________
____________
_______
___
The total length equates to half the area of a v² square. And if was a 2kg cannonball the same constant force won't stop it in 5 seconds. This is why ½mv² applies.
If we would bother to learn the magnetic equivalent of the fulcrum, imagine the possibilities.
What is the magnetic equivalent of the fulcrum?
Turns ratio?
The electromagnetic equivalent of the fulcrum is the screw thread. Look at the right hand rule on wikipedia and note the reference to the corkscrew rule. Also see the caption under the second picture that reads the right-hand rule as applied to motion produced with screw threads. If you turn a dynamo it shoves current up the wire. The rotational motion is converted into linear motion, like driving a screw. If you push current up the wire it turns a motor. The linear motion is converted into rotational motion, like a pump-action screwdriver. You can see it in Minkowski's Space and Time which surely everybody has read:
"In the description of the field caused by the electron itself, then it will appear that the division of the field into electric and magnetic forces is a relative one with respect to the time-axis assumed; the two forces considered together can most vividly be described by a certain analogy to the force-screw in mechanics; the analogy is, however, imperfect."
It's also there in Maxwell's On Physical Lines of Force. See wiki page 53 where Maxwell says this:
"A motion of translation along an axis cannot produce a rotation about that axis unless it meets with some special mechanism, like that of a screw."
Search me why this isn't common knowledge.
The corkscrew rule sounds more like the electromagnetic equivalent of ... well, a screw thread, rather than a fulcrum.The electromagnetic equivalent of the fulcrum is the screw thread.
Perhaps the electric equivalent of a lever is a transformer: you can have more voltage at lower current and vice versa.
I'm not kidding you, Strange. A fulcrum changes linear motion this way into linear motion that way, and vice versa. A screw thread changes rotational motion this way into linear motion that way and vice versa. Maxwell and Minkowski didn't talk about screws for nothing. That's the way electromagnetism is, and incredibly hardly anybody seems to know about it.
Very good, you are quite close, it does indeed involve the right hand rule. It is about utilizing the point of maximum efficiency, to obtain the most leverage in extracting energy by harnessing the actual structure of the electricity.The electromagnetic equivalent of the fulcrum is the screw thread. Look at the right hand rule on wikipedia and note the reference to the corkscrew rule. Also see the caption under the second picture that reads the right-hand rule as applied to motion produced with screw threads. If you turn a dynamo it shoves current up the wire. The rotational motion is converted into linear motion, like driving a screw. If you push current up the wire it turns a motor. The linear motion is converted into rotational motion, like a pump-action screwdriver. You can see it in Minkowski's Space and Time which surely everybody has read:
"In the description of the field caused by the electron itself, then it will appear that the division of the field into electric and magnetic forces is a relative one with respect to the time-axis assumed; the two forces considered together can most vividly be described by a certain analogy to the force-screw in mechanics; the analogy is, however, imperfect."
It's also there in Maxwell's On Physical Lines of Force. See wiki page 53 where Maxwell says this:
"A motion of translation along an axis cannot produce a rotation about that axis unless it meets with some special mechanism, like that of a screw."
Search me why this isn't common knowledge.
Correct again! The structure we are talking about is the double helix, which is the electrical equivalent of the fulcrum, and as Farsight correctly identified in linear motion as the equivalent of the screw.
So why does electricity form a double helix in a wire? and why, when creating plasma, form a double helix on the outside of the wire? Could Thompson be wrong or shall we just ignore the physical evidence?
What you say makes sense. Apart from the fact of comparing it to a fulcrum. As you say, a fulcrum/lever converts linear motion (and more importantly has a relationship between force and distance). But a screw thread does something different.
Everyone is taught the corkscrew rules. Is a corkscrew substantially different from a screw thread? What am I missing here?That's the way electromagnetism is, and incredibly hardly anybody seems to know about it
No.
It's probably to do with what Minkowski said: the analogy is, however, imperfect. You know how when we talk of gravity we usually start with a sphere where the "force" of gravity diminished with distance on an 1/r² basis? Only then we sometimes talk about a mass configured like a long rod, where force diminishes on a 1/r basis? To go from one to the other you take an equatorial slice through the sphere, copy it n times, and then stack all the slices on top of one another to form a rod. The current in the wire is a bit like this in that the electron's electromagnetic field has a spherically symmetric disposition, but when you have a column of electrons moving past a column of protons, the spherically symmetry has gone and is replaced by rotational symmetry around the wire. The linear forces cancel, so they're gone too and you only get the rotational force. We indicate that with the concentric "magnetic field lines". If we had only a column of electrons we'd see linear force too, and we'd indicate that with the radial "electric field lines". But because it's the electromagnetic field we ought to depict it with something that combines the concentric and radial lines. Such a depiction would resemble the frame-dragging you see in artist's impressions of gravitomagnetic field. Have a read of The role of the potentials in electromagnetism by Percy Hammond for something more formal. See the bit near the end: "We conclude that the field describes the curvature that characterizes the electromagnetic interaction."
[QUOTE=Farsight;357497]It is one of my biggest torments, the Kinetic, maybe I'm jealous of that Boy, Issac.
When we integrate, we take Triangulation. And very very very small Triangulation.
It is at best, an approximation, but the finest ever.
I like his concept of momentum, it is brilliant.
But I do not like his Inverse Square Law...
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