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Levers - The PjProblemStrings


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Strings (SiPjAjk) = S7P3A32     Base Sequence = 12735     String Sequence = 12735 - 3 - 32

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Levers - The PjProblemStrings
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Levers The PjProblemStrings

Levers are simple machines. Figure 128.1 illustrates a 6-inch file scraper (brown) being used to pry up the lid of a can.

(a) Name the other types of simple machines.
(b) What type of lever is the file scraper illustrated in figure 128.1?
(c) The blue arrows associated with the file scraper are
implicitly PjProblemStrings. Make them explicit.
(d) What is the mechanical advantage of the file scraper,
given that MN is 1 inch and NQ is 5 inches?

The strings: S7P3A32 (Force-Push).

The math:
Pj Problem of Interest is of type force (push/pull).

Levers The PjProblemStrings

(a) There are six explicit types of simple machines (lever, inclined plane, block and tackle, wheel and axle, screw and gear). However, physicists group simple machines into levers and inclined planes since block and tackle, wheel and axle and gears can be considered as levers while screws can be considered as inclined planes.

(b) There are three types of levers: first class, second class and third class.
First Class: fulcrum is located between resistance and effort
Second Class: fulcrum is at one end, effort at the other end and resistance is somewhere between the fulcrum and the effort.
Third Class : fulcrum is at one end, resistance is at the other end and effort is somewhere between the fulcrum and the resistance.

So, the file scraper illustrated in figure 128.1 is a first class lever.

(c) Assuming a multi-matter-multi-dynamic space (S7) because of the dynamism of atoms of materials and the fact that there are several matter in the space.
Both the resistance and effort arrows are linearly directed forces (push).
So, the PjProblemStrings S7P3A32 and S7P4A41 are implied.
There is static equilibrium at the fulcrum
So, the PjProblemString (S7P7A71) is implied.

(d) Mechanical Advantage is essentially the gain in effort or the loss in effort. In other words, gain in effort implies the Resistance overcomed is greater than the Effort applied while loss in effort implies the Resistance overcomed is less than the Effort applied.
Mathematical equation for Mechanical Advantage (M.A):
M.A = Reistance/Effort = L/l
Where L = length of effort arm (NQ)
l = length of resistance arm (MN).

So, for the file scraper of figure 128.1, M.A = 5/1 = 5
That is the effort can overcome a resistance that is five times the effort applied.

First Class and Second Class levers provide M.A > 1.
Third Class levers provide fractional M.A. They are often used to speed up resistance at the expense of effort. In other words, effort applied is greater than resistance overcomed because of the desire to overcome the resistance speedily.

The point . is a mathematical abstraction. It has negligible size and a great sense of position. Consequently, it is front and center in abstract existential reasoning.
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