How can small forces move great weights?
How can small sentiments saturate one’s heart?
Here, we think of the concept of forevers levers.
Three elements in the lever:
· Fulcrum
o Acts as centre; a point that remains stationary.
· Two weights
o The one which causes the movement
o The one that is moved
Principle:
The ratio of the weight moved, to the weight moving it is the inverse ratio of the distances from the centre.
The greater the distance from the fulcrum, the more easily it will move.
The reason has been given before that the point further from the centre describes the greater circle; so that by the use of the same force, when the motive force is farther from the lever, it will cause greater movement.
In Archimedes’ On the Equilibrium of Planes (Propositions 6 and 7 of Book I), the Law of Lever states that:
“Magnitudes are in equilibrium at distances reciprocally proportional to their weights.”
Summary of On Equilibrium of Planes
1. Equal weights at equal distances are in equilibrium, and equal weights at unequal distances are not in equilibrium but incline towards the weight which is at the greater distance.
a. When two things weigh the same and are the same distance away from the middle, they will be at equilibrium. And if one of the objects is further away, it will be lower on the balance.
2. When weights at certain distances are in equilibrium, something is added to one of the weights, they are not in equilibrium but incline towards that weight to which the addition was made.
a. When there are 2 objects with same weight, they are at equilibrium, but when more weight is added to one of the objects, it will be lower the balance.
3. If anything be taken away from one of the weights, they are not in equilibrium but incline towards the weight from which nothing was taken.
a. If something is removed from one of the sides, that side will end-up being raised.
4. When equal and similar plane figures coincide if applied to one another, their centres of gravity similarly coincide.
a. If 2 objects coincide, they will be in equilibrium
5. In figures which are unequal but similar the centres of gravity will be similarly situated. By points similarly figures, I mean points such that, if straight lines be drawn from them to the equal angles, they make equal angles with the corresponding sides.
a. When 2 objects have different weights, they will not be at equilibrium
6. If the magnitudes at certain distances be in equilibrium, other magnitudes equal to them will also be in equilibrium at the same distances.
a. If 2 of the same weighted objects are equally moved further or closer from the centre, they will still be at equilibrium
7. In any figure whose perimeter is concave in (one and) the same direction the centre of gravity must be within the figure
a. If the objects shape is different in any way, the centre of gravity will stay within the figure.
If two persons are roughly exerting the same effort, situated at points equidistant from the core that holds them, will never get the balance they’re both looking for. Simply, one will always have a heavier load than the other. The one with the heavier burden will have to move closer to the core reason that holds them, to achieve that equilibrium. Altering the distance of two persons from the fulcrum obviously affects both sides.
We all want every relationship to work out perfectly. And by work, there should be an effort exerted in maintaining the bond even over a distance. But in reality, there is no “lever” to do all the work...allowing to lift the burdens you’d never be able to budge yourself.
Reference:
Dijksterhuis, E.J.(1987). Archimedes. Princeton, N.J., USA: Princeton University Press.
Hett, W.S. (1936). Aristotle:Minor works. Harvard University Press, Cambridge, 25(3), 353-355.
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