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Sinking body

When a solid body of density $1, 80 g c m^{- 3}$ sinks at constant velocity in viscous oil of density $0, 90 g c m^{- 3}$ , then …

A … no gravitational force acts on the body.

B … the mass of the body equals the mass of the displaced fluid.

C … the gravitational force on the body is balanced by the drag force.

D … the buoyant force on the body equals the drag force.

Topic: Newtonian Mechanics, Thermodynamics, Electromagnetism Metodi: Physical Modeling, Free-Body Diagram, Conservation Laws Competenze: Physical Reasoning, Mathematical Modeling, Diagrammatic Reasoning Objects: — Fonte: Testo (PDF) — p.5

Sinking body

Quando un corpo solido di densità $1, 80 g c m^{- 3}$ si scende a velocità costante in olio viscoso di densità $0, 90 g c m^{- 3}$ , allora …

A … non agisce forza gravitazionale sul corpo.

B … la massa del corpo è pari alla massa del fluido spostato.

La forza gravitazionale sul corpo è bilanciata dalla forza di trazione.

D … la forza buoyant sul corpo equivale alla forza di trazione.

The following is the list of the types of vessels that are subject to the provisions of this Regulation:

When a solid body of density $1, 80 g c m^{- 3}$ sinks at constant velocity in viscous oil of density $0, 90 g c m^{- 3}$ , then …

A … no gravitational force acts on the body.

B … the mass of the body equals the mass of the displaced fluid.

The gravitational force on the body is balanced by the drag force.

The buoyant force on the body equals the drag force.

Cork in a bucket

A bucket filled with water is suspended from a rope. Inside the bucket there is a cork attached to the bottom of the bucket by a thread. When the thread is cut, the cork rises to the water surface. When the rope holding the bucket is cut, the bucket falls downward together with its contents.

How does the cork move relative to the bucket immediately after the rope and the thread are cut simultaneously?

A The cork rises faster to the water surface.

B The cork rises to the water surface at exactly the same speed.

C The cork remains at rest.

D The cork sinks to the bottom of the bucket.

Topic: Fluid Mechanics, Newtonian Mechanics Metodi: Free-Body Diagram, Physical Modeling Competenze: Physical Reasoning Objects: Container, String Fonte: Testo (PDF) — p.5

Cork in a bucket

Un secchio pieno di acqua è sospeso da una corda. All’interno del secchio c’è un cannuccio attaccato al fondo del secchio da un filo. Quando il filo è tagliato, il canne si eleva alla superficie dell’acqua. Quando la corda che tiene il secchio viene tagliata, il secchio cade verso il basso insieme al suo contenuto.

Come si muove il canne rispetto al secchio immediatamente dopo che la corda e il filo sono tagliati simultaneamente?

Il cork si eleva più velocemente alla superficie dell’acqua.

B Il canne si eleva alla superficie dell’acqua alla stessa velocità.

C. La corteccia resta a rest.

D Il canne si scende al fondo del secchio.

Topic: Fluid Mechanics, Newtonian Mechanics Metodi: Free-Body Diagram, Physical Modeling Competenze: Physical Reasoning Objects: Container, String Fonte: Testo (PDF) — p.5

Cork in a bucket

How does the cork move relative to the bucket immediately after the rope and the thread are cut simultaneously?

A. The cork rises faster to the water surface.

B The cork rises to the water surface at exactly the same speed.

C The cork remains at rest.

D The cork sinks to the bottom of the bucket.

Topic: Fluid Mechanics, Newtonian Mechanics Metodi: Free-Body Diagram, Physical Modeling Competenze: Physical Reasoning Objects: Container, String Fonte: Testo (PDF) — p.5

Stone in a glass of water

A glass filled with water of density $1000 kg m^{- 3}$ stands on a balance. The balance is brought into equilibrium by placing a weight on it.

Now a stone with a volume of $300 c m^{3}$ and a density of $3000 kg m^{- 3}$ is immersed in the water, hanging from a thin thread attached to a stand, without touching the bottom.

