OII 2006 1° Livello

Qui sotto sono indicate la lunghezza e l’area della sezione di cinque pezzi di filo di rame, tutti alla stessa temperatura. Quale filo ha la resistenza maggiore?

Filo	Lunghezza (m)	Area della sez. (m²)
A	10	$1\times 10^{-6}$
B	10	$2\times 10^{-6}$
C	5	$1\times 10^{-6}$
D	1	$2\times 10^{-6}$
E	1	$1\times 10^{-6}$

Topic: Circuits Metodi: Physical Modeling Competenze: Physical Reasoning Objects: Wire Fonte: Testo (PDF) — p.3 Risposta: A · Soluzioni (PDF)

The length and section area of five pieces of copper wire, all at the same temperature, are given below. Which thread has the greatest resistance?

♪ Fibre length ♪ Seed area ♪ (m²) | |------|--------------|----------------------| | A | 10 | $1\times 10^{-6}$ | | B | 10 | $2\times 10^{-6}$ | | C | 5 | $1\times 10^{-6}$ | | D | 1 | $2\times 10^{-6}$ | | E | 1 | $1\times 10^{-6}$ |

Topic: Circuits Metodi: Physical Modeling Competenze: Physical Reasoning Objects: Wire Fonte: Testo (PDF) — p.3 The Commission has also adopted a number of proposals for the implementation of the ‘European Union’s strategy for the protection of the environment.

Un pianeta $P$ si muove intorno al Sole $S$ lungo un’orbita ellittica, come mostrato in figura. Quando il pianeta si sposta dal punto $P$ al punto $P^{\prime }$, come cambiano la sua energia cinetica e la sua energia potenziale?

• A. L’energia cinetica diminuisce, l’energia potenziale diminuisce.
• B. L’energia cinetica diminuisce, l’energia potenziale aumenta.
• C. L’energia cinetica aumenta, l’energia potenziale diminuisce.
• D. L’energia cinetica aumenta, l’energia potenziale aumenta.
• E. L’energia cinetica e l’energia potenziale non variano.

p.3 — Orbita ellittica del pianeta attorno al Sole

Topic: Gravitation, Conservation of Energy Metodi: Physical Modeling Competenze: Physical Reasoning Objects: Planet, Star Fonte: Testo (PDF) — p.3 Risposta: C · Soluzioni (PDF)

A planet $P$ moves around the Sun $S$ along an elliptical orbit, as shown in the figure. Quando il pianeta si sposta dal punto $P$ al punto $P^{\prime }$, come cambiano la sua energia cinetica e la sua energia potenziale?

• A. Kinetic energy decreases, potential energy decreases.
• B. Kinetic energy decreases, potential energy increases.
• C. Kinetic energy increases, potential energy decreases.
• D. Kinetic energy increases, potential energy increases.
• E. The kinetic energy and the potential energy do not vary.

p.3 — Orbita ellittica del pianeta attorno al Sole

Topic: Gravitation, Conservation of Energy Metodi: Physical Modeling Competenze: Physical Reasoning Objects: Planet, Star Fonte: Testo (PDF) — p.3 Risposta: C · Soluzioni (PDF)

Durante il processo di fusione del piombo, c’è un cambiamento apprezzabile:

• A. della temperatura.
• B. del calore di fusione.
• C. del valore medio dell’energia cinetica delle molecole.
• D. del valore medio dell’energia potenziale delle molecole.
• E. della massa. Topic: Thermodynamics Metodi: Physical Modeling Competenze: Physical Reasoning Objects: — Fonte: Testo (PDF) — p.3 Risposta: D · Soluzioni (PDF)

During the lead smelting process, there is a noticeable change:

• **A ** of the temperature.
• ** B ** of the melting heat.
• **C ** of the mean kinetic energy of the molecules.
• ** D ** of the mean value of the potential energy of the molecules.
• **E ** of the mass. Topic: Thermodynamics Metodi: Physical Modeling Competenze: Physical Reasoning Objects: — Fonte: Testo (PDF) — p.3 The Commission has also adopted a proposal for a Regulation (EC) on the common organization of the market in milk and milk products.

La figura mostra quattro cannoni che stanno sparando proiettili di massa diversa e con diversi angoli di alzata (angolo tra l’orizzontale e la direzione di sparo), raggiungendo diverse gittate (distanza sul piano orizzontale tra il punto di sparo e quello di caduta del proiettile). Nei quattro casi la componente orizzontale della velocità dei proiettili è uguale. Si supponga trascurabile la resistenza dell’aria.

In quale caso la gittata del cannone è massima?

• A. Caso 1
• B. Caso 2
• C. Caso 3
• D. Caso 4
• E. Casi 2 e 3, dato che i due cannoni hanno la stessa gittata.

p.4 — Quattro cannoni con diversi angoli di alzata

Topic: Newtonian Mechanics Metodi: Physical Modeling Competenze: Physical Reasoning Objects: Projectile Fonte: Testo (PDF) — p.3 Risposta: D · Soluzioni (PDF)

The figure shows four guns firing bullets of different mass and with different angles of lift (angle between the horizontal and the direction of firing), reaching different ranges (distance on the horizontal plane between the point of firing and the point of falling of the bullet). In all four cases the horizontal component of the bullet velocity is the same. Let’s assume the air resistance is negligible.

In which case is the gun’s range maximum?

• A. Case 1
• B. Case 2
• C. Case 3
• D. Case 4
• E. Cases 2 and 3, since the two guns have the same range.

Four guns with different angles of lift

Topic: Newtonian Mechanics Metodi: Physical Modeling Competenze: Physical Reasoning Objects: Projectile Fonte: Testo (PDF) — p.3 The Commission has also adopted a proposal for a Regulation (EC) on the common organization of the market in milk and milk products.

Una pila da $4,5\text{V}$ è collegata a quattro resistori che formano il semplice circuito indicato nella seguente figura. Quant’è la differenza di potenziale fra il punto $B$ e il punto $D$?

• A. $+1\text{V}$
• B. $+2\text{V}$
• C. $+2,5\text{V}$
• D. $+3,5\text{V}$
• E. $+4,5\text{V}$

p.4 — Circuito con pila e quattro resistori

Topic: Circuits Metodi: Physical Modeling Competenze: Physical Reasoning Objects: Battery, Resistor Fonte: Testo (PDF) — p.4 Risposta: A · Soluzioni (PDF)

A $4,5\text{V}$ stack is connected to four resistors forming the simple circuit shown in the following figure. What is the potential difference between the $B$ point and the $D$ point?

• A. $+1\text{V}$
• B. $+2\text{V}$
• C. $+2,5\text{V}$
• D. $+3,5\text{V}$
• E. $+4,5\text{V}$

**p.4 ** Battery circuit and four resistors

Topic: Circuits Metodi: Physical Modeling Competenze: Physical Reasoning Objects: Battery, Resistor Fonte: Testo (PDF) — p.4 The Commission has also adopted a number of proposals for the implementation of the ‘European Union’s strategy for the protection of the environment.

Un pallone viene riempito con gas elio ed utilizzato per sollevare in aria un corpo di volume trascurabile e massa di $300\text{kg}$, molto maggiore di quella del pallone. Quale dei seguenti valori approssima meglio il minimo volume di elio richiesto?

(NOTA: in condizioni standard la densità dell’aria vale $1,29{\text{kg/m}}^3$ e quella dell’elio $0,18{\text{kg/m}}^3$; si può assumere che l’elio nel pallone sia a pressione atmosferica.)

