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‹intestazione›
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Leonardo e la sua scienza
•= 3;
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•= 3;
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Argomenti di fisica
• Nel Cod= ice Atlantico, Leonardo traccia alcuni problemi concettuali che diventeranno c= on Galileo e Newton i temi basilari dell’edificazione della fisica classica. Vengono inoltre anticipate alcune osservazioni semplici che oggi sappiamo spiegare grazie alla fisica moderna.
•
•FISICA CLASSICA <= /b>
•
•= Attrito = ;
•= Il volo = ;
•<= span style=3D'font-family:"Times New Roman";font-size:67%;mso-special-format:la= stCR; display:none'>
•FISICA MODERNA
•
<= span style=3D'font-family:"Times New Roman";font-size:67%'>•= Tensione superficiale
<= span style=3D'font-family:"Times New Roman";font-size:67%'>•= Tensione lineare
<= span style=3D'font-family:"Times New Roman";font-size:67%'>•= Proprietà dei metalli
<= span style=3D'font-family:"Times New Roman";font-size:67%'>•= Transizioni di fase
<= span style=3D'font-family:"Times New Roman";font-size:67%'>•= Diffrazione della luce
<= span style=3D'font-family:"Times New Roman";font-size:67%;visibility:hidden'>• = ;
• = ;
•= ➱= torna a Leonardo e la sua scienza
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Moto perpetuo
•
•Leonardo progetta al= cune macchine a moto perpetuo. Dal secolo scorso è ben nota l’impossibilità del moto perpetuo, sancita dalle leggi della termodinamica. Anche se la cronaca ogni tanto riporta notizie curiose…
•
•Primo principio della termodinamica: l’energia si conserva. Come dire: se lascio cadere un pallone, dopo il rimbalzo esso raggiungerà al massimo l‘altezza iniziale… <= /span>
•
•Secondo principio de= lla termodinamica: …ma siccome c‘è l’= attrito (dove?) il pallone tornerà = in un punto ad altezza minore rispetto al punto di partenza (e l’energia da „meccanica“ si trasforma parzialmente anche in „termica“, difficilmente riconvertibile per intero)
•
• <= span lang=3DDE style=3D'font-family:"Times New Roman";font-size:88%'>Fogli= o 25 – recto; foglio 40 – recto
• Fogl= io 179 -verso
•
• <= /span>
• <= /div>
➱torna a Argomenti di= Fisica
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Attriti =
=
•L’attrito è la causa della trasformazione dell<= span lang=3DDE style=3D'mso-ascii-font-family:"Times New Roman";mso-bidi-font-f= amily: "Times New Roman";font-size:75%'>’energia meccanica in
= •calore. Oltre a sott= rarre energia alla macchina, effetto che si può
= •minimizzare utilizza= ndo olio o vari = congegni antifrizione, il
•calore può danneggiare la macchina (pensiamo ai computer):
= •per evitare questo, Leonardo progetta di immergere la macchina
= •in acqua corrente. &= #13;
= • C.A.: Foglio 83 – verso
•Leonard= o pensa anche a come sfruttare questo calore:
•progett= i di acciarini (con pietra focaia)
<= span style=3D'mso-special-format:nobullet;display:none'>• C.A.:= Fog= lio 158
•Ma pens= a anche all’attrito con l’aria e così nasce l’idea del = paracadute
= • C.A.: Foglio 1058 R= 11; verso
•
•
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Congegni antifrizione
• Oggi si usano i cusc= inetti a sfera, che trasformano uno strisciamento in un rotolamento. Il vantaggio è che il secondo (attrito volvente) è minore del primo (attr= ito radente), come deve aver scoperto quel nostro antenato che ha inventato la ruota!
•
• Leonardo progetta dei precursori dei cuscinetti a sfera (rulli, sfere), dei perni di diamante e delle ruote d&#= 8217;acciaio temperato.
•       C.A= .: = Foglio 91 - recto<= /b>; Foglio 91 – recto
<= span style=3D'font-family:"Arial Unicode MS";font-size:44%;visibility:hidden'><= span class=3DBB style=3D'position:absolute;left:-4.24%'>•
• <= /span>
= 226;
•
➱torna a Argomenti di= Fisica
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Galleggiamento
•Quando si galleggia e quando invece si affonda? Dipende dalla densità relativa dei due co= rpi. Il corpo galleggia se la sua densità è minore di quella dell= ’acqua. Attenzione, anche un oggetto di fe= rro può galleggiare…basta che sia cavo!