To bring the balance back into equilibrium, one must …

A … do nothing, since the balance stays in equilibrium.

B … place a weight of mass $0, 3 kg$ on the left-hand side of the balance.

C … place a weight of mass $0, 6 kg$ on the left-hand side of the balance.

D … place a weight of mass $0, 9 kg$ on the left-hand side of the balance.

Topic: Fluid Mechanics, Newtonian Mechanics Metodi: Hydrostatic Equilibrium, Free-Body Diagram Competenze: Physical Reasoning Objects: Container, String Fonte: Testo (PDF) — p.6

Stone in a glass of water

Un bicchiere pieno di acqua di densità $1000 kg m^{- 3}$ è in equilibrio. Il equilibrio viene portato in equilibrio mettendo un peso su di esso.

Ora una pietra con un volume di $300 c m^{3}$ e una densità di $3000 kg m^{- 3}$ è immersa nell’acqua, appesa a un filo sottile attaccato a un stand, senza toccare il fondo.

Per riportare l’equilibrio, bisogna

A … non fare nulla, dal momento che il bilancio resta in equilibrio.

B … place a weight of mass $0, 3 kg$ on the left hand side of the balance.

C … place a weight of mass $0, 6 kg$ on the left hand side of the balance.

D … place a weight of mass $0, 9 kg$ on the left hand side of the balance.

Topic: Fluid Mechanics, Newtonian Mechanics Metodi: Hydrostatic Equilibrium, Free-Body Diagram Competenze: Physical Reasoning Objects: Container, String Fonte: Testo (PDF) — p.6

Stone in a glass of water

A glass filled with water of density $1000 kg m^{- 3}$ stands on a balance. The balance is brought into balance by placing a weight on it.

Now a stone with a volume of $300 c m^{3}$ and a density of $3000 kg m^{- 3}$ is immersed in the water, hanging from a thin thread attached to a stand, without touching the bottom.

To bring the balance back into balance, one must

A … do nothing, since the balance stays in balance.

B … place a weight of mass $0, 3 kg$ on the left hand side of the balance.

C … place a weight of mass $0, 6 kg$ on the left hand side of the balance.

D … place a weight of mass $0, 9 kg$ on the left hand side of the balance.

Topic: Fluid Mechanics, Newtonian Mechanics Metodi: Hydrostatic Equilibrium, Free-Body Diagram Competenze: Physical Reasoning Objects: Container, String Fonte: Testo (PDF) — p.6

Ice cubes in a glass

An ice cube floats in each of three glasses filled with water. The ice cube in glass 1 has an air bubble inside, the ice cube in glass 2 has a core of liquid water, and in glass 3 floats an ice cube with an aluminium core.

What can be said about the water levels in the glasses immediately after the ice cubes have melted?

A The water level in glass 1 has risen, those in the other glasses are unchanged.

B The water level in glass 3 has fallen, those in the other glasses are unchanged.

C The water levels in glasses 1 and 3 have risen, that in glass 2 is unchanged.

D The water levels in all glasses are unchanged.

Topic: Fluid Mechanics, Thermodynamics Metodi: Hydrostatic Equilibrium, Physical Modeling Competenze: Physical Reasoning Objects: Bubble, Container Fonte: Testo (PDF) — p.6

Ice cubes in a glass

Un cubo di ghiaccio flotta in ciascuno dei tre bicchieri pieni di acqua. Il cubo di ghiaccio in vetro 1 ha una bolla d’aria all’interno, il cubo di ghiaccio in vetro 2 ha un nucleo di acqua liquida, e in vetro 3 galleggia un cubo di ghiaccio con un nucleo di alluminio.

Cosa si può dire dei livelli d’acqua nei bicchieri immediatamente dopo che i cubetti di ghiaccio sono fusi?

A. Il livello di acqua in vetro 1 è aumentato, quelli negli altri bicchieri sono invariati.

B Il livello di acqua in vetro 3 è diminuito, quelli negli altri bicchieri sono invariati.

