OII 2012 1° Livello

Un corpo di massa pari a $2.0\text{kg}$ pesa $10.0\text{N}$ sul pianeta X.

L’accelerazione di gravità sul pianeta X vale

• A. $0.20{\text{m s}}^{-2}$
• B. $0.50{\text{m s}}^{-2}$
• C. $5.0{\text{m s}}^{-2}$
• D. $9.8{\text{m s}}^{-2}$
• E. $20{\text{m s}}^{-2}$ Topic: Newtonian Mechanics, Gravitation Metodi: Free-Body Diagram, Newton’s Law of Gravitation Competenze: Physical Reasoning Objects: Planet Fonte: Testo (PDF) — p.3 Risposta: C · Soluzioni (PDF)

A body of mass equal to $2.0\text{kg}$ weighs $10.0\text{N}$ on planet X.

The acceleration of gravity on planet X is

• A. $0.20{\text{m s}}^{-2}$
• B. $0.50{\text{m s}}^{-2}$
• C. $5.0{\text{m s}}^{-2}$
• D. $9.8{\text{m s}}^{-2}$
• E. $20{\text{m s}}^{-2}$ Topic: Newtonian Mechanics, Gravitation Metodi: Free-Body Diagram, Newton’s Law of Gravitation Competenze: Physical Reasoning Objects: Planet Fonte: Testo (PDF) — p.3 The Commission has also adopted a number of measures to combat the use of the ‘sustainable energy’ technology.

In una regione è presente un campo uniforme di induzione magnetica $\vec{B}$. Una particella di carica $Q$ e quantità di moto $\vec{p}$ entra nella regione viaggiando ad angolo retto rispetto al campo e viene deflessa di $90°$ per azione della forza magnetica, come mostrato nel diagramma. Tutte le altre forze si possono trascurare.

Quale delle seguenti è l’espressione corretta per la lunghezza $s$ della traiettoria nella regione di campo magnetico?

• A. $\frac{pQ}{4B}$
• B. $\frac{\pi p}{2BQ}$
• C. $\frac{\pi pQ}{2B}$
• D. $\frac{\pi p}{BQ}$
• E. $\frac{\pi pQ}{B}$

Particle deflected 90° in magnetic field

Topic: Magnetism, Newtonian Mechanics Metodi: Lorentz Force Analysis, Kinematic Equations Competenze: Physical Reasoning, Mathematical Modeling Objects: Point Charge Fonte: Testo (PDF) — p.3 Risposta: B · Soluzioni (PDF)

A uniform magnetic induction field $\vec{B}$ is present in a region. A charge particle $Q$ and motion quantity $\vec{p}$ enters the region travelling at a right angle to the field and is deflected by $90°$ by action of the magnetic force, as shown in the diagram. All other forces can be overlooked.

Which of the following is the correct expression for the trajectory length $s$ in the magnetic field region?

• A. $\frac{pQ}{4B}$
• B. $\frac{\pi p}{2BQ}$
• C. $\frac{\pi pQ}{2B}$
• D. $\frac{\pi p}{BQ}$
• E. $\frac{\pi pQ}{B}$

Particle deflected in magnetic field

Topic: Magnetism, Newtonian Mechanics Metodi: Lorentz Force Analysis, Kinematic Equations Competenze: Physical Reasoning, Mathematical Modeling Objects: Point Charge Fonte: Testo (PDF) — p.3 The Commission has also adopted a proposal for a regulation on the protection of the environment and the environment in the Member States.

La potenza meccanica sviluppata dal motore di un’automobile che viaggia alla velocità $v=100\text{km/h}$ è $P=45\text{kW}$. Il rendimento del motore è $\eta =40\%$ e il potere calorifico del carburante è $q=42\text{MJ/L}$.

Il consumo, convenzionalmente espresso in «litri/100 km», è:

• A. $2.4$
• B. $2.7$
• C. $9.6$
• D. $10$
• E. $15$ Topic: Thermodynamics, Newtonian Mechanics Metodi: Energy Conservation Method, Dimensional Analysis Competenze: Physical Reasoning, Unit Conversion Objects: Heat Engine Fonte: Testo (PDF) — p.3 Risposta: C · Soluzioni (PDF)

The mechanical power developed by the engine of an automobile travelling at $v=100\text{km/h}$ speed is $P=45\text{kW}$. The engine performance is $\eta =40\%$ and the fuel heat output is $q=42\text{MJ/L}$.

The consumption, conventionally expressed in litres/100 km, is:

• A. $2.4$
• B. $2.7$
• C. $9.6$
• D. $10$
• E. $15$ Topic: Thermodynamics, Newtonian Mechanics Metodi: Energy Conservation Method, Dimensional Analysis Competenze: Physical Reasoning, Unit Conversion Objects: Heat Engine Fonte: Testo (PDF) — p.3 The Commission has also adopted a number of measures to combat the use of the ‘sustainable energy’ technology.

Si sottrae una quantità $Q=14.5\text{MJ}$ di energia termica a $5.0\text{kg}$ di vapor acqueo inizialmente a $150°\text{C}$ che si trova in un recipiente chiuso. Si adotti come valore medio del calore specifico del vapor acqueo $c_V=1.53{\text{kJkg}}^{-1}{\text{K}}^{-1}$.

Il risultato dell’operazione è:

• A. Vapor acqueo.
• B. Miscuglio di vapor acqueo e acqua liquida.
• C. Acqua liquida.
• D. Miscuglio di acqua liquida e ghiaccio.
• E. Ghiaccio. Topic: Thermodynamics Metodi: First Law of Thermodynamics, Ideal Gas Law Competenze: Physical Reasoning, Mathematical Modeling Objects: Gas, Container Fonte: Testo (PDF) — p.3 Risposta: D · Soluzioni (PDF)

Subtract a quantity of heat energy $Q=14.5\text{MJ}$ to $5.0\text{kg}$ from water vapor initially to $150°\text{C}$ in a closed container. The mean specific heat value of water vapor $c_V=1.53{\text{kJkg}}^{-1}{\text{K}}^{-1}$ shall be adopted.

The result of the operation is:

• Water vapor. - The water vapor is not used.
• B. Mix of water vapor and liquid water.
• **C ** Liquid water.
• D. Mix of liquid water and ice.
• MSK0/>E** Ice. Topic: Thermodynamics Metodi: First Law of Thermodynamics, Ideal Gas Law Competenze: Physical Reasoning, Mathematical Modeling Objects: Gas, Container 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.

Quale dei seguenti processi descrive una trasformazione isoterma reversibile di un gas perfetto?

• A. La pressione decresce lentamente, il volume cresce lentamente e non c’è scambio di calore.
• B. Il volume rimane costante e il sistema assorbe calore.
• C. Il volume diminuisce bruscamente e il sistema cede calore.
• D. La pressione diminuisce lentamente, il volume cresce lentamente e il sistema assorbe calore.
• E. La pressione rimane costante e il sistema cede calore. Topic: Thermodynamics Metodi: Ideal Gas Law, Thermodynamic Cycle Analysis Competenze: Physical Reasoning Objects: Gas Fonte: Testo (PDF) — p.3 Risposta: D · Soluzioni (PDF)

Which of the following processes describes a reversible isothermal transformation of a perfect gas?