• A. $50{\text{m}}^3$
• B. $95{\text{m}}^3$
• C. $135{\text{m}}^3$
• D. $270{\text{m}}^3$
• E. $540{\text{m}}^3$ Topic: Fluid Mechanics Metodi: Physical Modeling Competenze: Physical Reasoning Objects: Gas Fonte: Testo (PDF) — p.4 Risposta: D · Soluzioni (PDF)

A balloon is filled with helium gas and used to lift a body of negligible volume and mass of $300\text{kg}$, much larger than that of the balloon. Which of the following values best approximates the minimum volume of helium required?

(NOTE: under standard conditions the density of air is $1,29{\text{kg/m}}^3$ and that of helium is $0,18{\text{kg/m}}^3$; the helium in the balloon can be assumed to be at atmospheric pressure.)

• A. $50{\text{m}}^3$
• B. $95{\text{m}}^3$
• C. $135{\text{m}}^3$
• D. $270{\text{m}}^3$
• E. $540{\text{m}}^3$ Topic: Fluid Mechanics Metodi: Physical Modeling Competenze: Physical Reasoning Objects: Gas Fonte: Testo (PDF) — p.4 The Commission has also adopted a proposal for a Regulation (EC) on the common organization of the market in milk and milk products.

Una particella di massa $m$, che inizialmente si sta muovendo lungo l’asse $x$ con una velocità $v$, urta una particella di massa $2m$ inizialmente ferma. In seguito all’urto la prima particella si ferma, mentre la seconda particella si divide in due parti di uguale massa che si muovono in direzioni che formano uno stesso angolo $\theta \ne 0$ con l’asse $x$, come mostrato in figura.

Quale delle seguenti affermazioni descrive correttamente la velocità delle due parti?

• A. Entrambe le parti si muovono con velocità $v$.
• B. Una delle due parti si muove con velocità $v$, l’altra con velocità minore di $v$.
• C. Entrambe le parti si muovono con velocità $v/2$.
• D. Una delle due parti si muove con velocità $v/2$, l’altra con velocità maggiore di $v/2$.
• E. Entrambe le parti si muovono con velocità maggiore di $v/2$.

p.5 — Urto e divisione in due frammenti

Topic: Newtonian Mechanics, Conservation of Momentum Metodi: Physical Modeling Competenze: Physical Reasoning Objects: — Fonte: Testo (PDF) — p.4 Risposta: E · Soluzioni (PDF)

A mass particle $m$, which is initially moving along the $x$ axis with a speed $v$, strikes an initially stationary mass particle $2m$. After impact the first particle stops, while the second particle splits into two equal-mass parts moving in directions that form the same angle $\theta \ne 0$ with the $x$ axis, as shown in Figure 1.

Which of the following statements correctly describes the speed of the two parts?

• A. Both parts are moving at $v$ speed.
• B. One of the two parts moves at $v$ speed, the other at $v$ speed.
• C. Both parts are moving at $v/2$ speed.
• D. One of the two parts moves at $v/2$ speed, the other at a speed greater than $v/2$.
• E. Both parts move at speeds greater than $v/2$.

**p.5 ** Strike and split into two fragments

Topic: Newtonian Mechanics, Conservation of Momentum Metodi: Physical Modeling Competenze: Physical Reasoning Objects: — Fonte: Testo (PDF) — p.4 The Commission has also adopted a proposal for a regulation on the protection of the environment and the environment.

La figura rappresenta due sorgenti, $A$ e $B$, di un ondoscopio. Che fenomeno si osserva nel punto $P$?

• A. Interferenza distruttiva
• B. Interferenza costruttiva
• C. Riflessione
• D. Rifrazione
• E. Diffrazione

p.5 — Sorgenti A e B di un ondoscopio

Topic: Newtonian Mechanics, Circuits, Fluid Mechanics Metodi: Kinematic Equations, Kirchhoff’s Laws, Conservation of Momentum, Impulse-Momentum Theorem, Ideal Gas Law, Hooke’s Law, Coulomb’s Law, Free-Body Diagram Competenze: Physical Reasoning, Mathematical Modeling, Diagrammatic Reasoning Objects: — Fonte: Testo (PDF) — p.5 Risposta: B · Soluzioni (PDF)

The figure represents two sources, $A$ and $B$, of a waveguide. What phenomenon is observed in $P$?

• A. Destructive interference
• B. Constructive interference
• C. Reflection
• D. Refraction
• E. Diffraction

**p.5 ** Sources A and B of a waveguide

Topic: Newtonian Mechanics, Circuits, Fluid Mechanics Metodi: Kinematic Equations, Kirchhoff’s Laws, Conservation of Momentum, Impulse-Momentum Theorem, Ideal Gas Law, Hooke’s Law, Coulomb’s Law, Free-Body Diagram Competenze: Physical Reasoning, Mathematical Modeling, Diagrammatic Reasoning Objects: — Fonte: Testo (PDF) — p.5 The Commission has also adopted a proposal for a regulation on the protection of the environment and the environment.

Nella figura, le superfici $A$ e $B$ del blocco di legno hanno lo stesso grado di levigatura. L’area della superficie $B$ è doppia dell’area della superficie $A$.

Se $F$ è la forza orizzontale necessaria per far scivolare a velocità costante il blocco con la superficie $A$ a contatto con il tavolo, quanto vale approssimativamente la forza necessaria per far scivolare a velocità costante il blocco con la superficie $B$ a contatto con il tavolo?

• A. $F$
• B. $2F$
• C. $F/2$
• D. $4F$
• E. $F/4$

p.5 — Blocco di legno con superfici A e B

Topic: Newtonian Mechanics, Electrostatics, Nuclear & Particle Physics Metodi: Kinematic Equations, Conservation of Momentum, Conservation of Energy, Coulomb’s Law, Mass-Energy Equivalence, Wave Equation Competenze: Physical Reasoning, Mathematical Modeling, Estimation & Approximation Objects: Block Fonte: Testo (PDF) — p.5 Risposta: A · Soluzioni (PDF)

In the figure, the surfaces $A$ and $B$ of the wood block have the same degree of smoothing. The surface area $B$ shall be twice the surface area $A$.

If $F$ is the horizontal force required to cause the block with the surface $A$ to slide at a constant speed in contact with the table, what is the approximate force required to cause the block with the surface $B$ to slide at a constant speed in contact with the table?

• A. $F$
• B. $2F$
• C. $F/2$
• D. $4F$
• E. $F/4$

**p.5 ** Wood block with surfaces A and B

Topic: Newtonian Mechanics, Electrostatics, Nuclear & Particle Physics Metodi: Kinematic Equations, Conservation of Momentum, Conservation of Energy, Coulomb’s Law, Mass-Energy Equivalence, Wave Equation Competenze: Physical Reasoning, Mathematical Modeling, Estimation & Approximation Objects: Block Fonte: Testo (PDF) — p.5 The Commission has also adopted a number of proposals for the implementation of the ‘Settlement of the European Union’s financial perspective.

Uno studente che si trova su una piccola collinetta lancia una palla orizzontalmente, da un’altezza di $4,5\text{m}$ sul livello del suolo, verso una ciminiera che si trova a una distanza orizzontale di $6,0\text{m}$. La palla colpisce la ciminiera dopo $0,65\text{s}$ dal lancio (si trascuri l’attrito dell’aria).