•
•        = ;            &n= bsp;      approfondimenti: = la spinta di Archimede
•
•La stessa cosa vale nell&#= 8217;aria (mongolfiere)
•
•E gli aerei allora? Sono piu pesanti dell’aria!
•        = ;            &n= bsp;     vai a = Il volo
••C.A.: Foglio 26 – recto
• = ;
•
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Bombarde e balistica
•Leonardo sembra consapevole della = traiettoria parabolica dei proiettili
•
•Inoltre la= gittata massima si ottiene proprio per alzo 45°, = come diseg= nato da Leonardo
•
•C.A.: Foglio 33 – = recto; Foglio 48 – recto;
•Foglio 72 – recto
<= span style=3D'font-family:"Times New Roman";font-size:75%;visibility:hidden'>•
•
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Moto parabolico
• Qualsi= asi moto può essere scomposto secondo dei “moti componenti” perpendicolari tra loro. Il moto di un proiettile è costituito allo= ra da un avanzamento per inerzia (moto rettilineo uniforme), a velocità costante e senza forze applicate (se trascuriamo l’attrito dell’aria) che avviene contemporaneamente ad una caduta verticale (m= oto uniformemente accelerato), dove la velocità aumenta regolarmente perché è presente una forza costante (la gravità).= 3;
• Combina= ndo le due equazioni del moto si ottiene la relazione tra la posizione x dell’avanzame= nto e la posizione y del= la caduta. Si ottiene che i punti (x,y) descrivono una parabola.
•
•
•
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Tensione superficiale dell’acqua
• Prova a depositare uno spillo (o una vecchia monetina da 5 lire) orizzontalmente sull’acqua: gal= leggia! <= span lang=3DDE style=3D'font-family:"Times New Roman";font-size:88%'>Eppure l’oggetto è metallico e non è cavo. Cosa succede? • Tra le molecole d’acqua si e= sercita una forza attrattiva sufficientemente elevata da vincere la forza peso dello spillo.
•
•C.A.:= <= span lang=3DEN-US style=3D'font-family:"Times New Roman";font-size:88%'>Fogl= io 42 – recto
<= span style=3D'font-family:"Times New Roman";visibility:hidden'>•
•
➱torna a Argomenti di= Fisica
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Il Tempo
•Il tempo è una delle „variabili“ piu comuni in fisica. La fisica stessa nasce dalla constatazione che gli oggetti si trovano in posizioni diverse al var= iare del tempo (cosa fa sì che gli oggetti si spostino?)
•
•Nonostante sia un co= ncetto molto utilizzato in fisica e nella vita di tutti i giorni, il tempo &egrav= e; un’idea affascina= nte la cui natura è ancora oggi di grande interesse e discussione per gli scienziati.
•
•
•= Approfondimento: la misur= a del tempo
•
•&#= 13;
• Foglio 42 - verso
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Orologi
• Per fare un orologio bisogna individuare un fenomeno che avviene con regolarità.
•
• C.A.:= = Fogl= io 65 - verso (= acqua che riempie il secchio, il galleggiante fa poi svuotare e si riparte) =
•
• <= /nobr>
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Equilibrio tra forze
• Leonar= do illustra un
• modo di legare i bastoni: l’obiettivo = è quello di far sì che la somma totale delle forze (in questo caso so= no le „reazioni vincolari“, cioè le forze dovute al contat= to tra corpi impenetrabili) sia zero.
•
• C.A.:= = Fogl= io 58 - verso
➱torna a Argomenti di= Fisica
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Metalli: duttili e malleabili
<= span style=3D'font-family:"Times New Roman"'>•Le proprietà dei metalli: da cosa derivano?
•
•Ci sono dei legami chimici molto forti tra gli atomi componenti: questo= fa sì che si possano lavorare anche in fogli o fili sottilissimi
<= span style=3D'font-family:"Times New Roman";visibility:hidden'>•
<= span style=3D'font-family:"Times New Roman"'>•= Approfondimento tecnico➱torna a Argomenti di= Fisica
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Pressione
•Spuntoni  : gli effetti dell’applicazione di una forza dipendono anche dalla superficie = di contatto. In particolare, si preferisce usare in questi casi il concetto di pressione, cioè la forza applicata per unità di superficie.
•
•Un oggetto sar&agrav= e; maggiormente penetrante se, a parità di forza esercitata, la superf= icie di contatto è minore.