• A. Pressure decreases slowly, volume increases slowly and there is no heat exchange.
• B. The volume remains constant and the system absorbs heat.
• C. The volume decreases sharply and the system gives off heat.
• D. The pressure decreases slowly, the volume increases slowly and the system absorbs heat.
• E. The pressure remains constant and the system gives off heat. Topic: Thermodynamics Metodi: Ideal Gas Law, Thermodynamic Cycle Analysis Competenze: Physical Reasoning Objects: Gas 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 motore che ha una potenza massima di $8.1\times 10^4\text{W}$ viene utilizzato per un montacarichi che pesa $1.8\times 10^4\text{N}$.

Qual è il massimo peso del carico posto nel montacarichi che questo motore può sollevare ad una velocità media di $3.0{\text{m s}}^{-1}$?

• A. $0.9\times 10^4\text{N}$
• B. $1.8\times 10^4\text{N}$
• C. $2.4\times 10^4\text{N}$
• D. $2.7\times 10^4\text{N}$
• E. $9.0\times 10^4\text{N}$ Topic: Newtonian Mechanics, Conservation of Energy Metodi: Energy Conservation Method, Free-Body Diagram Competenze: Physical Reasoning, Mathematical Modeling Objects: — Fonte: Testo (PDF) — p.3 Risposta: A · Soluzioni (PDF)

An engine with a maximum power of $8.1\times 10^4\text{W}$ is used for a load mount weighing $1.8\times 10^4\text{N}$.

What is the maximum load weight placed on the loading equipment that this engine can lift at an average speed of $3.0{\text{m s}}^{-1}$?

• A. $0.9\times 10^4\text{N}$
• B. $1.8\times 10^4\text{N}$
• C. $2.4\times 10^4\text{N}$
• D. $2.7\times 10^4\text{N}$
• E. $9.0\times 10^4\text{N}$ Topic: Newtonian Mechanics, Conservation of Energy Metodi: Energy Conservation Method, Free-Body Diagram Competenze: Physical Reasoning, Mathematical Modeling Objects: — Fonte: Testo (PDF) — p.3 The Commission has also adopted a number of measures to ensure that the Commission’s proposals are implemented in accordance with the common position adopted by the Council.

Un oggetto è collocato davanti ad uno specchio sferico concavo. La lunghezza focale è $0.10\text{m}$.

A quale distanza dal vertice dello specchio può trovarsi l’oggetto, fra quelle indicate sotto, perché si formi un’immagine virtuale?

• A. $0.05\text{m}$
• B. $0.15\text{m}$
• C. $0.25\text{m}$
• D. $0.35\text{m}$
• E. $0.45\text{m}$ Topic: Geometric Optics Metodi: Thin Lens & Mirror Equation, Ray Tracing Competenze: Physical Reasoning, Mathematical Modeling Objects: Mirror Fonte: Testo (PDF) — p.4 Risposta: A · Soluzioni (PDF)

An object is placed in front of a concave spherical mirror. The focal length is $0.10\text{m}$.

How far from the top of the mirror can the object be, among those shown below, to form a virtual image?

• A. $0.05\text{m}$
• B. $0.15\text{m}$
• C. $0.25\text{m}$
• D. $0.35\text{m}$
• E. $0.45\text{m}$ Topic: Geometric Optics Metodi: Thin Lens & Mirror Equation, Ray Tracing Competenze: Physical Reasoning, Mathematical Modeling Objects: Mirror Fonte: Testo (PDF) — p.4 The Commission has also adopted a number of measures to ensure that the Commission’s proposals are implemented in accordance with the common position adopted by the Council.

Un oggetto di $0.40\text{kg}$ è attaccato ad una corda lunga $0.80\text{m}$. La massa e la corda vengono fatte ruotare in un piano verticale attorno all’altra estremità della corda.

Qual è la tensione della corda quando l’oggetto si trova nel punto più alto, se in quel punto il modulo della velocità è $3.0{\text{m s}}^{-1}$?

• A. $0\text{N}$
• B. $0.29\text{N}$
• C. $0.58\text{N}$
• D. $4.5\text{N}$
• E. $5.8\text{N}$ Topic: Newtonian Mechanics Metodi: Free-Body Diagram, Kinematic Equations Competenze: Physical Reasoning, Mathematical Modeling Objects: String Fonte: Testo (PDF) — p.4 Risposta: C · Soluzioni (PDF)

An object of $0.40\text{kg}$ is attached to a long string $0.80\text{m}$. The mass and rope are rotated vertically around the other end of the rope.

What is the tension of the rope when the object is at the highest point, if at that point the speed formula is $3.0{\text{m s}}^{-1}$?

• A. $0\text{N}$
• B. $0.29\text{N}$
• C. $0.58\text{N}$
• D. $4.5\text{N}$
• E. $5.8\text{N}$ Topic: Newtonian Mechanics Metodi: Free-Body Diagram, Kinematic Equations Competenze: Physical Reasoning, Mathematical Modeling Objects: String Fonte: Testo (PDF) — p.4 The Commission has also adopted a number of measures to combat the use of the ‘sustainable energy’ technology.

Una piccola moneta è appoggiata su un disco orizzontale che ruota a $33.3$ giri al minuto. Il coefficiente di attrito statico tra la moneta e la superficie del disco è $0.30$.

Qual è la massima distanza dall’asse di rotazione a cui la moneta può restare appoggiata sul disco senza scivolare?

• A. $0.024\text{m}$
• B. $0.048\text{m}$
• C. $0.12\text{m}$
• D. $0.24\text{m}$
• E. $0.48\text{m}$ Topic: Newtonian Mechanics, Rotational Dynamics Metodi: Free-Body Diagram, Kinematic Equations Competenze: Physical Reasoning, Mathematical Modeling Objects: Disk Fonte: Testo (PDF) — p.4 Risposta: D · Soluzioni (PDF)

A small coin is supported on a horizontal disc that rotates at $33.3$ rotations per minute. The static friction coefficient between the coin and the disk surface is $0.30$.

What is the maximum distance from the axis of rotation at which the coin can remain resting on the disc without slipping?

• A. $0.024\text{m}$
• B. $0.048\text{m}$
• C. $0.12\text{m}$
• D. $0.24\text{m}$
• E. $0.48\text{m}$ Topic: Newtonian Mechanics, Rotational Dynamics Metodi: Free-Body Diagram, Kinematic Equations Competenze: Physical Reasoning, Mathematical Modeling Objects: Disk 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 condensatore da $3.0\mu \text{F}$ è collegato in serie con uno da $6.0\mu \text{F}$.

Se si applica una differenza di potenziale di $300\text{V}$ al blocco formato dai due condensatori, qual è l’energia totale immagazzinata?

• A. $0.09\text{J}$
• B. $0.18\text{J}$
• C. $0.27\text{J}$
• D. $0.41\text{J}$
• E. $0.81\text{J}$ Topic: Electrostatics, Circuits Metodi: Equivalent Circuit Reduction, Electric Potential Method Competenze: Physical Reasoning, Mathematical Modeling Objects: Capacitor Fonte: Testo (PDF) — p.4 Risposta: A · Soluzioni (PDF)

A capacitor of $3.0\mu \text{F}$ is connected in series with one of $6.0\mu \text{F}$.

If a potential difference of $300\text{V}$ is applied to the block of the two capacitors, what is the total energy stored?

• A. $0.09\text{J}$
• B. $0.18\text{J}$
• C. $0.27\text{J}$
• D. $0.41\text{J}$
• E. $0.81\text{J}$ Topic: Electrostatics, Circuits Metodi: Equivalent Circuit Reduction, Electric Potential Method Competenze: Physical Reasoning, Mathematical Modeling Objects: Capacitor Fonte: Testo (PDF) — p.4 The Commission has also adopted a number of measures to ensure that the Commission’s proposals are implemented in accordance with the common position adopted by the Council.

