Fisica 1 , Ghigo Gianluca, Appunti + QUIZ Esame + Temi Esame (Polito)

Fisica 1 “Appunti completi del corso + integrazioni ed esempi pratici + raccolta temi d’esame + quiz dal 2013 al 2015 + lista domande/dimostrazioni richieste all’orale” validi per il corso del prof: Ghigo Gianluca

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Politecnico di Torino – Compito scritto di fisica I – 15 settembre 2015

Cognome e nome matricola crediti

Una massa m = 1 kg ruota con velocità angolare costante in un piano verticale attorno al punto O per effetto di una fune inestensibile e di massa trascurabile, di lunghezza L = 1 m. Se la massima tensione che la fune può esercitare prima di rompersi (carico di rottura) è T_max = 50 N, qual è la massima velocità angolare che si può imprimere alla massa m?

• ω_max = 40 rad/s
• ω_max = 6.3 rad/s
• ω_max = 19.5 rad/s
• ω_max = 12.6 rad/s

Un punto materiale si muove su un piano orizzontale privo di attrito, essendo legato ad una molla ideale.

• Quando la compressione della molla è massima la velocità del punto è massima.
• Quando l’allungamento della molla è massimo la velocità del punto è massima.
• Quando la molla ha lunghezza pari a quella a riposo, la velocità del punto è massima.
• Quando la molla ha lunghezza pari a quella a riposo, il modulo della velocità del punto è nullo.

Una grandezza A è definita come il rapporto tra la variazione della quantità di moto e l’impulso della forza, entrambe riferite allo stesso punto materiale. Cosa si può dire di A?

• Che le sue dimensioni sono [M L T^-1].
• Che le sue dimensioni sono [L T^-2].
• Che è adimensionata.
• Che nel Sistema Internazionale si misura in kg·m·s^-1.

Una sfera di alluminio (densità ρ_Al = 2700 kg/m³) di raggio R = 75 cm presenta all’interno una cavità vuota. La sfera è in equilibrio all’interno di un recipiente contenente acqua (ρ_acqua = 1000 kg/m³). Qual è il volume della cavità?

• V_cavità = 1.1 m³
• V_cavità = 0.55 m³
• V_cavità = 0.11 m³
• V_cavità = 0.33 m³

Un cilindro omogeneo di raggio R e massa m si muove su un piano orizzontale sotto l’effetto di una forza F₀ orizzontale costante applicata al centro di massa. Quanto vale l’accelerazione del centro di massa se il moto è di puro rotolamento?

• a_CM = 2F₀/(3m)
• a_CM = F₀/m
• a_CM = 3F₀/(2m)
• a_CM = F₀/(3m)

Se il pendolo appeso all’interno del carrello in figura forma un angolo 49° con la verticale, quanto vale l’accelerazione del carrello?

• a = 6.4 m/s²
• a = 7.4 m/s²
• a = 8.2 m/s²
• a = 11.3 m/s²

Nel condotto in figura scorre un liquido ideale, tra le sezioni A (di area S) e B (di area 2S). La differenza di altezza delle due sezioni è h = 0.75 m. Quale deve essere la velocità del liquido nella sezione A affinché la pressione nelle sezioni A e B sia la stessa?

• v_A = 5.83 m/s
• v_A = 7.15 m/s
• v_A = 12.1 m/s
• v_A = 4.43 m/s

L’equazione di una trasformazione adiabatica reversibile del gas ideale si può scrivere come: [γ = c_p/c_V, calori specifici a p e a V costante]

• TP^(1-γ)/γ
• TV^γ-1
• TVP^(1-γ)/γ
• pV^γ

Il campo elettrico all’interno di una sfera piena uniformemente carica:

• È nullo.
• Varia linearmente con la distanza dal centro della sfera.
• Varia quadraticamente con la distanza dal centro della sfera.
• È costante in tutto il volume della sfera.

Un satellite artificiale è in orbita circolare intorno alla Terra. Se il raggio della traiettoria raddoppia, come varia l’energia potenziale?

• Si dimezza.
• Raddoppia.
• Quadruplica.
• Si riduce a un quarto.

0.25 moli di gas ideale a temperatura T = 50 K sono contenute nella parte inferiore A di un contenitore adiabatico, separata da una parte B in cui c’è il vuoto da un pistone di massa m. Il sistema è in equilibrio termodinamico con il pistone a distanza h = 1 m dal fondo del cilindro. Calcolare il valore della massa m del pistone. [R = 8.314 J/mol K]

• m = 8.2 kg
• m = 80 kg
• m = 5.3 kg
• m = 11 kg

Si consideri una macchina termica di Carnot reversibile che opera tra due sorgenti. La sorgente più fredda è alla temperatura di 5 °C e la macchina ha un rendimento del 30%. Di quanti gradi Celsius si deve aumentare la temperatura della sorgente più calda per portare il rendimento al 40%?

• 2.3 °C
• 66 °C
• 1.2 °C
• 93 °C

Politecnico di Torino – Compito scritto di fisica I – 15 settembre 2014

Cognome e nome matricola date non gradite per l’esame note orale (tra quelle indicate dal docente)

Esercizio 1

Una barretta omogenea di massa M = 5 kg è sostenuta agli estremi da due molle ideali identiche, appese a due sostegni. La lunghezza a riposo delle molle è L₀ = 20 cm, mentre quando il sistema in figura è all’equilibrio esse assumono una lunghezza pari a L = 21 cm.

a) Qual è la costante elastica k delle due molle?

Da un punto sopra la barretta, ad una quota h = 1 m, viene lasciata cadere una piccola sfera di massa m = 100 g, che colpisce la barretta nel suo centro e rimbalza. L’urto è perfettamente elastico. Determinare:

b) La velocità v₀ della sfera appena prima dell’urto con la barretta;

c) L’altezza h’ a cui rimbalza la sfera;

d) L’ampiezza del moto oscillatorio che la barretta acquista dopo l’urto.

m h L M

Esercizio 2

Un cilindro omogeneo di massa M = 5 kg e raggio R = 15 cm viene tirato da una fune avvolta su di esso. La fune scorre poi su una puleggia P e reca all’altro estremo un corpo di massa m = 2 kg (vedi figura). Si supponga che la puleggia abbia massa e attrito trascurabili e che la fune sia inestensibile e di massa trascurabile. Se il cilindro rotola senza strisciare, si determini:

a) Il rapporto tra l’accelerazione del centro di massa del cilindro, a_CM, e l’accelerazione istantanea del punto A (che è uguale all’accelerazione di ogni