•
•La differenza di pre= ssione è la causa del = volo e degli „effetti“ nel = movimento di una palla (calcio, baseball, volley…)&= #13;
•
• C.A= .: = Fogl= io 68 - recto
➱torna a Argomenti di= Fisica
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Macchine battiloro
= •L'oro e l'argento in foglia sono usati nella decorazione di ambienti esterni e interni, di vetri artistici, mosaici, sculture, insegne, cornici, mobili, libri, articoli in pelle e in molte altre svariate applicazioni.
•
•C.A.: = Fogl= io 67 - recto, A
➱torna a Argomenti di= Fisica
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Tensione lineare
•Leonardo si interroga sulla resist= enza di un filo m= etallico 
• C.A.: Foglio 222-recto=
• e di una corda
• C.A.: Foglio 393-recto=
• = ;
•Oggi diremmo che con= degli esperimenti di trazione possiamo determinare l’intensità delle forze d= i = legame tra le partic= elle costituenti il filo
➱torna a Argomenti di= Fisica
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il Volo
•Progetto di ali:
•
•C.A.: Foglio 166-recto;  
• Foglio 70 - recto, B
•
•
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Azione e Reazione
• Leonardo a= nalizza il „rinculo“ di una bombarda. La bombarda spinge il proiettile= , ma anche il proiettile spinge la bombarda. Le due forze sono uguali, ma non le due masse su cui si esercitano. Il moto del proiettile è dunque mol= to maggiore di quello della bombarda. Questo effetto è noto anche come= conserv= azione della quantità di moto di un sistema isolato
• = 3;
• C.A= .: Foglio 79 - verso=
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Esplosione
• = I framment= i di un ordigno costituiscono un sistema isolato. Inizialmente sono fermi e uniti = l’uno all&#= 8217;altro: la quantità di moto totale del sistema (l’ordigno) è quindi nulla. Lo sviluppo di forze interne= al sistem= a non cambia tale quantità, che rimane nulla anche in seguito all‘esplosione: infatti ogni frammento si muove con la stessa direzi= one e verso opposto di un qualche altro frammento.
<= span style=3D'font-family:"Times New Roman";font-size:75%;visibility:hidden'>•
<= span style=3D'font-family:"Times New Roman";font-size:56%;visibility:hidden'>•
<= span style=3D'font-family:"Times New Roman";font-size:56%;visibility:hidden'>•
• C.A.: <= span lang=3DEN-US style=3D'font-family:"Times New Roman";font-size:75%'>Fogl= io 79 - verso
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Altri concetti dinamici
•Leonardo prova a definire concetti= come = moto e potenza…
<= span style=3D'font-family:"Times New Roman";visibility:hidden'>•
• C.A.: Foglio 183-recto=
• = ;
<= span style=3D'font-family:"Times New Roman";font-size:88%'>•…e come peso, = massa e gravità
<= span style=3D'font-family:"Times New Roman";font-size:88%;visibility:hidden'>•
• C.A.: Foglio 197-verso
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Massa, Peso, Gravità
•Massa: quantità di materia; si misura in Kg
•
•Peso: è una forza, si misura in Newton; in particolare è la forza attrattiva (Forza di gravità) a cui è soggetto qualunque corpo sulla superficie di = un pianeta, e cambia al cambiare del pianeta
•
•Esempio: una persona ha massa 80 kg; sulla Terra il suo peso è circa 800 Newton, sulla Luna è cir= ca 130 Newton
•
•…e se il medico vi chiede quanto pesate, rispondete…
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Moto; potenza
•<= /span>Moto: il cambiamento della posizio= ne di un c= orpo al trascorrere del tempo.