Nell’istante in cui la palla lascia la mano del ragazzo, la componente orizzontale della sua velocità è, approssimativamente,

• A. $0,96{\text{m s}}^{-1}$
• B. $1,1{\text{m s}}^{-1}$
• C. $4,5{\text{m s}}^{-1}$
• D. $6,0{\text{m s}}^{-1}$
• E. $9,2{\text{m s}}^{-1}$

p.6 — Collinetta, lancio orizzontale verso ciminiera

Topic: Newtonian Mechanics Metodi: Kinematic Equations, Vector Decomposition Competenze: Physical Reasoning, Mathematical Modeling Objects: Ball Fonte: Testo (PDF) — p.5 Risposta: E · Soluzioni (PDF)

A student standing on a small hill throws a ball horizontally from a height of $4,5\text{m}$ above ground level towards a chimney located at a horizontal distance of $6,0\text{m}$. The ball hits the chimney after $0,65\text{s}$ from the pitch (air friction is neglected).

The moment the ball leaves the boy’s hand, the horizontal component of his speed is, approximately,

• A. $0,96{\text{m s}}^{-1}$
• B. $1,1{\text{m s}}^{-1}$
• C. $4,5{\text{m s}}^{-1}$
• D. $6,0{\text{m s}}^{-1}$
• E. $9,2{\text{m s}}^{-1}$

**p.6 ** Hill, horizontal throw to the chimney

Topic: Newtonian Mechanics Metodi: Kinematic Equations, Vector Decomposition Competenze: Physical Reasoning, Mathematical Modeling Objects: Ball Fonte: Testo (PDF) — p.5 The Commission has also adopted a proposal for a regulation on the protection of the environment and the environment.

Un getto d’acqua di densità $\rho$, area della sezione trasversale $A$ e velocità $v$ colpisce una parete verticale perpendicolare alla direzione del getto, come mostrato in figura. L’acqua poi fluisce parallelamente alla parete, in modo simmetrico rispetto alla direzione del getto.

La forza esercitata dal getto sulla parete è

• A. $\rho A{v}^2$
• B. $\rho Av/2$
• C. $\rho ghA$
• D. $\rho A{v}^2/\rho$
• E. $\rho A{v}^2/2$

p.6 — Getto d’acqua contro parete verticale

Topic: Fluid Mechanics, Newtonian Mechanics Metodi: Impulse-Momentum Theorem, Continuity Equation Competenze: Physical Reasoning, Mathematical Modeling Objects: — Fonte: Testo (PDF) — p.5 Risposta: A · Soluzioni (PDF)

A jet of water of $\rho$ density, cross section area $A$ and velocity $v$ hits a vertical wall perpendicular to the direction of the jet, as shown in Figure 1. The water then flows parallel to the wall, symmetrically with respect to the direction of the jet.

The force exerted by the throw on the wall is

• A. $\rho A{v}^2$
• B. $\rho Av/2$
• C. $\rho ghA$
• D. $\rho A{v}^2/\rho$
• E. $\rho A{v}^2/2$

The following conditions shall apply:

Topic: Fluid Mechanics, Newtonian Mechanics Metodi: Impulse-Momentum Theorem, Continuity Equation Competenze: Physical Reasoning, Mathematical Modeling Objects: — Fonte: Testo (PDF) — p.5 The Commission has also adopted a number of proposals for the implementation of the ‘Settlement of the European Union’s financial perspective.

Una quantità pari a $1,0\text{mol}$ di gas perfetto, contenuta in un recipiente ermeticamente chiuso e a pareti rigide, viene scaldata fino a che la velocità quadratica media delle sue molecole risulta raddoppiata.

Di quale fattore risulta variata la pressione?

• A. $0,5$
• B. $1$
• C. $2$
• D. $4$
• E. $8$ Topic: Kinetic Theory, Thermodynamics Metodi: Ideal Gas Law, Kinetic Theory of Gases Competenze: Physical Reasoning, Mathematical Modeling Objects: Gas, Container Fonte: Testo (PDF) — p.6 Risposta: D · Soluzioni (PDF)

A quantity of $1,0\text{mol}$ of perfect gas, contained in a tightly sealed container, is heated until the average square velocity of its molecules is doubled.

What is the variation in pressure?

• A. $0,5$
• B. $1$
• C. $2$
• D. $4$
• E. $8$ Topic: Kinetic Theory, Thermodynamics Metodi: Ideal Gas Law, Kinetic Theory of Gases Competenze: Physical Reasoning, Mathematical Modeling Objects: Gas, Container Fonte: Testo (PDF) — p.6 The Commission has also adopted a proposal for a Regulation (EC) laying down the rules for the implementation of the common fisheries policy.

Un oggetto viene lanciato verso l’alto in una direzione che forma un angolo di $45°$ con il verso positivo dell’asse $x$ posto orizzontalmente. Trascurando la resistenza dell’aria, quali dei precedenti grafici della velocità in funzione del tempo meglio rappresentano, rispettivamente, $v_x$ in funzione di $t$ e $v_y$ in funzione di $t$?

	$v_x(t)$	$v_y(t)$
A	I	IV
B	I	III
C	II	III
D	II	V
E	IV	V

p.7 — Cinque grafici velocita in funzione del tempo

Topic: Newtonian Mechanics Metodi: Kinematic Equations, Vector Decomposition Competenze: Physical Reasoning, Diagrammatic Reasoning Objects: Projectile Fonte: Testo (PDF) — p.6 Risposta: C · Soluzioni (PDF)

An object is thrown upwards in a direction that forms an angle of $45°$ with the positive side of the $x$ axis placed horizontally. If the air resistance is not taken into account, which of the previous time-speed graphs best represent $v_x$ as a function of $t$ and $v_y$ as a function of $t$, respectively?

	$v_x(t)$	$v_y(t)$
A	I	IV
B, I, III, and I.
♪ C is the second ♪
D	II	V
E	IV	V

**p.7 ** Five time-speed charts

Topic: Newtonian Mechanics Metodi: Kinematic Equations, Vector Decomposition Competenze: Physical Reasoning, Diagrammatic Reasoning Objects: Projectile Fonte: Testo (PDF) — p.6 The Commission has also adopted a proposal for a Regulation (EC) laying down the rules for the implementation of the common fisheries policy.

Il grafico mostra la relazione tra l’allungamento di una molla e la forza applicata che lo provoca. Quanto vale la costante elastica della molla?

• A. $0,020{\text{N m}}^{-1}$
• B. $2,0{\text{N m}}^{-1}$
• C. $25{\text{N m}}^{-1}$
• D. $50{\text{N m}}^{-1}$
• E. $75{\text{N m}}^{-1}$

p.7 — Grafico allungamento molla in funzione forza

Topic: Newtonian Mechanics Metodi: Hooke’s Law, Graph Linearization Competenze: Physical Reasoning, Experimental Data Analysis Objects: Spring Fonte: Testo (PDF) — p.6 Risposta: D · Soluzioni (PDF)

The graph shows the relationship between the elongation of a spring and the force applied causing it. How much is the spring’s elastic constant worth?

• A. $0,020{\text{N m}}^{-1}$
• B. $2,0{\text{N m}}^{-1}$
• C. $25{\text{N m}}^{-1}$
• D. $50{\text{N m}}^{-1}$
• E. $75{\text{N m}}^{-1}$

**p.7 ** Strength-based spring extension chart

Topic: Newtonian Mechanics Metodi: Hooke’s Law, Graph Linearization Competenze: Physical Reasoning, Experimental Data Analysis Objects: Spring Fonte: Testo (PDF) — p.6 The Commission has also adopted a proposal for a Regulation (EC) laying down the rules for the implementation of the common fisheries policy.