Una barriera di scogli, posta vicino alla costa, viene investita dalle onde del mare. Nella barriera c’è un’apertura attraverso cui le onde entrano. Dopo aver attraversato la barriera, le onde si allargano per diffrazione.

L’allargamento è più o meno accentuato in funzione …

• A. … dell’ampiezza e della frequenza dell’onda incidente.
• B. … della lunghezza d’onda e della velocità dell’onda incidente.
• C. … della lunghezza d’onda e della larghezza dell’apertura.
• D. … dell’ampiezza dell’onda e della larghezza dell’apertura.
• E. … solo della larghezza dell’apertura. Topic: Wave Optics, Oscillations & Waves Metodi: Interference & Diffraction Analysis, Superposition Principle Competenze: Physical Reasoning Objects: — Fonte: Testo (PDF) — p.4 Risposta: C · Soluzioni (PDF)

A rock barrier, set near the coast, is hit by the waves of the sea. There’s a hole in the barrier through which the waves enter. After crossing the barrier, the waves expand by diffraction.

The expansion is more or less accentuated as a function of…

• A. … the width and frequency of the incident wave.
• B. … the wavelength and speed of the incident wave.
• C. … the wavelength and width of the opening.
• D. … the wavelength and width of the opening.
• E. … Just the width of the opening. Topic: Wave Optics, Oscillations & Waves Metodi: Interference & Diffraction Analysis, Superposition Principle Competenze: Physical Reasoning Objects: — Fonte: Testo (PDF) — p.4 The Commission has also adopted a number of measures to combat the use of the ‘sustainable energy’ technology.

In un’operazione di soccorso, un salvagente viene lasciato cadere verticalmente da un elicottero che si libra immobile in aria a favore di una persona che non sta nuotando e che viene trascinata dalla corrente del fiume a velocità costante $v$. L’elicottero si trova ad un’altezza di $9.8\text{m}$ e nell’istante in cui il salvagente è lasciato cadere la persona si trova a $6.0\text{m}$ di distanza a monte del punto posto perpendicolarmente sotto l’elicottero. Il salvagente cade davanti alla persona a $2.0\text{m}$ di distanza. Trascurare la resistenza dell’aria.

Qual è la velocità della corrente d’acqua del fiume?

• A. $13{\text{m s}}^{-1}$
• B. $9.8{\text{m s}}^{-1}$
• C. $6.3{\text{m s}}^{-1}$
• D. $2.8{\text{m s}}^{-1}$
• E. $2.4{\text{m s}}^{-1}$ Topic: Newtonian Mechanics Metodi: Kinematic Equations, Free-Body Diagram Competenze: Physical Reasoning, Mathematical Modeling Objects: Projectile Fonte: Testo (PDF) — p.4 Risposta: D · Soluzioni (PDF)

In a rescue operation, a lifeguard is dropped vertically by a helicopter hovering motionless in the air in favor of a person who is not swimming and is dragged by the current of the river at constant speed $v$. The helicopter is at a height of $9.8\text{m}$ and the moment the lifeguard is dropped the person is $6.0\text{m}$ away from the point perpendicular to the helicopter. The lifeguard falls in front of the person at $2.0\text{m}$ distance. Ignore the air resistance.

What is the speed of the river’s water flow?

• A. $13{\text{m s}}^{-1}$
• B. $9.8{\text{m s}}^{-1}$
• C. $6.3{\text{m s}}^{-1}$
• D. $2.8{\text{m s}}^{-1}$
• E. $2.4{\text{m s}}^{-1}$ Topic: Newtonian Mechanics Metodi: Kinematic Equations, Free-Body Diagram Competenze: Physical Reasoning, Mathematical Modeling Objects: Projectile 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.

Una pattinatrice sta ruotando su se stessa con le braccia allargate alla velocità angolare di $3.0{\text{rad s}}^{-1}$. In tale situazione il suo momento di inerzia vale $0.8{\text{kg m}}^2$. Ad un certo istante chiude le braccia lungo il corpo e la sua velocità angolare raggiunge i $7{\text{rad s}}^{-1}$. Si può trascurare qualsiasi forma di attrito e la resistenza dell’aria.

Qual è il momento di inerzia della ragazza con le braccia lungo il corpo?

• A. $0.15{\text{kg m}}^2$
• B. $0.34{\text{kg m}}^2$
• C. $0.56{\text{kg m}}^2$
• D. $1.5{\text{kg m}}^2$
• E. $1.8{\text{kg m}}^2$ Topic: Rotational Dynamics Metodi: Torque & Angular Momentum Analysis, Conservation of Momentum Competenze: Physical Reasoning, Mathematical Modeling Objects: — Fonte: Testo (PDF) — p.5 Risposta: B · Soluzioni (PDF)

A skater is rotating on herself with arms extended at an angular speed of $3.0{\text{rad s}}^{-1}$. In this situation its moment of inertia is $0.8{\text{kg m}}^2$. At a certain moment, he closes his arms along his body and his angular velocity reaches $7{\text{rad s}}^{-1}$. You can ignore any form of friction and air resistance.

What’s the moment of inertia of the girl with her arms around her body?

• A. $0.15{\text{kg m}}^2$
• B. $0.34{\text{kg m}}^2$
• C. $0.56{\text{kg m}}^2$
• D. $1.5{\text{kg m}}^2$
• E. $1.8{\text{kg m}}^2$ Topic: Rotational Dynamics Metodi: Torque & Angular Momentum Analysis, Conservation of Momentum Competenze: Physical Reasoning, Mathematical Modeling 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 in the Member States.

Due mattoni identici e omogenei di lunghezza $L$ sono posti sopra un tavolo e impilati uno sopra l’altro come mostrato in figura.

Di quale distanza $S$ il bordo del mattone superiore può sporgere, al massimo, dal bordo del tavolo in modo tale che il sistema rimanga ancora in equilibrio?

• A. $L/2$
• B. $2L/3$
• C. $3L/4$
• D. $7L/8$
• E. $L$ Topic: Rigid Body Statics, Newtonian Mechanics Metodi: Torque & Angular Momentum Analysis, Free-Body Diagram Competenze: Physical Reasoning, Diagrammatic Reasoning Objects: Block Fonte: Testo (PDF) — p.5 Risposta: C · Soluzioni (PDF)

Two identical and homogeneous bricks $L$ length are placed on a table and stacked on top of each other as shown in the figure.

At what distance $S$ can the upper brick edge rise, at most, from the table edge so that the system remains in balance?

• A. $L/2$
• B. $2L/3$
• C. $3L/4$
• D. $7L/8$
• E. $L$ Topic: Rigid Body Statics, Newtonian Mechanics Metodi: Torque & Angular Momentum Analysis, Free-Body Diagram Competenze: Physical Reasoning, Diagrammatic Reasoning Objects: Block Fonte: Testo (PDF) — p.5 The Commission has also adopted a number of measures to combat the use of the ‘sustainable energy’ technology.

Un oggetto posto su un piatto di una bilancia a bracci uguali è equilibrato da una massa campione di $12\text{kg}$. Quando è appeso ad un dinamometro, lo strumento misura $118\text{N}$. Ogni cosa (bilancia, dinamometro, massa campione e oggetto) viene ora trasportata sulla Luna dove l’accelerazione gravitazionale è circa un sesto di quella presente sulla Terra.

