The Screw - The PjProblemStrings

**Strings (S _{i}P_{j}A_{jk}) = S_{7}P_{3}A_{32} Base Sequence = 12735 String Sequence = 12735 - 3 - 32**

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The Screw - The PjProblemStrings

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Figure 132.1 illustrates a jack screw. This machine belongs to the class of simple machines called the *screw*. Some common members of this group are the micrometer, the foodprocessor used to grind meat, the rigger's vice and the friction brake.

(a) Physicists say, the screw is a type of an inclined plane. What simple experiment shows that the screw is an adaptation of the inclined plane?

(b) What is the theoretical mechanical advantage of the jack screw of 132.1 if R = 24 and p = 1/4?

(c) Why is it that most of the theoretical mechanical advantage of the jack screw is lost to friction?

(d) Write the PjProblemStrings at play with respect to the jack screw of figure 132.1

**The strings**:
S_{7}P_{3}A_{32} (Force-Push).
**The math**:

Pj Problem of Interest is of type *force* (push).

(a) A *screw* is an adaptation of an inclined plane. A simple experiment that supports this fact is as follows:

Cut a sheet of paper in the shape of a right triangle to represent an inclined plane. Wind the right triangle paper around a cylindrical pencil by turning the pencil such that the hypotenuse of the right triangle forms a spiral thread as shown in figure 132.2.

(b) The *theoretical mechanical advantage* (T.M.A) ignores the effect of *friction*. TMA = distance effort moves/distance resistance moves = Resistance/effort.

So, for the jack screw in figure 132.1:

T.M.A = 2πR/p where p is the pitch of the screw.

So, T.M.A = (2 x 3.14x 24)/(1/4) = 602.88.

(c) The Jack screw has much friction loss because the threads are cut such that the force used to overcome friction is greater than the force used to do useful work so that the load does not slip down when the effort is released.

(d) Assuming a multi-matter-multi-dynamic space (S_{7}) because of the dynamism of atoms of materials and the fact that there are several matter in the space.

Forces at play of type *push*. PjProblemStrings S_{7}P_{3}A_{32}

Motion at play, *rotational* at effort, linear at load. PjProblemStrings S_{7}P_{4}A_{42} at effort and S_{7}P_{4}A_{41} at load

static equilibrium at load when effort is released. PjProblemStrings S_{7}P_{7}A_{71}

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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