•
•<= /span>Osservazione importante: per avere= del moto n= on è necessaria l’applicazione di una forza
•= (caso del moto rettilineo un= iforme o “inerzia”)
•
•La potenza è la forza applicata nell’unità di tempo, si misura in Watt (=3DNewton/secondo)
➱torna a Argomenti di= Fisica
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Formazione della pioggia
•Leonardo cerca di capire il meccanismo di = formazione della pioggia
•
•= C.A.: Foglio 205-recto
•
•Oggi sappiamo che si tratta di una transizione di fa= se: in seguito all’abbassarsi della temperatura e all’aumentare = del numero delle molecole (tasso di umidità), l’acqua passa dallo stato gassoso (f= orze m= olto deboli tra le molecole) allo stato liquido (le = molecole si attraggo= no reciprocamente con più forza)
➱torna a Argomenti di= Fisica
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Riflessione della luce
&#= 8226;Leonardo enuncia correttamente, nell’ambito di un modello “a raggi”= ; della luce, la legge= della r= iflessione: l’angolo di riflessione è uguale all’angolo = di incidenza
•
• C.A.: Foglio 226-recto; Foglio 240
• = ;
•
➱torna a Argomenti di= Fisica
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Diffrazione della luce
•Sembra che Leonardo fosse consapevole dei limiti del modello “a raggi”= ; della luce: quando l= a luce passa attraverso un forellino, sembra diffondersi attorno = all’apertura&#= 13;
<= span style=3D'font-family:"Times New Roman";font-size:88%;visibility:hidden'>•
• C.A.: Foglio 226-recto
• = ;
•Oggi chiamiamo questo fenomeno e lo = = spieghiamo ricorrend= o ad un modello ondulatorio della luce
<= span style=3D'font-family:"Times New Roman";font-size:88%;visibility:hidden'>•
<= span style=3D'font-family:"Times New Roman";font-size:88%;visibility:hidden'>•
➱torna a Argomenti di= Fisica
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Modelli per la luce
•Leonardo sembra utilizzare soprattutto il modello a raggi, = per il quale la luce &eg= rave; interpretata come raggi che si propagano in modo rettilineo dall= a loro sorgente; in particolare i raggi del Sole sono considerati paralleli tra loro…
<= span style=3D'font-family:"Times New Roman";font-size:75%;visibility:hidden'>•
•…ma è a= nche a conoscenza del moto ondoso, che presenta nella stessa pagina = ma non utilizza per interpretare i fenomeni luminosi
<= span style=3D'font-family:"Times New Roman";font-size:75%;visibility:hidden'>•
• C.A.: Foglio  226-recto
➱torna a Argomenti di= Fisica
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Il Metodo secondo Leonardo
•Leonardo si definisce “omo sanza lettere= ”. C’&eg= rave; però un vantaggio in questa mancanza di cultura: la necessità= ; di ricorrere a dimostrazioni e a fatti per argomentare le sue idee, piuttosto= che ricorrere alla citazione degli antichi senza utilizzare le proprie capacit= à;
•
•Da Vinci esprime esplicitamente dei criteri di verità per le regole scientifiche&= #13;
<= span style=3D'font-family:"Times New Roman";font-size:75%;visibility:hidden'>•
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Argomenti di Matematica
•Problemi di geometria dei solidi: piramide, cilindro, cono, <= /span>= cubo <= /span>
•
• <= /span>
•= ➱= torna a Leonardo e la sua scienza
•
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Numeri Irrazionali
• I numeri irrazionali sono costituiti da un numero infinito di cifre decimali per le quali non è possibile trovare alcuna periodicità. Esempi son= o pi greca &#= 960; , il numero di Nepe= ro e, la radice quadrata= di 2.
•
• Leonardo tenta il calcolo della radice cubica di 12= 8 e = riconosce che si tra= tta di un numero irrazionale.
•
• C.A.: Foglio 161-recto
• = ;
•
•
➱torna a Argomenti di Matematica
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Operazioni con frazioni
•Leonardo spiega le regole per i ca= lcoli con le fr= azioni….
•
• C.A.: Foglio 191-verso=
•
•….e tu, le conosci?  = Prova!
•
• <= /span>
•
➱torna a Argomenti di Matematica
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Testa le tue abilità con le frazioni
➱torna a Argomenti di Matematica
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• = C.A.: Foglio 212-recto = ;
•
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• C.A.: Foglio 43 – verso
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➱torna a Argomenti di Matematica
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Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" 5 Macchine semplici 5
Radice cubica
• Leonardo sa svolgere le radici cubiche <= /div>
•
• C.A.: Foglio 72 – recto
•
• e sa utilizzarle nel= la risoluzione di = problemi = = geometrici
•
• C.A.:= <= span lang=3DEN-US style=3D'font-family:"Times New Roman";font-size:88%'>Fogl= io 72 – recto
•
➱torna a Argomenti di Matematica
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Duplicazione del cubo
•Di quanto occorre aumentare il lat= o di un cubo p= er raddoppiarne il volume?
• Prova a pensarci e poi controlla la = risposta!
•
<= span style=3D'font-family:"Times New Roman"'>•Leonardo sapeva risolvere questo problema
<= span style=3D'font-family:"Times New Roman";visibility:hidden'>•
• C.A.: Foglio 244-recto=
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Raddoppiare il cubo…
➱torna a Argomenti di Matematica
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Geometria della piramide
•Leonardo svolge alcuni problemi:
•
•- Ricerca del baricentro di un tronco di piramide
•
• C.A.: Foglio 228-verso
•
-- Suddivisione di una piramide in piramidi
-
-= C.A.: Foglio 334-recto
-
➱torna a Argomenti di Matematica
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‹intestazione›
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