Cinque cariche positive di valore $q$ sono disposte in modo simmetrico lungo una circonferenza di raggio $r$. Qual è la forza elettrica risultante su ognuna di esse?

• A. $0$
• B. $\frac{k{q}^2}{r^2}$
• C. $5\frac{k{q}^2}{r^2}$
• D. $\frac{k{q}^2}{4r^2}$
• E. Non è zero, ma dipende dalla posizione della carica sulla circonferenza. Topic: Electrostatics Metodi: Coulomb’s Law, Symmetry Argument, Vector Decomposition Competenze: Physical Reasoning, Mathematical Modeling Objects: Point Charge Fonte: Testo (PDF) — p.7 Risposta: A · Soluzioni (PDF)

Five positive charges of $q$ value are symmetrically arranged along a radius circumference $r$. What is the resulting electrical force on each of them?

• A. $0$
• B. $\frac{k{q}^2}{r^2}$
• C. $5\frac{k{q}^2}{r^2}$
• D. $\frac{k{q}^2}{4r^2}$
• E. It is not zero, but depends on the position of the charge on the circumference. Topic: Electrostatics Metodi: Coulomb’s Law, Symmetry Argument, Vector Decomposition Competenze: Physical Reasoning, Mathematical Modeling Objects: Point Charge Fonte: Testo (PDF) — p.7 The Commission has also adopted a number of proposals for the implementation of the ‘Settlement of the European Union’s financial perspective.

In una gara di salto in lungo, un atleta raggiunge una gittata orizzontale di $8,0\text{m}$ saltando con un angolo di $30°$ rispetto all’orizzontale. Quanto è approssimativamente la velocità iniziale del salto?

• A. $4{\text{m s}}^{-1}$
• B. $7{\text{m s}}^{-1}$
• C. $9{\text{m s}}^{-1}$
• D. $10{\text{m s}}^{-1}$
• E. $13{\text{m s}}^{-1}$

p.8 — Salto con angolo di alzata

Topic: Newtonian Mechanics Metodi: Kinematic Equations, Vector Decomposition Competenze: Physical Reasoning, Mathematical Modeling Objects: Projectile Fonte: Testo (PDF) — p.7 Risposta: B · Soluzioni (PDF)

In a long jump race, an athlete reaches a horizontal range of $8,0\text{m}$ by jumping at an angle of $30°$ to the horizontal. What is the initial jump speed approximately?

• A. $4{\text{m s}}^{-1}$
• B. $7{\text{m s}}^{-1}$
• C. $9{\text{m s}}^{-1}$
• D. $10{\text{m s}}^{-1}$
• E. $13{\text{m s}}^{-1}$

The following table shows the results of the test:

Topic: Newtonian Mechanics Metodi: Kinematic Equations, Vector Decomposition Competenze: Physical Reasoning, Mathematical Modeling Objects: Projectile Fonte: Testo (PDF) — p.7 The Commission has also adopted a proposal for a regulation on the protection of the environment and the environment.

Tre resistori, di resistenza $R_1=3\Omega$, $R_2=6\Omega$ e $R_3=10\Omega$, sono collegati come mostrato in figura a un generatore di f.e.m. $\mathcal{E}=10\text{V}$ con resistenza interna trascurabile. Qual è la corrente che fluisce attraverso $R_3$?

• A. $0,33\text{A}$
• B. $0,50\text{A}$
• C. $1,0\text{A}$
• D. $1,5\text{A}$
• E. $2,0\text{A}$ Topic: Circuits Metodi: Kirchhoff’s Laws, Equivalent Circuit Reduction Competenze: Physical Reasoning, Mathematical Modeling Objects: Resistor, Battery Fonte: Testo (PDF) — p.7 Risposta: C · Soluzioni (PDF)

Three resistors, $R_1=3\Omega$, $R_2=6\Omega$ and $R_3=10\Omega$, are connected as shown in Figure 1 to an f.e.m. generator. $\mathcal{E}=10\text{V}$ with negligible internal resistance. Qual è la corrente che fluisce attraverso $R_3$?

• A. $0,33\text{A}$
• B. $0,50\text{A}$
• C. $1,0\text{A}$
• D. $1,5\text{A}$
• E. $2,0\text{A}$ Topic: Circuits Metodi: Kirchhoff’s Laws, Equivalent Circuit Reduction Competenze: Physical Reasoning, Mathematical Modeling Objects: Resistor, Battery Fonte: Testo (PDF) — p.7 Risposta: C · Soluzioni (PDF)

Una forza costante $F$ agisce su un corpo di massa $m$ inizialmente fermo. Dopo un tempo $t$ il corpo ha percorso una distanza $d$. Se la stessa forza agisce su un corpo di massa $2m$ inizialmente fermo per lo stesso tempo $t$, quale distanza percorre?

• A. $d/4$
• B. $d/2$
• C. $d$
• D. $2d$
• E. $4d$ Topic: Newtonian Mechanics Metodi: Kinematic Equations, Free-Body Diagram Competenze: Physical Reasoning, Mathematical Modeling Objects: Block Fonte: Testo (PDF) — p.7 Risposta: B · Soluzioni (PDF)

A constant force $F$ acts on an initially stationary mass body $m$. After a time $t$ the body has traveled a distance $d$. If the same force acts on a body of mass $2m$ initially stationary for the same time $t$, what distance does it travel?

• A. $d/4$
• B. $d/2$
• C. $d$
• D. $2d$
• E. $4d$ Topic: Newtonian Mechanics Metodi: Kinematic Equations, Free-Body Diagram Competenze: Physical Reasoning, Mathematical Modeling Objects: Block Fonte: Testo (PDF) — p.7 The Commission has also adopted a proposal for a regulation on the protection of the environment and the environment.

La figura mostra un raggio di luce che incide su una superficie piana che separa due mezzi trasparenti. L’angolo di incidenza è $60°$ e l’angolo di rifrazione è $45°$. Qual è il rapporto degli indici di rifrazione $n_2/n_1$?

• A. $0,58$
• B. $0,71$
• C. $0,82$
• D. $1,22$
• E. $1,73$

p.9 — Raggio di luce su superficie di separazione

Topic: Geometric Optics Metodi: Snell’s Law Competenze: Physical Reasoning, Mathematical Modeling Objects: — Fonte: Testo (PDF) — p.8 Risposta: B · Soluzioni (PDF)

The figure shows a beam of light striking a flat surface separating two transparent media. The angle of incidence is $60°$ and the angle of refraction is $45°$. What is the ratio of refractive indices $n_2/n_1$?

• A. $0,58$
• B. $0,71$
• C. $0,82$
• D. $1,22$
• E. $1,73$

The following conditions shall apply:

Topic: Geometric Optics Metodi: Snell’s Law Competenze: Physical Reasoning, Mathematical Modeling Objects: — Fonte: Testo (PDF) — p.8 The Commission has also adopted a proposal for a regulation on the protection of the environment and the environment.

Una quantità di gas biatomico ideale subisce una trasformazione isobara (a pressione costante). Se la temperatura assoluta raddoppia, di quale fattore varia il volume?

• A. $\sqrt{2}$
• B. $2$
• C. $4$
• D. $1/2$
• E. $1$

p.9 — Cinque diagrammi di trasformazione del gas

Topic: Thermodynamics Metodi: Ideal Gas Law Competenze: Physical Reasoning Objects: Gas Fonte: Testo (PDF) — p.8 Risposta: A · Soluzioni (PDF)

An ideal amount of biatomic gas undergoes an isobar transformation (at constant pressure). If the absolute temperature doubles, what factor changes the volume?