C I livelli di acqua nei bicchieri 1 e 3 sono aumentati, che in bicchiere 2 è invariato.

D I livelli di acqua in tutti i bicchieri sono invariati.

Topic: Fluid Mechanics, Thermodynamics Metodi: Hydrostatic Equilibrium, Physical Modeling Competenze: Physical Reasoning Objects: Bubble, Container Fonte: Testo (PDF) — p.6

Ice cubes in a glass

What can be said about the water levels in the glasses immediately after the ice cubes have melted?

A The water level in glass 1 has risen, those in the other glasses are unchanged.

B The water level in glass 3 has fallen, those in the other glasses are unchanged.

C The water levels in glasses 1 and 3 have risen, that in glass 2 is unchanged.

D The water levels in all glasses are unchanged.

Topic: Fluid Mechanics, Thermodynamics Metodi: Hydrostatic Equilibrium, Physical Modeling Competenze: Physical Reasoning Objects: Bubble, Container Fonte: Testo (PDF) — p.6

Displacement of a ruler

The end of a ruler rests on a cylindrical can, which in turn rests on a table. The ruler is moved horizontally so that the can rolls across the table. Neither the ruler nor the can slips.

By what distance has the ruler moved relative to the table when the can has made one full revolution?

A Half the circumference of the can

B The circumference of the can

C Twice the circumference of the can

D More than twice the circumference of the can

Topic: Newtonian Mechanics, Rotational Dynamics Metodi: Kinematic Equations, Physical Modeling Competenze: Physical Reasoning, Diagrammatic Reasoning Objects: Cylinder, Rod Fonte: Testo (PDF) — p.7

Displacement of a ruler

L’estremità di un ruoter si trova su un cilindrico, che a sua volta si trova su un tavolo. Il ruoter è spostato orizzontalmente in modo che il can ruota attraverso il tavolo. Né il ruoter né il can slips.

Per quale distanza si è spostato il rucker rispetto al tavolo quando il lattino ha fatto una rivoluzione completa?

A Half the circumference of the can

B La circonferenza del can

C Due volte la circonferenza del contenitore

D Più di due volte la circonferenza del contenitore

The following table shows the results of the tests:

The end of a ruler rests on a cylindrical can, which in turn rests on a table. The ruler is moved horizontally so that the can rolls across the table. Neither the ruler nor the can slips.

By what distance has the ruler moved relative to the table when the can has made one full revolution?

A half the circumference of the can

B The circumference of the can

C Twice the circumference of the can

D More than twice the circumference of the can

Motion!

The graph alongside shows the acceleration $a$ of a body in a one-dimensional motion as a function of time $t$ .

Which of the following graphs correctly represents the velocity $v$ of the body as a function of time? (Answer options A–D are each a $v$ - $t$ diagram.)

Topic: Newtonian Mechanics Metodi: Kinematic Equations, Calculus-Integration Competenze: Graph Linearization, Physical Reasoning Objects: — Fonte: Testo (PDF) — p.7

Motion!

The graph alongside shows the acceleration $a$ of a body in a one-dimensional motion as a function of time $t$ .

Quale dei seguenti grafici rappresenta correttamente la velocità $v$ del corpo come funzione di tempo? (AD sono ciascuna un diagramma $v$ - $t$ .)

Topic: Newtonian Mechanics Metodi: Kinematic Equations, Calculus-Integration Competenze: Graph Linearization, Physical Reasoning Objects: — Fonte: Testo (PDF) — p.7

Motion!

The graph alongside shows the acceleration $a$ of a body in a one-dimensional motion as a function of time $t$ .

Which of the following graphs correctly represents the velocity $v$ of the body as a function of time? (ADs are each a $v$ - $t$ diagram.)

Topic: Newtonian Mechanics Metodi: Kinematic Equations, Calculus-Integration Competenze: Graph Linearization, Physical Reasoning Objects: — Fonte: Testo (PDF) — p.7

Sliding boxes

Two boxes slide frictionlessly down inclined planes from the same height. The two inclined planes have different slopes, but both boxes descend the same total height difference. One box is twice as heavy as the other.