Le nuove letture dei due strumenti sono ora rispettivamente …

• A. … $2\text{kg}$, $20\text{N}$
• B. … $2\text{kg}$, $118\text{N}$
• C. … $12\text{kg}$, $20\text{N}$
• D. … $12\text{kg}$, $118\text{N}$
• E. … $12\text{kg}$, $708\text{N}$ Topic: Newtonian Mechanics, Gravitation Metodi: Free-Body Diagram, Newton’s Law of Gravitation Competenze: Physical Reasoning, Estimation & Approximation Objects: — Fonte: Testo (PDF) — p.5 Risposta: C · Soluzioni (PDF)

An object placed on a plate of equal arm balances is balanced by a sample mass of $12\text{kg}$. When suspended from a dynamometer, the instrument measures $118\text{N}$. Everything (balance, dynamometer, sample mass and object) is now transported to the Moon where gravitational acceleration is about one sixth of that on Earth.

The new readings of the two instruments are now …

• A. … $2\text{kg}$, $20\text{N}$
• B. … $2\text{kg}$, $118\text{N}$
• C. … $12\text{kg}$, $20\text{N}$
• D. … $12\text{kg}$, $118\text{N}$
• E. … $12\text{kg}$, $708\text{N}$ Topic: Newtonian Mechanics, Gravitation Metodi: Free-Body Diagram, Newton’s Law of Gravitation Competenze: Physical Reasoning, Estimation & Approximation Objects: — Fonte: Testo (PDF) — p.5 The Commission has also adopted a number of measures to combat the use of the ‘sustainable energy’ technology.

Un ascensore sta scendendo alla velocità di $3.8{\text{m s}}^{-1}$. In prossimità del piano di arrivo viene frenato e rallenta con accelerazione costante di $1.5{\text{m s}}^{-2}$.

Cosa indica, all’incirca, una bilancia sulla quale è salita una persona di $55\text{kg}$, che si trova nell’ascensore mentre questo sta frenando?

• A. $330\text{N}$
• B. $450\text{N}$
• C. $540\text{N}$
• D. $620\text{N}$
• E. $750\text{N}$ Topic: Newtonian Mechanics Metodi: Free-Body Diagram, Kinematic Equations Competenze: Physical Reasoning, Mathematical Modeling Objects: — Fonte: Testo (PDF) — p.5 Risposta: D · Soluzioni (PDF)

An elevator is descending at $3.8{\text{m s}}^{-1}$. In the vicinity of the arrival plane it is braking and slowing down at a constant acceleration of $1.5{\text{m s}}^{-2}$.

Cosa indica, all’incirca, una bilancia sulla quale è salita una persona di $55\text{kg}$, che si trova nell’ascensore mentre questo sta frenando?

• A. $330\text{N}$
• B. $450\text{N}$
• C. $540\text{N}$
• D. $620\text{N}$
• E. $750\text{N}$ Topic: Newtonian Mechanics Metodi: Free-Body Diagram, Kinematic Equations Competenze: Physical Reasoning, Mathematical Modeling Objects: — Fonte: Testo (PDF) — p.5 Risposta: D · Soluzioni (PDF)

Un asciugacapelli elettrico consuma una quantità $E=6.0\times 10^5\text{J}$ di energia quando funziona a $220\text{V}$ per $30$ minuti.

Durante il funzionamento, nell’asciugacapelli approssimativamente circola una corrente efficace di:

• A. $0.5\text{A}$
• B. $1.0\text{A}$
• C. $1.5\text{A}$
• D. $2.0\text{A}$
• E. $2.5\text{A}$ Topic: Circuits, Electromagnetism Metodi: Kirchhoff’s Laws, Equivalent Circuit Reduction Competenze: Physical Reasoning, Mathematical Modeling Objects: — Fonte: Testo (PDF) — p.5 Risposta: C · Soluzioni (PDF)

An electric hair dryer consumes a $E=6.0\times 10^5\text{J}$ amount of energy when it operates at $220\text{V}$ for $30$ minutes.

During operation, an effective current of approximately:

• A. $0.5\text{A}$
• B. $1.0\text{A}$
• C. $1.5\text{A}$
• D. $2.0\text{A}$
• E. $2.5\text{A}$ Topic: Circuits, Electromagnetism Metodi: Kirchhoff’s Laws, Equivalent Circuit Reduction Competenze: Physical Reasoning, Mathematical Modeling Objects: — Fonte: Testo (PDF) — p.5 The Commission has also adopted a number of measures to combat the use of the ‘sustainable energy’ technology.

In figura è rappresentata la legge oraria di un moto rettilineo.

In quale punto l’accelerazione dell’oggetto in moto è negativa?

• A. A
• B. B
• C. C
• D. D
• E. E

Position vs time graph with labeled points

Topic: Newtonian Mechanics Metodi: Kinematic Equations, Graph Linearization Competenze: Diagrammatic Reasoning, Physical Reasoning Objects: — Fonte: Testo (PDF) — p.5 Risposta: E · Soluzioni (PDF)

The time law of a straight-line motion is shown in the figure.

At what point is the acceleration of the moving object negative?

• A. A
• B. B
• C. C
• D. D
• E. E

The following table shows the position vs time graph with labeled points:

Topic: Newtonian Mechanics Metodi: Kinematic Equations, Graph Linearization Competenze: Diagrammatic Reasoning, Physical Reasoning Objects: — Fonte: Testo (PDF) — p.5 The Commission has also adopted a number of measures to ensure that the Commission’s proposals are implemented in accordance with the common position adopted by the Council.

Qual è, tra le seguenti, quella che approssima meglio la capienza di un cucchiaio da minestra?

• A. $1.2\times 10^{-3}{\text{m}}^3$
• B. $120\text{mL}$
• C. $12\times 10^{-3}\text{L}$
• D. $1.2{\text{cm}}^3$
• E. $0.12\times 10^{-3}{\text{dm}}^3$ Topic: Order-of-Magnitude Estimation Metodi: Order-of-Magnitude Estimation, Dimensional Analysis Competenze: Estimation & Approximation, Unit Conversion Objects: — Fonte: Testo (PDF) — p.6 Risposta: C · Soluzioni (PDF)

Which of the following approximates the capacity of a tablespoon best?

• A. $1.2\times 10^{-3}{\text{m}}^3$
• B. $120\text{mL}$
• C. $12\times 10^{-3}\text{L}$
• D. $1.2{\text{cm}}^3$
• E. $0.12\times 10^{-3}{\text{dm}}^3$ Topic: Order-of-Magnitude Estimation Metodi: Order-of-Magnitude Estimation, Dimensional Analysis Competenze: Estimation & Approximation, Unit Conversion Objects: — Fonte: Testo (PDF) — p.6 The Commission has also adopted a number of measures to combat the use of the ‘sustainable energy’ technology.

La figura qui riportata mostra un blocco di massa $m=7.0\text{kg}$ appoggiato su una superficie orizzontale liscia. Una forza di $100\text{N}$ viene applicata sul blocco formando un angolo di $30°$ rispetto al piano.

Qual è all’incirca l’intensità della forza $F$ che agisce orizzontalmente sul blocco sapendo che il blocco resta fermo sul pavimento?