• A. $\sqrt{2}$
• B. $2$
• C. $4$
• D. $1/2$
• E. $1$

The following table shows the results of the calculation of the gas conversion rate:

Topic: Thermodynamics Metodi: Ideal Gas Law Competenze: Physical Reasoning Objects: Gas Fonte: Testo (PDF) — p.8 The Commission has also adopted a number of proposals for the implementation of the ‘European Union’s strategy for the protection of the environment.

Un oggetto è posto davanti a uno specchio concavo di raggio di curvatura $R=40\text{cm}$, a una distanza di $60\text{cm}$ dallo specchio. Dove si forma l’immagine?

• A. $12\text{cm}$ dallo specchio, dallo stesso lato dell’oggetto
• B. $20\text{cm}$ dallo specchio, dallo stesso lato dell’oggetto
• C. $30\text{cm}$ dallo specchio, dallo stesso lato dell’oggetto
• D. $60\text{cm}$ dallo specchio, dal lato opposto all’oggetto
• E. All’infinito

p.11 — Grafico coordinata immagine in funzione tempo

Topic: Geometric Optics Metodi: Thin Lens & Mirror Equation Competenze: Physical Reasoning, Mathematical Modeling Objects: Mirror Fonte: Testo (PDF) — p.8 Risposta: C · Soluzioni (PDF)

An object is placed in front of a concave mirror with a radius of curvature $R=40\text{cm}$, at a distance of $60\text{cm}$ from the mirror. Where does the image form?

• A. $12\text{cm}$ from the mirror, from the same side of the object
• B. $20\text{cm}$ from the mirror, from the same side of the object
• C. $30\text{cm}$ from the mirror, from the same side of the object
• D. $60\text{cm}$ from the mirror, on the opposite side of the object
• E. To the endless

The following table shows the number of images in the image:

Topic: Geometric Optics Metodi: Thin Lens & Mirror Equation Competenze: Physical Reasoning, Mathematical Modeling Objects: Mirror Fonte: Testo (PDF) — p.8 The Commission has also adopted a proposal for a regulation on the protection of the environment and the environment.

Un filo rettilineo percorso da corrente $I$ è immerso in un campo magnetico uniforme $\vec{B}$ perpendicolare al filo. La forza per unità di lunghezza sul filo è $F/L$. Se la corrente è raddoppiata e il campo è dimezzato, come cambia $F/L$?

• A. rimane invariata
• B. raddoppia
• C. si dimezza
• D. quadruplica
• E. si riduce a un quarto Topic: Magnetism, Electromagnetism Metodi: Lorentz Force Analysis Competenze: Physical Reasoning Objects: Wire Fonte: Testo (PDF) — p.8 Risposta: D · Soluzioni (PDF)

A straight wire travelling by $I$ current is immersed in a uniform magnetic field $\vec{B}$ perpendicular to the wire. The force per unit length on the wire is $F/L$. If the current doubles and the field halves, how does $F/L$ change?

• A. remains unchanged
• **B ** doubles
• **C ** is halved
• **D ** four times
• E is reduced to a quarter Topic: Magnetism, Electromagnetism Metodi: Lorentz Force Analysis Competenze: Physical Reasoning Objects: Wire Fonte: Testo (PDF) — p.8 The Commission has also adopted a proposal for a Regulation (EC) on the common organization of the market in milk and milk products.

Un satellite di massa $m$ orbita attorno alla Terra di massa $M$ a una quota $h$ al di sopra della superficie terrestre di raggio $R_T$. Qual è la velocità orbitale del satellite?

• A. $\sqrt{\frac{GM}{R_T+h}}$
• B. $\sqrt{\frac{GM}{R_T}}$
• C. $\sqrt{\frac{g{R}_T^2}{R_T+h}}$
• D. $\sqrt{g(R_T+h)}$
• E. $\sqrt{\frac{2GM}{R_T+h}}$ Topic: Gravitation, Newtonian Mechanics Metodi: Newton’s Law of Gravitation, Kinematic Equations Competenze: Physical Reasoning, Mathematical Modeling Objects: Satellite, Planet Fonte: Testo (PDF) — p.9 Risposta: E · Soluzioni (PDF)

A mass $m$ satellite orbiting the Earth of mass $M$ at a height $h$ above the Earth’s surface of radius $R_T$. What is the satellite’s orbital speed?

• A. $\sqrt{\frac{GM}{R_T+h}}$
• B. $\sqrt{\frac{GM}{R_T}}$
• C. $\sqrt{\frac{g{R}_T^2}{R_T+h}}$
• D. $\sqrt{g(R_T+h)}$
• E. $\sqrt{\frac{2GM}{R_T+h}}$ Topic: Gravitation, Newtonian Mechanics Metodi: Newton’s Law of Gravitation, Kinematic Equations Competenze: Physical Reasoning, Mathematical Modeling Objects: Satellite, Planet Fonte: Testo (PDF) — p.9 The Commission has also adopted a proposal for a regulation on the protection of the environment and the environment.

Un condensatore piano di capacità $C$ è collegato a un generatore di tensione $V$. Le armature sono separate da una distanza $d$. Se si raddoppia la distanza tra le armature mantenendo il condensatore collegato al generatore, come varia la carica $Q$ sulle armature?

• A. $Q$ raddoppia
• B. $Q$ si dimezza
• C. $Q$ rimane invariata
• D. $Q$ quadruplica
• E. $Q$ si riduce a un quarto

p.10 — Cinque schemi di armature con tensione

Topic: Electrostatics, Circuits Metodi: Electric Potential Method, Physical Modeling Competenze: Physical Reasoning Objects: Capacitor, Battery Fonte: Testo (PDF) — p.9 Risposta: D · Soluzioni (PDF)

A $C$ capacitor plane is connected to a $V$ voltage generator. The armor shall be separated by a distance $d$. If the distance between the frames is doubled while keeping the capacitor connected to the generator, how does the $Q$ charge on the frames change?

• **A ** $Q$ doubles
• **B ** $Q$ is halved
• C. $Q$ remains unchanged
• **D ** $Q$ four times
• **E ** $Q$ is reduced to one quarter

The following is the list of the components of the vehicle:

Topic: Electrostatics, Circuits Metodi: Electric Potential Method, Physical Modeling Competenze: Physical Reasoning Objects: Capacitor, Battery Fonte: Testo (PDF) — p.9 The Commission has also adopted a proposal for a Regulation (EC) on the common organization of the market in milk and milk products.

Una sonda spaziale viene lanciata dalla Terra con una velocità $v_0$ diretta verso il Sole. Trascurando tutti i corpi del Sistema Solare tranne il Sole e la Terra, quale delle seguenti affermazioni è corretta mentre la sonda si avvicina al Sole?

• A. La velocità della sonda aumenta e la sua energia meccanica totale aumenta.
• B. La velocità della sonda aumenta e la sua energia meccanica totale diminuisce.
• C. La velocità della sonda aumenta e la sua energia meccanica totale rimane costante.
• D. La velocità della sonda diminuisce e la sua energia meccanica totale rimane costante.
• E. La velocità della sonda rimane costante e la sua energia meccanica totale rimane costante. Topic: Gravitation, Conservation of Energy Metodi: Conservation Laws, Newton’s Law of Gravitation Competenze: Physical Reasoning Objects: Satellite, Star Fonte: Testo (PDF) — p.9 Risposta: D · Soluzioni (PDF)

A space probe is launched from Earth at a speed of $v_0$ directed toward the Sun. Ignoring all the bodies in the Solar System except the Sun and the Earth, which of the following claims is correct as the probe approaches the Sun?

