pulleys, dollies, workaholies

[AntonioLao]

Pulleys and dollies all provide mechanical advantages when lifting or moving loads against the forces of gravity and inertia, but as the number of strand or pulley increases the distance traveled by the load decreases. This phenomenon disguises the fundamental working principle behind Archimedes’ lever.

In 2D, Archimedes’ lever is denoted by F1·R1=F2·R2, a scalar inner dot product. In 3D, its description is the equivalent of a torque t=F´R, a vector outer cross product. Since vector outer cross product is not commutative, F´R=-R´F. This is analogous to a vector potential. The scalar potential is just F·R and it is commutative that is F·R= R·F. In order to transform these into each other, it is necessary to take the squares of both expressions. The math is easy to do but the physics becomes complicated. However, the square of energy can be expressed as E= F1´R1·F2´R2. When expanded by Lagrange’s identity E=(F1·R2)(F2·R1)-(F1·F2)(R1·R2) and E=(F1·F2)(R1·R2)-(F1·R2)(F2·R1). The physical meaning of each scalar product needs to be explained further.

[Guille]

Antonio, I really find interesting these points about the square of energy. I have several questions:

1. By stating that E=(F1·F2)(R1·R2)-(F1·R2)(F2·R1)=(F1·R2)(F2·R1)-(F1·F2)(R1·R2) and that E=F1·R1=F2·R2 then do you mean that the square of energy is the inverse of Energy? Or if not, then what does the alteration of the F1, F2 and R1, R2 mean?

2. By the equation E= F1´R1·F2´R2 do you mean that E is the vector product of E with itself? If so, what would the square of energy be/mean if it was the scalar product of E with itself?

3. By equating that (square of the force times the sqaure of the distance)-(energy of 1 times energy of 2) do you mean that the square of energy is the square of force times the square of distance too? It would be logical. But here the important question would be: just like we can expand to mv the momentum in QM, is it not permitted to expand E to FR? And, ultimatelly, what do R and F mean? And what could RE and FE mean?

4. As you don't right the type of multiplication being done in the brackets (in the formula about the square of energy), is it scalar or vector? (Im refering to the multiplication like (F1·F2)(R1·R2), what is the multiplication between the brackets, scalar or vector?).

[AntonioLao]

I have several questions:

A comprehensive answer to all the questions is that energy or square of energy are all scalars. To get a scalar from vector, one uses the scalar inner dot product. This is fine in math but the physics of F dot F becomes meaningless unless it means orthogonal forces and the product vanishes.

[mkirkpatrick]

You have made some interesting points Antonio.A very long lever can move much,what could an Idea move do you think?What is the weight of say heavy
thoughts,could you use a lever to lighten them.just a thought.



kind regards michael.

[AntonioLao]

what could an Idea move

It can move mountain, split the atom, land a man on the moon, wipeout infectious diseases, reach the bottom of the deepest ocean, remember the name of every person on planet Earth, while there is a will of an idea there is a way.

[mkirkpatrick]

It can move mountain, split the atom, land a man on the moon, wipeout infectious diseases, reach the bottom of the deepest ocean, remember the name of every person on planet Earth, while there is a will of an idea there is a way.

Well then let us formulate the idea together to
bring about fusion,and let us have the will to do this,so that the planet can have free limitless power,and banish hunger and poverty forever.

kindest regards michael.

[AntonioLao]

let us formulate the idea together to
bring about fusion,and let us have the will to do this,so that the planet can have free limitless power,and banish hunger and poverty forever.

That's a tall order. But I think it is doable. For my part first I need to find the mechanism that would directly derive energy from the vacuum. Watch for more relevant posts.