• A. $50\text{N}$
• B. $87\text{N}$
• C. $100\text{N}$
• D. $150\text{N}$
• E. $187\text{N}$

Block on surface with angled applied force

Topic: Newtonian Mechanics, Rigid Body Statics Metodi: Free-Body Diagram, Vector Decomposition Competenze: Physical Reasoning, Diagrammatic Reasoning Objects: Block Fonte: Testo (PDF) — p.6 Risposta: B · Soluzioni (PDF)

The figure shown here shows a mass block $m=7.0\text{kg}$ resting on a smooth horizontal surface. A force of $100\text{N}$ is applied to the block forming an angle of $30°$ with respect to the plane.

What is the intensity of the force $F$ acting horizontally on the block knowing that the block remains stationary on the floor?

• A. $50\text{N}$
• B. $87\text{N}$
• C. $100\text{N}$
• D. $150\text{N}$
• E. $187\text{N}$

Block on surface with angled applied force

Topic: Newtonian Mechanics, Rigid Body Statics Metodi: Free-Body Diagram, Vector Decomposition Competenze: Physical Reasoning, Diagrammatic Reasoning Objects: Block Fonte: Testo (PDF) — p.6 The Commission has also adopted a proposal for a regulation on the protection of the environment and the environment in the Member States.

Una molla più leggera è attaccata ad una più pesante per un estremo. Entrambe le molle sono ideali. Il sistema è disposto orizzontalmente. Un impulso si propaga in quella più leggera incidendo sulla giunzione tra le due.

In questo punto l’impulso verrà…

• A. … totalmente riflesso.
• B. … totalmente assorbito.
• C. … totalmente trasmesso alla molla più pesante.
• D. … parzialmente riflesso e parzialmente trasmesso alla molla più pesante.
• E. … parzialmente riflesso e parzialmente assorbito. Topic: Oscillations & Waves Metodi: Superposition Principle, Wave Equation Competenze: Physical Reasoning Objects: Spring Fonte: Testo (PDF) — p.6 Risposta: D · Soluzioni (PDF)

A lighter spring is attached to a heavier spring for an extreme. Both springs are ideal. The system is horizontally arranged. A pulse propagates into the lighter one affecting the junction between the two.

At this point, the impulse will come…

• A. … I’m totally reflective.
• B. … It’s totally absorbed.
• C. … It is fully transmitted to the heaviest spring.
• D. … partially reflected and partially transmitted to the heavier spring.
• E. … partially reflected and partially absorbed. Topic: Oscillations & Waves Metodi: Superposition Principle, Wave Equation Competenze: Physical Reasoning Objects: Spring Fonte: Testo (PDF) — p.6 The Commission has also adopted a number of proposals for the implementation of the ‘European Union’s strategy for the protection of the environment.

Una carica elettrica è uniformemente distribuita all’interno di una sfera di raggio $a$.

Quale dei seguenti grafici meglio rappresenta l’intensità del campo elettrico in funzione della distanza dal centro della sfera?

Five graphs of E-field vs distance from center

Topic: Electrostatics Metodi: Gauss’s Law, Symmetry Argument Competenze: Physical Reasoning, Diagrammatic Reasoning Objects: Sphere Fonte: Testo (PDF) — p.6 Risposta: D · Soluzioni (PDF)

An electrical charge is evenly distributed within a sphere of radius $a$.

Which of the following graphs best represents the intensity of the electric field in relation to the distance from the center of the sphere?

Five graphs of E-field vs distance from center

Topic: Electrostatics Metodi: Gauss’s Law, Symmetry Argument Competenze: Physical Reasoning, Diagrammatic Reasoning Objects: Sphere Fonte: Testo (PDF) — p.6 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 costruttore dichiara che un’automobile può accelerare da ferma a $24{\text{m s}}^{-1}$ in $6\text{s}$.

Che distanza percorrerà, partendo da ferma, in $10\text{s}$ con questa accelerazione supposta costante?

• A. $40\text{m}$
• B. $120\text{m}$
• C. $144\text{m}$
• D. $200\text{m}$
• E. $240\text{m}$ Topic: Newtonian Mechanics Metodi: Kinematic Equations Competenze: Physical Reasoning, Mathematical Modeling Objects: — Fonte: Testo (PDF) — p.6 Risposta: D · Soluzioni (PDF)

A manufacturer declares that a vehicle can accelerate from stop to $24{\text{m s}}^{-1}$ in $6\text{s}$.

What distance will it travel, starting from a stationary point, in $10\text{s}$ at this assumed constant acceleration?

• A. $40\text{m}$
• B. $120\text{m}$
• C. $144\text{m}$
• D. $200\text{m}$
• E. $240\text{m}$ Topic: Newtonian Mechanics Metodi: Kinematic Equations Competenze: Physical Reasoning, Mathematical Modeling Objects: — Fonte: Testo (PDF) — p.6 The Commission has also adopted a number of proposals for the implementation of the ‘European Union’s strategy for the protection of the environment.

Due resistori e tre amperometri sono collegati ad un generatore come in figura.

Qual è la forza elettromotrice fornita dal generatore?

• A. $60\text{V}$
• B. $120\text{V}$
• C. $220\text{V}$
• D. $440\text{V}$
• E. $500\text{V}$

Circuit with two resistors and three ammeters

Topic: Circuits, Electromagnetism Metodi: Kirchhoff’s Laws, Equivalent Circuit Reduction Competenze: Physical Reasoning, Diagrammatic Reasoning Objects: Resistor, Battery Fonte: Testo (PDF) — p.6 Risposta: B · Soluzioni (PDF)

Two resistors and three amperometers are connected to a generator as shown in the figure.

What is the electromotive force supplied by the generator?

• A. $60\text{V}$
• B. $120\text{V}$
• C. $220\text{V}$
• D. $440\text{V}$
• E. $500\text{V}$

Circuit with two resistors and three ammeters

Topic: Circuits, Electromagnetism Metodi: Kirchhoff’s Laws, Equivalent Circuit Reduction Competenze: Physical Reasoning, Diagrammatic Reasoning Objects: Resistor, Battery Fonte: Testo (PDF) — p.6 The Commission has also adopted a proposal for a regulation on the protection of the environment and the environment in the Member States.

Un campione di una sostanza di massa $5.00\text{kg}$ assorbe calore da una sorgente che ne fornisce in maniera costante nel tempo una quantità pari a $41.9\text{kJ}$ ogni minuto. Il grafico rappresenta la temperatura del campione al trascorrere del tempo.

Il calore di vaporizzazione della sostanza è pari a

• A. $12.6{\text{kJkg}}^{-1}$
• B. $62.9{\text{kJkg}}^{-1}$
• C. $126{\text{kJkg}}^{-1}$
• D. $210{\text{kJkg}}^{-1}$
• E. $629{\text{kJkg}}^{-1}$

Temperature vs time graph for phase transition

Topic: Thermodynamics Metodi: First Law of Thermodynamics, Experimental Data Analysis Competenze: Diagrammatic Reasoning, Physical Reasoning Objects: — Fonte: Testo (PDF) — p.7 Risposta: C · Soluzioni (PDF)

A sample of a substance of mass $5.00\text{kg}$ absorbs heat from a source which constantly provides a quantity of $41.9\text{kJ}$ over time per minute. The graph represents the temperature of the sample over time.

The heat of vaporization of the substance is equal to

• A. $12.6{\text{kJkg}}^{-1}$
• B. $62.9{\text{kJkg}}^{-1}$
• C. $126{\text{kJkg}}^{-1}$
• D. $210{\text{kJkg}}^{-1}$
• E. $629{\text{kJkg}}^{-1}$

The following table shows the results of the calculations for the period of the transition period:

Topic: Thermodynamics Metodi: First Law of Thermodynamics, Experimental Data Analysis Competenze: Diagrammatic Reasoning, Physical Reasoning Objects: — Fonte: Testo (PDF) — p.7 The Commission has also adopted a number of measures to combat the use of the ‘sustainable energy’ technology.