• A. The speed of the probe increases and its total mechanical energy increases.
• B. The speed of the probe increases and its total mechanical energy decreases.
• C. The speed of the probe increases and its total mechanical energy remains constant.
• D. The speed of the probe decreases and its total mechanical energy remains constant. The speed of the probe remains constant and its total mechanical energy remains constant. Topic: Gravitation, Conservation of Energy Metodi: Conservation Laws, Newton’s Law of Gravitation Competenze: Physical Reasoning Objects: Satellite, Star Fonte: Testo (PDF) — p.9 The Commission has also adopted a proposal for a Regulation (EC) on the common organization of the market in milk and milk products.

Un’onda sonora si propaga nell’aria a $340{\text{m s}}^{-1}$ con frequenza $680\text{Hz}$. Qual è la lunghezza d’onda?

• A. $0,25\text{m}$
• B. $0,5\text{m}$
• C. $1,0\text{m}$
• D. $2,0\text{m}$
• E. $4,0\text{m}$ Topic: Oscillations & Waves Metodi: Wave Equation Competenze: Physical Reasoning, Mathematical Modeling Objects: — Fonte: Testo (PDF) — p.9 Risposta: B · Soluzioni (PDF)

A sound wave propagates in the air at $340{\text{m s}}^{-1}$ with frequency $680\text{Hz}$. What’s the wavelength?

• A. $0,25\text{m}$
• B. $0,5\text{m}$
• C. $1,0\text{m}$
• D. $2,0\text{m}$
• E. $4,0\text{m}$ Topic: Oscillations & Waves Metodi: Wave Equation Competenze: Physical Reasoning, Mathematical Modeling Objects: — Fonte: Testo (PDF) — p.9 The Commission has also adopted a proposal for a regulation on the protection of the environment in the Member States of the European Union.

Un elettrone e un protone sono accelerati dalla stessa differenza di potenziale $V$. Qual è il rapporto tra la velocità finale dell’elettrone $v_e$ e quella del protone $v_p$?

• A. $v_e/v_p=1$
• B. $v_e/v_p=m_p/m_e$
• C. $v_e/v_p=\sqrt{m_p/m_e}$
• D. $v_e/v_p=m_e/m_p$
• E. $v_e/v_p=\sqrt{m_e/m_p}$ Topic: Electrostatics, Modern-Quantum Physics Metodi: Energy Conservation Method, Electric Potential Method Competenze: Physical Reasoning, Mathematical Modeling Objects: Electron, Nucleus Fonte: Testo (PDF) — p.9 Risposta: D · Soluzioni (PDF)

An electron and a proton are accelerated by the same potential difference $V$. What is the ratio of the electron $v_e$ to the proton $v_p$ end speed?

• A. $v_e/v_p=1$
• B. $v_e/v_p=m_p/m_e$
• C. $v_e/v_p=\sqrt{m_p/m_e}$
• D. $v_e/v_p=m_e/m_p$
• E. $v_e/v_p=\sqrt{m_e/m_p}$ Topic: Electrostatics, Modern-Quantum Physics Metodi: Energy Conservation Method, Electric Potential Method Competenze: Physical Reasoning, Mathematical Modeling Objects: Electron, Nucleus Fonte: Testo (PDF) — p.9 The Commission has also adopted a proposal for a Regulation (EC) on the common organization of the market in milk and milk products.

Un corpo di massa $m$ appeso a una molla verticale di costante elastica $k$ oscilla con periodo $T$. Se la massa è quadruplicata e la costante della molla è raddoppiata, qual è il nuovo periodo?

• A. $T/2$
• B. $T\sqrt{2}$
• C. $T\sqrt{2}/2$
• D. $2T$
• E. $T\sqrt{2}/\sqrt{2}$ Topic: Oscillations & Waves Metodi: Simple Harmonic Motion Analysis Competenze: Physical Reasoning, Mathematical Modeling Objects: Spring Fonte: Testo (PDF) — p.10 Risposta: D · Soluzioni (PDF)

A mass body $m$ suspended from a vertical spring of an elastic constant $k$ oscillates with a period $T$. If the mass is quadrupled and the spring constant is doubled, what is the new period?

• A. $T/2$
• B. $T\sqrt{2}$
• C. $T\sqrt{2}/2$
• D. $2T$
• E. $T\sqrt{2}/\sqrt{2}$ Topic: Oscillations & Waves Metodi: Simple Harmonic Motion Analysis Competenze: Physical Reasoning, Mathematical Modeling Objects: Spring Fonte: Testo (PDF) — p.10 The Commission has also adopted a proposal for a Regulation (EC) on the common organization of the market in milk and milk products.

Un carrello di massa $M$ è fermo su una rotaia orizzontale priva di attrito. Un proiettile di massa $m$ e velocità $v$ viene sparato orizzontalmente e si conficca nel carrello. Qual è la velocità del sistema carrello+proiettile dopo l’urto?

• A. $\frac{mv}{M}$
• B. $\frac{mv}{M+m}$
• C. $\frac{Mv}{M+m}$
• D. $\frac{(M+m)v}{M}$
• E. $v$ Topic: Newtonian Mechanics, Conservation of Momentum Metodi: Conservation of Momentum, Impulse-Momentum Theorem Competenze: Physical Reasoning, Mathematical Modeling Objects: Cart, Projectile Fonte: Testo (PDF) — p.10 Risposta: C · Soluzioni (PDF)

A mass cart $M$ is fixed on a non-friction horizontal rail. A bullet of mass $m$ and speed $v$ is fired horizontally and becomes stuck in the cart. What’s the velocity of the carriage system after the impact?

• A. $\frac{mv}{M}$
• B. $\frac{mv}{M+m}$
• C. $\frac{Mv}{M+m}$
• D. $\frac{(M+m)v}{M}$
• E. $v$ Topic: Newtonian Mechanics, Conservation of Momentum Metodi: Conservation of Momentum, Impulse-Momentum Theorem Competenze: Physical Reasoning, Mathematical Modeling Objects: Cart, Projectile Fonte: Testo (PDF) — p.10 The Commission has also adopted a proposal for a regulation on the protection of the environment and the environment.

Due sfere identiche, conduttrici e isolate, vengono caricate con cariche $+3q$ e $-q$ rispettivamente. Le sfere si trovano a distanza $d$ grande rispetto al loro diametro. Quale è la forza tra le sfere prima che vengano messe a contatto?

• A. $\frac{k\cdot 3q^2}{d^2}$ repulsiva
• B. $\frac{3k{q}^2}{d^2}$ attrattiva
• C. $\frac{k{q}^2}{d^2}$ attrattiva
• D. $\frac{3k{q}^2}{d^2}$ repulsiva
• E. Zero Topic: Electrostatics Metodi: Coulomb’s Law Competenze: Physical Reasoning Objects: Conducting Sphere Fonte: Testo (PDF) — p.10 Risposta: B · Soluzioni (PDF)

Two identical spheres, conductive and isolated, are loaded with $+3q$ and $-q$ loads respectively. The spheres are located at $d$ greater than their diameter. What is the force between the spheres before they are put into contact?

