CONTENT: inclined plane, screw and wedge
TOOLS USED: multimedia presentation (Microsoft PowerPoint), video projector
PLACE: multimedia lab
DURATION: 2 hours
The lesson takes place in the multimedia lab, where it is disponibile la postazione PC del docente e il videoproiettore necessari alla presentazione dei contenuti della lezione.
Questa volta la lezione inizia in maniera un po’più “allegra” per gli allievi invitandoli da subito “a provare” un paio di applets riguardanti il piano inclinato. Diciamo che si vuole un po’cambiare il tradizionale approccio seguito nel corso delle precedenti lezioni per destare un po’di curiosità e forse stupore.
Si noti che la cosa è possibile perché in realtà l’argomento “piano inclinato” dovrebbe essere già stato trattato nel corso di fisica nei precedenti anni scolastici.
In particolare viene proposto un first applet that simulates the descent of a body from an inclined plane and a second applet where you can see, inter alia, the breakdown of the forces driving and tough.
Once this phase is to return to work as in previous lessons:
a power point presentation will illustrate the arguments and the same comment by the teacher will clarify the proposed contents.
The slides will try to present the basic theoretical concepts to minimize the necessary formulas and mathematical omitting some steps or considerations "individuals" because as I said the topic is not new.
The inclined is particularly useful when lifting heavy bodies, when you have a space plan "b" large enough to lift the height "h".
A tangible example of this simple machine in the example you have access ramps to public entities for the reduction of architectural barriers or the streets of our cities to facilitate the passage of prams and strollers in city driving.
In particular to analyze the characteristics of the inclined plane will consider two possibilities for the application of power.
a. driving force directed along the inclined plane
split the weight Q in both directions parallel (Q1) and perpendicular to the slope (Q2), the assumption of neglecting the resistance due to friction, we have that the resisting force is represented only by the parallel component Q1 floor
b. driving force applied horizontally
with the component Q2, similar considerations will not affect the equilibrium to the next upward movement, so:
In regard to the final evaluation of the benefit that can be achieved with the installation the inclined plane would:
in the first case the slope is always advantageous as the sine of the angle never exceeds unity, while in the second case the system is beneficial as long as the angle exceeds 45 º 45 º sz = 1 being over the limit, the tangent is higher than one and the system becomes uneconomical.
Another example of simple machine is the screw used as a lifting mechanism that is outlined below
It essentially consists of a threaded rod (a) that engages in fixing nut (M), so that by exerting a horizontal force (F) at the end of the arm (b) firmly fixed to the auction itself, it is placed in rotation and, due to the inclination of the thread, took a slow upward motion. If the end of the screw applies a load (Q), it moves upward dragged by the screw itself.
The screw consists of a cylindrical body (called stem) engraved with a spiral groove, the projection (thread) that fits into a groove groove identical insertion within a body (nut).
pitch p (distance between two grooves along a generatrix later) of a screw can be determined, note the angle α of the groove to the plane perpendicular to the propeller shaft and the radius r media, according to the formula
where we have developed the threads in the drawing plane resulting in a right triangle where the length of the catheter is 2πr basic step height is given by "p" or the schematic done so we can bring the calculation of the screw to the inclined plane with driving force parallel to the base (case b).
If we now denote by F 'the driving force agent along the average circumference of the screw Recalling the "F = Q tg α" obtained in case b, we have:
note that F 'acts tangentially to the screw arm r and the effective driving force F act at the end of the arm operation (b).
At this point, and identify the value of F will be enough to impose the condition of equilibrium of moments from the axis of rotation:
and simplifying
the ultimate benefit of the screw will be inversely proportional the thread pitch "p" and directly proportional to the length of the arm di manovra “b”:
Concludiamo questa rassegna delle principali macchine semplici considerando "il cuneo"
Il cuneo è un prisma avente per sezione un triangolo isoscele molto allungato e quindi con un angolo al vertice molto allungato; nelle applicazioni pratiche esso è formato da due piani inclinati (fianchi) uniti per la base. In esso la resistenza è applicata perpendicolarmente ai fianchi (AC e BC), mentre la potenza viene applicata alla testa (AB). L’angolo di apertura del cuneo determina il rapporto tra potenza e resistenza: tanto minore è questo angolo tanto maggiore è la resistenza che può venire equilibrata da una given power. The wedge is a machine advantageous (ie, the applied power is less than the resistance to win) and is normally used to cause the separation of two parts of a body. They exploit the principle of the wedge all the objects that are used to cut or penetrate (the blades of knives, axes, nails, etc...)
Decomposing F in two directions normal to the sides AC and BC has, apart from friction:
which
then reduce to a minimum ratio of the length of the head and the hips, and then increase his lead, it means in practice that the cutting edge of the wedge can be sharper, that is, the angle should have small values.
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