Una lente convergente forma in un certo punto l’immagine di un oggetto.

Cosa succede dell’immagine se la metà superiore della lente viene coperta con un cartoncino completamente opaco?

• A. Metà dell’immagine scompare.
• B. L’immagine rimane intera ma di dimensioni dimezzate.
• C. L’immagine scompare.
• D. L’immagine appare più sbiadita.
• E. L’immagine si forma sul cartoncino. Topic: Geometric Optics, Wave Optics Metodi: Ray Tracing, Superposition Principle Competenze: Physical Reasoning, Diagrammatic Reasoning Objects: Lens Fonte: Testo (PDF) — p.7 Risposta: D · Soluzioni (PDF)

A convergent lens forms at some point the image of an object.

What happens to the image if the upper half of the lens is covered with a completely opaque cardboard?

• Half of the image disappears.
• B. The image remains whole but half-sized.
• C. The image is missing.
• D. The image appears more blurred.
• E. The image is formed on the cardboard. Topic: Geometric Optics, Wave Optics Metodi: Ray Tracing, Superposition Principle Competenze: Physical Reasoning, Diagrammatic Reasoning Objects: Lens Fonte: Testo (PDF) — p.7 The Commission has also adopted a number of proposals for the implementation of the ‘European Union’s strategy for the protection of the environment.

I grafici qui riportati mostrano la relazione tra la pressione $P$ e il volume $V$ di una quantità assegnata di un gas perfetto che subisce una trasformazione termodinamica senza scambio di calore.

Quale di questi grafici meglio rappresenta la situazione?

Five P-V diagrams for adiabatic process

Topic: Thermodynamics Metodi: Thermodynamic Cycle Analysis, Ideal Gas Law Competenze: Diagrammatic Reasoning, Physical Reasoning Objects: Gas Fonte: Testo (PDF) — p.7 Risposta: A · Soluzioni (PDF)

The graphs shown here show the relationship between the pressure $P$ and the volume $V$ of an allocated amount of a perfect gas undergoing thermodynamic transformation without heat exchange.

Which of these graphs best represents the situation?

The following table shows the results of the study:

Topic: Thermodynamics Metodi: Thermodynamic Cycle Analysis, Ideal Gas Law Competenze: Diagrammatic Reasoning, Physical Reasoning Objects: Gas Fonte: Testo (PDF) — p.7 The Commission has also adopted a number of measures to ensure that the Commission’s proposals are implemented in accordance with the common position adopted by the Council.

Un blocco di un certo materiale avente massa $M=1.0\times 10^3\text{kg}$ assorbe una quantità $Q=2.4\times 10^3\text{kJ}$ di calore mentre la sua temperatura varia da $710°\text{C}$ a $720°\text{C}$.

Qual è il calore specifico del materiale di cui è fatto il blocco?

• A. $4.2\times 10^{-8}{\text{kJkg}}^{-1}{\text{K}}^{-1}$
• B. $4.2\times 10^{-7}{\text{kJkg}}^{-1}{\text{K}}^{-1}$
• C. $0.24{\text{kJkg}}^{-1}{\text{K}}^{-1}$
• D. $2.4{\text{kJkg}}^{-1}{\text{K}}^{-1}$
• E. $2.4\times 10^5{\text{kJkg}}^{-1}{\text{K}}^{-1}$ Topic: Thermodynamics Metodi: First Law of Thermodynamics, Ideal Gas Law Competenze: Physical Reasoning, Mathematical Modeling Objects: Block Fonte: Testo (PDF) — p.7 Risposta: C · Soluzioni (PDF)

A block of a certain material with a mass $M=1.0\times 10^3\text{kg}$ absorbs a quantity $Q=2.4\times 10^3\text{kJ}$ of heat while its temperature varies from $710°\text{C}$ to $720°\text{C}$.

What is the specific heat of the material the block is made of?

• A. $4.2\times 10^{-8}{\text{kJkg}}^{-1}{\text{K}}^{-1}$
• B. $4.2\times 10^{-7}{\text{kJkg}}^{-1}{\text{K}}^{-1}$
• C. $0.24{\text{kJkg}}^{-1}{\text{K}}^{-1}$
• D. $2.4{\text{kJkg}}^{-1}{\text{K}}^{-1}$
• E. $2.4\times 10^5{\text{kJkg}}^{-1}{\text{K}}^{-1}$ Topic: Thermodynamics Metodi: First Law of Thermodynamics, Ideal Gas Law Competenze: Physical Reasoning, Mathematical Modeling Objects: Block Fonte: Testo (PDF) — p.7 The Commission has also adopted a number of measures to combat the use of the ‘sustainable energy’ technology.

Quale combinazione di unità di misura si può adoperare per il lavoro di una forza?

• A. $\text{newton}\cdot \text{secondo}\cdot {\text{metro}}^{-1}$
• B. $\text{newton}\cdot \text{metro}\cdot {\text{secondo}}^{-1}$
• C. $\text{newton}\cdot {\text{metro}}^{-1}$
• D. $\text{newton}\cdot \text{metro}$
• E. $\text{newton}\cdot \text{metro}\cdot \text{secondo}$ Topic: Newtonian Mechanics Metodi: Dimensional Analysis Competenze: Unit Conversion, Physical Reasoning Objects: — Fonte: Testo (PDF) — p.7 Risposta: D · Soluzioni (PDF)

What combination of units of measurement can be used for the work of a force?

• A. $\text{newton}\cdot \text{secondo}\cdot {\text{metro}}^{-1}$
• B. $\text{newton}\cdot \text{metro}\cdot {\text{secondo}}^{-1}$
• C. $\text{newton}\cdot {\text{metro}}^{-1}$
• D. $\text{newton}\cdot \text{metro}$
• E. $\text{newton}\cdot \text{metro}\cdot \text{secondo}$ Topic: Newtonian Mechanics Metodi: Dimensional Analysis Competenze: Unit Conversion, Physical Reasoning Objects: — Fonte: Testo (PDF) — p.7 The Commission has also adopted a number of proposals for the implementation of the ‘European Union’s strategy for the protection of the environment.

In figura è mostrato un raggio di luce proveniente dalla base di un oggetto, che incide su una lente di cui il punto $F$ è un fuoco, e sono mostrati cinque possibili raggi uscenti dalla lente.

Qual è il corretto cammino che compie il raggio di luce?

Lens with incident ray and five candidate refracted rays

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

Figure 1 shows a beam of light coming from the base of an object, which hits a lens whose point $F$ is a fire, and shows five possible beams coming from the lens.

What is the correct path that makes the light beam?

Lens with incident ray and five candidate refracted rays

Topic: Geometric Optics Metodi: Ray Tracing, Thin Lens & Mirror Equation Competenze: Diagrammatic Reasoning, Physical Reasoning Objects: Lens Fonte: Testo (PDF) — p.8 The Commission has also adopted a number of measures to combat the use of the ‘sustainable energy’ technology.

In un incidente automobilistico un passeggero avente massa di $44\text{kg}$ e velocità di $15{\text{m s}}^{-1}$ viene fermato in $0.10\text{s}$.

Qual è l’intensità della forza media che agisce sul passeggero durante l’incidente?