• A $\frac{k\cdot 3q^2}{d^2}$ repulsive
• **B ** $\frac{3k{q}^2}{d^2}$ attractive
• C. $\frac{k{q}^2}{d^2}$ attractive
• **D ** $\frac{3k{q}^2}{d^2}$ repulsive
• E. Zero Topic: Electrostatics Metodi: Coulomb’s Law Competenze: Physical Reasoning Objects: Conducting Sphere Fonte: Testo (PDF) — p.10 The Commission has also adopted a proposal for a regulation on the protection of the environment in the Member States of the European Union.

Un carrello parte da ferma in un punto $A$ e scende lungo un piano inclinato liscio fino al punto $B$, posto a $20\text{m}$ più in basso. Se l’attrito può essere trascurato, quale sarà la velocità del carrello nel punto $B$?

• A. $14{\text{m s}}^{-1}$
• B. $20{\text{m s}}^{-1}$
• C. $22{\text{m s}}^{-1}$
• D. $26{\text{m s}}^{-1}$
• E. $31{\text{m s}}^{-1}$

p.13 — Profilo del percorso con punti A e B

Topic: Newtonian Mechanics, Conservation of Energy Metodi: Energy Conservation Method, Kinematic Equations Competenze: Physical Reasoning, Mathematical Modeling Objects: Cart, Inclined Plane Fonte: Testo (PDF) — p.10 Risposta: B · Soluzioni (PDF)

A cart shall start from a stop at a point $A$ and descend along a smooth sloping plane to the point $B$, located at $20\text{m}$ below. If friction can be neglected, what will be the cart speed at $B$?

• A. $14{\text{m s}}^{-1}$
• B. $20{\text{m s}}^{-1}$
• C. $22{\text{m s}}^{-1}$
• D. $26{\text{m s}}^{-1}$
• E. $31{\text{m s}}^{-1}$

p.13 Route profile with points A and B

Topic: Newtonian Mechanics, Conservation of Energy Metodi: Energy Conservation Method, Kinematic Equations Competenze: Physical Reasoning, Mathematical Modeling Objects: Cart, Inclined Plane Fonte: Testo (PDF) — p.10 The Commission has also adopted a proposal for a regulation on the protection of the environment in the Member States of the European Union.

Qual è la potenza sviluppata da una forza $F=20\text{N}$ che agisce su un oggetto in moto con velocità $v=4{\text{m s}}^{-1}$ nella stessa direzione della forza?

• A. $5\text{W}$
• B. $16\text{W}$
• C. $24\text{W}$
• D. $80\text{W}$
• E. $160\text{W}$ Topic: Newtonian Mechanics Metodi: Kinematic Equations, Energy Conservation Method Competenze: Physical Reasoning, Mathematical Modeling Objects: — Fonte: Testo (PDF) — p.11 Risposta: B · Soluzioni (PDF)

What is the power developed by a force $F=20\text{N}$ acting on an object moving at a speed $v=4{\text{m s}}^{-1}$ in the same direction as the force?

• A. $5\text{W}$
• B. $16\text{W}$
• C. $24\text{W}$
• D. $80\text{W}$
• E. $160\text{W}$ Topic: Newtonian Mechanics Metodi: Kinematic Equations, Energy Conservation Method Competenze: Physical Reasoning, Mathematical Modeling Objects: — Fonte: Testo (PDF) — p.11 The Commission has also adopted a proposal for a regulation on the protection of the environment in the Member States of the European Union.

Un trasformatore ideale ha un avvolgimento primario di $200$ spire e uno secondario di $50$ spire. La tensione efficace al primario è $220\text{V}$. Qual è la tensione efficace al secondario?

• A. $55\text{V}$
• B. $110\text{V}$
• C. $220\text{V}$
• D. $440\text{V}$
• E. $880\text{V}$ Topic: Electromagnetic Induction, Electromagnetism Metodi: Faraday’s Law of Induction Competenze: Physical Reasoning, Mathematical Modeling Objects: Coil Fonte: Testo (PDF) — p.11 Risposta: C · Soluzioni (PDF)

An ideal transformer has a primary winding of $200$ spire and a secondary winding of $50$ spire. The effective voltage at primary is $220\text{V}$. What’s the effective voltage at the secondary?

• A. $55\text{V}$
• B. $110\text{V}$
• C. $220\text{V}$
• D. $440\text{V}$
• E. $880\text{V}$ Topic: Electromagnetic Induction, Electromagnetism Metodi: Faraday’s Law of Induction Competenze: Physical Reasoning, Mathematical Modeling Objects: Coil Fonte: Testo (PDF) — p.11 The Commission has also adopted a proposal for a regulation on the protection of the environment and the environment.

Su due sfere identiche, conduttrici e isolate, vengono depositate due cariche elettriche uguali. Le sfere si trovano a distanza $d$ grande rispetto al loro diametro e si respingono con forza $F$. Una terza sfera conduttrice identica alle due precedenti, ma scarica, viene posta in contatto elettrico con la prima sfera e poi con la seconda, quindi viene allontanata definitivamente.

Qual è, ora, l’intensità della forza tra le due sfere?

• A. $\frac{3}{4}F$
• B. $\frac{5}{8}F$
• C. $\frac{1}{2}F$
• D. $\frac{3}{8}F$
• E. $\frac{1}{4}F$ Topic: Electrostatics Metodi: Coulomb’s Law, Physical Modeling Competenze: Physical Reasoning, Mathematical Modeling Objects: Conducting Sphere Fonte: Testo (PDF) — p.11 Risposta: D · Soluzioni (PDF)

On two identical spheres, conductive and isolated, two equal electric charges are deposited. The spheres are located at a distance $d$ greater than their diameter and are forcefully repelled $F$. A third conductive sphere identical to the previous two, but discharging, is placed in electrical contact with the first sphere and then with the second, and then is permanently removed.

What is the force intensity between the two spheres?

• A. $\frac{3}{4}F$
• B. $\frac{5}{8}F$
• C. $\frac{1}{2}F$
• D. $\frac{3}{8}F$
• E. $\frac{1}{4}F$ Topic: Electrostatics Metodi: Coulomb’s Law, Physical Modeling Competenze: Physical Reasoning, Mathematical Modeling Objects: Conducting Sphere Fonte: Testo (PDF) — p.11 The Commission has also adopted a proposal for a Regulation (EC) on the common organization of the market in milk and milk products.

Un’automobile, la cui massa è di $1000\text{kg}$, sta viaggiando alla velocità di $20{\text{m s}}^{-1}$ quando inizia a frenare con un’accelerazione costante di $-5{\text{m s}}^{-2}$, fino a fermarsi.

Quanta strada percorre la macchina durante la frenata?

• A. $10\text{m}$
• B. $20\text{m}$
• C. $40\text{m}$
• D. $80\text{m}$
• E. $100\text{m}$ Topic: Newtonian Mechanics Metodi: Kinematic Equations Competenze: Physical Reasoning, Mathematical Modeling Objects: — Fonte: Testo (PDF) — p.12 Risposta: C · Soluzioni (PDF)

A vehicle, whose mass is $1000\text{kg}$, is travelling at $20{\text{m s}}^{-1}$ speed when it starts braking at a constant acceleration of $-5{\text{m s}}^{-2}$ until it stops.

How many roads does the car take during braking?

• A. $10\text{m}$
• B. $20\text{m}$
• C. $40\text{m}$
• D. $80\text{m}$
• E. $100\text{m}$ Topic: Newtonian Mechanics Metodi: Kinematic Equations Competenze: Physical Reasoning, Mathematical Modeling Objects: — Fonte: Testo (PDF) — p.12 The Commission has also adopted a proposal for a regulation on the protection of the environment and the environment.