• A. $293\text{N}$
• B. $440\text{N}$
• C. $660\text{N}$
• D. $4400\text{N}$
• E. $6600\text{N}$ Topic: Newtonian Mechanics, Conservation of Momentum Metodi: Impulse-Momentum Theorem, Free-Body Diagram Competenze: Physical Reasoning, Mathematical Modeling Objects: — Fonte: Testo (PDF) — p.8 Risposta: E · Soluzioni (PDF)

In an automobile accident a passenger with mass $44\text{kg}$ and speed $15{\text{m s}}^{-1}$ is stopped at $0.10\text{s}$.

What is the intensity of the force acting on the passenger during the accident?

• A. $293\text{N}$
• B. $440\text{N}$
• C. $660\text{N}$
• D. $4400\text{N}$
• E. $6600\text{N}$ Topic: Newtonian Mechanics, Conservation of Momentum Metodi: Impulse-Momentum Theorem, Free-Body Diagram Competenze: Physical Reasoning, Mathematical Modeling Objects: — Fonte: Testo (PDF) — p.8 The Commission has also adopted a number of measures to ensure that the Commission’s proposals are implemented in accordance with the common position adopted by the Council.

Una serie di forze viene applicata, in successione, a due oggetti di massa diversa, A e B. I grafici mostrano l’andamento dell’accelerazione impressa su ciascun blocco dalle varie forze applicate.

In che relazione stanno fra loro le masse dei due oggetti?

• A. La massa di A è quattro volte più grande di quella di B
• B. La massa di A è il doppio di quella di B
• C. La massa è la stessa
• D. La massa di A è metà di quella di B
• E. La massa di A è un quarto di quella di B

Acceleration vs force graphs for objects A and B

Topic: Newtonian Mechanics Metodi: Free-Body Diagram, Graph Linearization Competenze: Diagrammatic Reasoning, Physical Reasoning Objects: Block Fonte: Testo (PDF) — p.8 Risposta: D · Soluzioni (PDF)

A series of forces is applied, in succession, to two objects of different mass, A and B. The graphs show the acceleration pattern printed on each block by the various forces applied.

What relationship do the masses of the two objects have?

• A. The mass of A is four times greater than that of B
• B. The mass of A is twice that of B
• C. The mass is the same
• D. The mass of A is half that of B
• E. The mass of A is one quarter of that of B

Acceleration vs force graphs for objects A and B

Topic: Newtonian Mechanics Metodi: Free-Body Diagram, Graph Linearization Competenze: Diagrammatic Reasoning, Physical Reasoning Objects: Block 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.

L’elettrone di un atomo d’idrogeno che si trova allo stato eccitato con numero quantico principale $n=2$ decade al livello fondamentale ($n=1$) ed emette un fotone.

Sapendo che l’energia di ionizzazione di un atomo d’idrogeno è $13.6\text{eV}$, quanto vale, approssimativamente, l’energia del fotone emesso?

• A. $5.4\times 10^{-19}\text{J}$
• B. $1.6\times 10^{-18}\text{J}$
• C. $5.4\times 10^{-18}\text{J}$
• D. $2.2\times 10^{-18}\text{J}$
• E. $7.4\times 10^{-18}\text{J}$ Topic: Modern-Quantum Physics, Astrophysics Metodi: Bohr Model & Quantization, Photon Energy Relation Competenze: Physical Reasoning, Mathematical Modeling Objects: Atom, Electron, Photon Fonte: Testo (PDF) — p.8 Risposta: B · Soluzioni (PDF)

The electron of a hydrogen atom in the excited state with the main quantum number $n=2$ decays to the fundamental level ($n=1$) and emits a photon.

Knowing that the ionization energy of a hydrogen atom is $13.6\text{eV}$, what is the energy of the photon emitted worth, approximately?

• A. $5.4\times 10^{-19}\text{J}$
• B. $1.6\times 10^{-18}\text{J}$
• C. $5.4\times 10^{-18}\text{J}$
• D. $2.2\times 10^{-18}\text{J}$
• E. $7.4\times 10^{-18}\text{J}$ Topic: Modern-Quantum Physics, Astrophysics Metodi: Bohr Model & Quantization, Photon Energy Relation Competenze: Physical Reasoning, Mathematical Modeling Objects: Atom, Electron, Photon Fonte: Testo (PDF) — p.8 The Commission has also adopted a proposal for a regulation on the protection of the environment and the environment in the Member States.

Un pezzo di ghiaccio cade verticalmente sulla superficie ghiacciata di un lago e si frantuma in tre pezzi che schizzano via parallelamente alla superficie del lago, come schematizzato in figura che rappresenta la situazione vista dall’alto.

Se il pezzo più grosso, di $4.0\text{kg}$, inizia a muoversi a $4.0{\text{m s}}^{-1}$, con che velocità partono i due pezzi più piccoli, entrambi di $2.0\text{kg}$?

• A. $4.1{\text{m s}}^{-1}$
• B. $4.9{\text{m s}}^{-1}$
• C. $5.7{\text{m s}}^{-1}$
• D. $5.9{\text{m s}}^{-1}$
• E. $9.8{\text{m s}}^{-1}$

Top view of ice fragment splitting into three pieces

Topic: Conservation of Momentum, Newtonian Mechanics Metodi: Conservation of Momentum, Vector Decomposition Competenze: Physical Reasoning, Diagrammatic Reasoning Objects: — Fonte: Testo (PDF) — p.8 Risposta: C · Soluzioni (PDF)

A piece of ice falls vertically on the icy surface of a lake and breaks into three pieces that slide away parallel to the surface of the lake, as outlined in a figure depicting the situation from above.

If the largest piece of $4.0\text{kg}$ starts moving at $4.0{\text{m s}}^{-1}$, at what speed do the two smaller pieces, both of $2.0\text{kg}$, leave?

• A. $4.1{\text{m s}}^{-1}$
• B. $4.9{\text{m s}}^{-1}$
• C. $5.7{\text{m s}}^{-1}$
• D. $5.9{\text{m s}}^{-1}$
• E. $9.8{\text{m s}}^{-1}$

Top view of ice fragment splitting into three pieces

Topic: Conservation of Momentum, Newtonian Mechanics Metodi: Conservation of Momentum, Vector Decomposition Competenze: Physical Reasoning, Diagrammatic Reasoning Objects: — Fonte: Testo (PDF) — p.8 The Commission has also adopted a number of measures to combat the use of the ‘sustainable energy’ technology.

Un’automobile di $1200\text{kg}$ di massa deve trainare un rimorchio che ha una massa di $700\text{kg}$ lungo una strada dritta in pianura.

Quando la macchina parte con un’accelerazione di $2.0{\text{m s}}^{-2}$, la forza che il rimorchio esercita sull’automobile vale

• A. $0\text{N}$
• B. $700\text{N}$
• C. $1400\text{N}$
• D. $2400\text{N}$
• E. $3800\text{N}$ Topic: Newtonian Mechanics Metodi: Free-Body Diagram, Kinematic Equations Competenze: Physical Reasoning, Mathematical Modeling Objects: — Fonte: Testo (PDF) — p.8 Risposta: C · Soluzioni (PDF)

A vehicle of $1200\text{kg}$ mass shall tow a trailer of $700\text{kg}$ mass along a straight road in the plain.