In un urto unidimensionale non relativistico, una particella di massa $2m$ colpisce una particella di massa $m$ inizialmente ferma. Se le particelle rimangono unite dopo l’urto, quale frazione dell’energia cinetica iniziale viene persa nell’urto?

• A. $0$
• B. $1/4$
• C. $1/3$
• D. $1/2$
• E. $2/3$ Topic: Newtonian Mechanics, Conservation of Momentum Metodi: Conservation of Momentum, Conservation of Energy Competenze: Physical Reasoning, Mathematical Modeling Objects: — Fonte: Testo (PDF) — p.13 Risposta: C · Soluzioni (PDF)

In a non-relativistic one-dimensional impact, a particle of mass $2m$ hits an initially stationary particle of mass $m$. If the particles remain united after impact, what fraction of the initial kinetic energy is lost in impact?

• A. $0$
• B. $1/4$
• C. $1/3$
• D. $1/2$
• E. $2/3$ Topic: Newtonian Mechanics, Conservation of Momentum Metodi: Conservation of Momentum, Conservation of Energy Competenze: Physical Reasoning, Mathematical Modeling Objects: — Fonte: Testo (PDF) — p.13 The Commission has also adopted a proposal for a regulation on the protection of the environment and the environment.

Il disegno schematizza un’onda d’acqua che si propaga alla velocità di $1{\text{m s}}^{-1}$ e mette in moto un tappo che compie $8$ oscillazioni in $4\text{s}$.

Qual è la lunghezza d’onda?

• A. $0,25\text{m}$
• B. $0,5\text{m}$
• C. $1\text{m}$
• D. $2\text{m}$
• E. $4\text{m}$

p.14 — Onda d’acqua che muove un tappo

Topic: Oscillations & Waves Metodi: Wave Equation Competenze: Physical Reasoning, Mathematical Modeling Objects: — Fonte: Testo (PDF) — p.13 Risposta: B · Soluzioni (PDF)

The drawing outlines a wave of water propagating at $1{\text{m s}}^{-1}$ and sets in motion a cap that performs $8$ oscillations in $4\text{s}$.

What’s the wavelength?

• A. $0,25\text{m}$
• B. $0,5\text{m}$
• C. $1\text{m}$
• D. $2\text{m}$
• E. $4\text{m}$

Wave of water moving a cap

Topic: Oscillations & Waves Metodi: Wave Equation Competenze: Physical Reasoning, Mathematical Modeling Objects: — Fonte: Testo (PDF) — p.13 The Commission has also adopted a proposal for a regulation on the protection of the environment and the environment.

Quando una studentessa beve dell’acqua fredda, il suo corpo scalda l’acqua fino al raggiungimento dell’equilibrio termico. Se la studentessa, nell’arco di una giornata, beve circa un litro e mezzo d’acqua a $8,0°\text{C}$, quanta energia — sotto forma di calore — deve fornire approssimativamente il suo corpo all’acqua?

(NOTA: si consideri la temperatura interna della studentessa pari a $37°\text{C}$.)

• A. $44\text{kJ}$
• B. $180\text{kJ}$
• C. $190\text{kJ}$
• D. $230\text{kJ}$
• E. $470\text{kJ}$ Topic: Thermodynamics Metodi: First Law of Thermodynamics, Physical Modeling Competenze: Physical Reasoning, Estimation & Approximation Objects: — Fonte: Testo (PDF) — p.13 Risposta: B · Soluzioni (PDF)

When a student drinks cold water, her body heats the water until the thermal balance is reached. If a student drinks about a liter of water at $8,0°\text{C}$ over the course of a day, how much energy in the form of heat should her body supply to water?

(NOTE: consider the student’s internal temperature as $37°\text{C}$.)

• A. $44\text{kJ}$
• B. $180\text{kJ}$
• C. $190\text{kJ}$
• D. $230\text{kJ}$
• E. $470\text{kJ}$ Topic: Thermodynamics Metodi: First Law of Thermodynamics, Physical Modeling Competenze: Physical Reasoning, Estimation & Approximation Objects: — Fonte: Testo (PDF) — p.13 The Commission has also adopted a proposal for a regulation on the protection of the environment and the environment.

A fianco sono indicate le masse di due particelle e un nucleo, espresse in unità di massa atomica (u), di cui è dato il valore. Qual è l’energia di legame del nucleo di ${}_3^6\text{Li}$?

Particella	Massa (u)
protone	$1,0073$
neutrone	$1,0087$
${}_3^6\text{Li}$	$6,0135$

$1\text{u}=1,66\times 10^{-27}\text{kg}$

• A. $4,52\text{pJ}$
• B. $5,15\text{pJ}$
• C. $9,18\text{pJ}$
• D. $457\text{pJ}$
• E. $597\text{pJ}$ Topic: Nuclear & Particle Physics Metodi: Mass-Energy Equivalence Competenze: Physical Reasoning, Mathematical Modeling Objects: Nucleus Fonte: Testo (PDF) — p.13 Risposta: B · Soluzioni (PDF)

The masses of two particles and a nucleus, expressed in atomic mass unit (u), are indicated next to each other, and the value is given. What is the bonding energy of the ${}_3^6\text{Li}$ nucleus?

♪ The part # The mass # |-----------|-----------| | protone | $1,0073$ | | neutrone | $1,0087$ | | ${}_3^6\text{Li}$ | $6,0135$ |

$1\text{u}=1,66\times 10^{-27}\text{kg}$

• A. $4,52\text{pJ}$
• B. $5,15\text{pJ}$
• C. $9,18\text{pJ}$
• D. $457\text{pJ}$
• E. $597\text{pJ}$ Topic: Nuclear & Particle Physics Metodi: Mass-Energy Equivalence Competenze: Physical Reasoning, Mathematical Modeling Objects: Nucleus Fonte: Testo (PDF) — p.13 Risposta: B · Soluzioni (PDF)

Un proiettile si sta muovendo a velocità $v$ nel punto più alto della sua traiettoria. Si faccia l’ipotesi che l’aria non influenzi apprezzabilmente il moto.

Come è rivolto il vettore accelerazione del proiettile in tale punto, indicato in figura?

• A. Nella direzione del moto (orizzontale)
• B. Verticalmente verso l’alto
• C. Verticalmente verso il basso
• D. In direzione obliqua verso il basso
• E. Il vettore accelerazione è nullo in quel punto

p.14 — Cinque traiettorie del proiettile con vertice

Topic: Newtonian Mechanics Metodi: Kinematic Equations, Free-Body Diagram Competenze: Physical Reasoning Objects: Projectile Fonte: Testo (PDF) — p.14 Risposta: D · Soluzioni (PDF)

A bullet is moving at $v$ speed at the highest point of its trajectory. Assume that the air does not significantly affect the engine.

How is the bullet acceleration vector turned at this point, as shown in the figure?

• A. In the direction of the engine (horizontal)
• B. Vertically up
• C. Vertically down
• D. In the oblique direction downwards
• E. The acceleration vector is zero at that point

The bullet is to be fired in the direction of the target.

Topic: Newtonian Mechanics Metodi: Kinematic Equations, Free-Body Diagram Competenze: Physical Reasoning Objects: Projectile Fonte: Testo (PDF) — p.14 The Commission has also adopted a proposal for a Regulation (EC) laying down the rules for the implementation of the common fisheries policy.