When the car starts at $2.0{\text{m s}}^{-2}$, the force exerted on the car by the trailer shall be:

• A. $0\text{N}$
• B. $700\text{N}$
• C. $1400\text{N}$
• D. $2400\text{N}$
• E. $3800\text{N}$ Topic: Newtonian Mechanics Metodi: Free-Body Diagram, Kinematic Equations Competenze: Physical Reasoning, Mathematical Modeling Objects: — Fonte: Testo (PDF) — p.8 The Commission has also adopted a number of measures to combat the use of the ‘sustainable energy’ technology.

Tra le 5 coppie di grafici che mostrano rispettivamente la distanza percorsa (in alto) e la velocità (in basso) di un oggetto in moto, quale descrive correttamente il caso in cui la risultante delle forze applicate al corpo è nulla?

Five pairs of position and velocity graphs

Net force vs time graph for accelerating object

Topic: Newtonian Mechanics Metodi: Kinematic Equations, Graph Linearization Competenze: Diagrammatic Reasoning, Physical Reasoning Objects: — Fonte: Testo (PDF) — p.9 Risposta: B · Soluzioni (PDF)

Of the 5 pairs of graphs showing the distance traveled (up) and the speed (down) of a moving object, which one correctly describes the case where the result of the forces applied to the body is zero?

Five pairs of position and speed graphs

The following table shows the data used for the calculation of the net force and time graph for accelerating object:

Topic: Newtonian Mechanics Metodi: Kinematic Equations, Graph Linearization Competenze: Diagrammatic Reasoning, Physical Reasoning Objects: — Fonte: Testo (PDF) — p.9 The Commission has also adopted a proposal for a regulation on the protection of the environment and the environment in the Member States.

Uno studente alto $1.6\text{m}$ sta in piedi a $5.0\text{m}$ da una lente convergente; questa ne forma un’immagine su uno schermo posto a $50\text{cm}$ oltre la lente.

Quanto è alta l’immagine dello studente sullo schermo?

• A. $0.016\text{m}$
• B. $0.16\text{m}$
• C. $0.80\text{m}$
• D. $1.6\text{m}$
• E. $8.0\text{m}$ Topic: Geometric Optics Metodi: Thin Lens & Mirror Equation, Ray Tracing Competenze: Physical Reasoning, Mathematical Modeling Objects: Lens, Screen Fonte: Testo (PDF) — p.9 Risposta: B · Soluzioni (PDF)

A high student $1.6\text{m}$ stands at $5.0\text{m}$ from a convergent lens; this forms an image of him on a screen placed at $50\text{cm}$ above the lens.

How high is the student’s image on the screen?

• A. $0.016\text{m}$
• B. $0.16\text{m}$
• C. $0.80\text{m}$
• D. $1.6\text{m}$
• E. $8.0\text{m}$ Topic: Geometric Optics Metodi: Thin Lens & Mirror Equation, Ray Tracing Competenze: Physical Reasoning, Mathematical Modeling Objects: Lens, Screen Fonte: Testo (PDF) — p.9 The Commission has also adopted a proposal for a regulation on the protection of the environment and the environment in the Member States.

Una bacchetta conduttrice lunga $\ell =20\text{cm}$ viene spostata alla velocità $v=3.0{\text{m s}}^{-1}$ in direzione perpendicolare alla sua lunghezza. Per la presenza di un campo di induzione magnetica uniforme, perpendicolare sia alla sbarretta che alla direzione di moto, si può misurare una d.d.p. tra i capi della sbarretta, $\Delta V=12\text{mV}$.

Quanto vale l’intensità del campo magnetico?

• A. $180\text{mT}$
• B. $20\text{mT}$
• C. $18\text{mT}$
• D. $13\text{mT}$
• E. $7.2\text{mT}$ Topic: Electromagnetic Induction, Magnetism Metodi: Faraday’s Law of Induction, Lorentz Force Analysis Competenze: Physical Reasoning, Mathematical Modeling Objects: Rod Fonte: Testo (PDF) — p.9 Risposta: B · Soluzioni (PDF)

A long $\ell =20\text{cm}$ conductive rod is moved at $v=3.0{\text{m s}}^{-1}$ speed in a direction perpendicular to its length. For the presence of a uniform magnetic induction field perpendicular to both the bar and the direction of motion, a D.D.P. may be measured. between the heads of the bar, $\Delta V=12\text{mV}$.

What’s the magnets of the magnetic field?

• A. $180\text{mT}$
• B. $20\text{mT}$
• C. $18\text{mT}$
• D. $13\text{mT}$
• E. $7.2\text{mT}$ Topic: Electromagnetic Induction, Magnetism Metodi: Faraday’s Law of Induction, Lorentz Force Analysis Competenze: Physical Reasoning, Mathematical Modeling Objects: Rod Fonte: Testo (PDF) — p.9 The Commission has also adopted a proposal for a regulation on the protection of the environment and the environment in the Member States.

In un laboratorio medico viene portato un campione di un isotopo radioattivo di $16\text{g}$. Dopo $6$ ore, si osserva che $12\text{g}$ del campione hanno subito un decadimento.

Qual è il tempo di dimezzamento (detto anche emivita) di quell’isotopo?

• A. $12$ ore
• B. $6$ ore
• C. $4$ ore
• D. $3$ ore
• E. $2$ ore Topic: Nuclear & Particle Physics, Modern-Quantum Physics Metodi: Radioactive Decay Law Competenze: Physical Reasoning, Mathematical Modeling Objects: Nucleus Fonte: Testo (PDF) — p.9 Risposta: D · Soluzioni (PDF)

A sample of a radioactive isotope of $16\text{g}$ is taken to a medical laboratory. After $6$ hours, it is observed that the $12\text{g}$ of the sample has decayed.

What is the half-life of that isotope?

• **A ** $12$ hours
• **B ** $6$ hours
• **C ** $4$ hours
• **D ** $3$ hours
• E. $2$ hours Topic: Nuclear & Particle Physics, Modern-Quantum Physics Metodi: Radioactive Decay Law Competenze: Physical Reasoning, Mathematical Modeling Objects: Nucleus Fonte: Testo (PDF) — p.9 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 con una massa di $2.0\text{kg}$ è accelerato partendo da fermo. La figura mostra il modulo della forza risultante in funzione del tempo.

Nell’istante $t=4.0\text{s}$ la velocità dell’oggetto è circa:

• A. $2.2{\text{m s}}^{-1}$
• B. $3.5{\text{m s}}^{-1}$
• C. $5.8{\text{m s}}^{-1}$
• D. $7.0{\text{m s}}^{-1}$
• E. $11{\text{m s}}^{-1}$ Topic: Newtonian Mechanics Metodi: Free-Body Diagram, Calculus-Integration Competenze: Diagrammatic Reasoning, Physical Reasoning Objects: — Fonte: Testo (PDF) — p.9 Risposta: B · Soluzioni (PDF)

An object with a mass of $2.0\text{kg}$ is accelerated from a stationary point. The figure shows the resulting force as a function of time.

In the instant $t=4.0\text{s}$ the object speed is approximately:

• A. $2.2{\text{m s}}^{-1}$
• B. $3.5{\text{m s}}^{-1}$
• C. $5.8{\text{m s}}^{-1}$
• D. $7.0{\text{m s}}^{-1}$
• E. $11{\text{m s}}^{-1}$ Topic: Newtonian Mechanics Metodi: Free-Body Diagram, Calculus-Integration Competenze: Diagrammatic Reasoning, Physical Reasoning Objects: — Fonte: Testo (PDF) — p.9 The Commission has also adopted a proposal for a regulation on the protection of the environment and the environment in the Member States.