Which of the following statements is true?

A Both boxes initially have the same potential energy.

B The boxes take the same time to slide down the inclined planes.

C At the bottom of the inclined planes both boxes have the same kinetic energy.

D At the bottom of the inclined planes both boxes have the same speed.

Topic: Newtonian Mechanics, Conservation of Energy Metodi: Energy Conservation Method, Kinematic Equations Competenze: Physical Reasoning Objects: Block, Inclined Plane Fonte: Testo (PDF) — p.8

Sliding boxes

Due scatole slide frictionlessly giù piani inclinati dalla stessa altezza. I due piani inclinati hanno pendenze diverse, ma entrambe le scatole discendono la stessa differenza totale di altezza. Una scatola è doppia più pesante dell’altra.

Quale delle seguenti affermazioni è vera?

Entrambe le scatole inizialmente hanno la stessa energia potenziale.

B Le scatole prendono lo stesso tempo per slide down gli aerei inclinati.

C Al fondo dei piani inclinati entrambe le scatole hanno la stessa energia cinetica.

D Al fondo dei piani inclinati entrambe le scatole hanno la stessa velocità.

The following table shows the following:

Which of the following statements is true?

A and B boxes initially have the same potential energy.

B The boxes take the same time to slide down the inclined planes.

C At the bottom of the inclined planes both boxes have the same kinetic energy.

D At the bottom of the inclined planes both boxes have the same speed.

Water jet

The bottom of a container filled with water is located at a height of $H_{unten} = 15 cm$ above the floor. The water level in the container is $H = 50 cm$ .

A small hole is now drilled into the container at a height $h$ above its bottom, so that a water jet pours out of the container and initially strikes the floor at a distance $x$ .

Which of the graphs correctly represents the distance $x$ of the impact point as a function of the height $h$ at which the hole is drilled? (Answer options A–D are each an $x$ - $h$ diagram for $0 \leq h \leq H$ .)

Topic: Fluid Mechanics, Newtonian Mechanics Metodi: Bernoulli’s Equation, Kinematic Equations Competenze: Physical Reasoning, Diagrammatic Reasoning Objects: Container Fonte: Testo (PDF) — p.9

Jet di acqua

Il fondo di un contenitore pieno di acqua è situato ad un’altezza di $H_{unten} = 15 cm$ sopra il pavimento. Il livello di acqua nel contenitore è $H = 50 cm$ .

Un piccolo buco è ora perforato nel contenitore ad un’altezza $h$ sopra il suo fondo, in modo che un jet d’acqua versare fuori dal contenitore e inizialmente colpisce il pavimento a una distanza $x$ .

Qual è il grafico che rappresenta correttamente la distanza $x$ del punto di impatto come funzione dell’altezza $h$ alla quale il buco è stato perforato? (AD sono ciascuna di $x$ - $h$ diagramma per $0 \leq h \leq H$ .)

The following is the list of the airlines operating in the Union:

The bottom of a container filled with water is located at a height of $H_{unten} = 15 cm$ above the floor. The water level in the container is $H = 50 cm$ .

A small hole is now drilled into the container at a height $h$ above its bottom, so that a water jet pours out of the container and initially strikes the floor at a distance $x$ .

Which of the graphs correctly represents the distance $x$ of the impact point as a function of the height $h$ at which the hole is drilled? (ADs are each on the $x$ - $h$ diagram for $0 \leq h \leq H$ .)

Puck on a thread

A very small puck can move frictionlessly on an air-cushion table. It is attached by a thin thread to a fixed rod and is now given a push so that it rotates around the rod, with the always-taut thread winding around the rod.

How does the orbital speed of the puck behave during the motion?

A It stays constant.

B It increases.

C It decreases.

D This cannot be answered as stated.

Topic: Rotational Dynamics, Newtonian Mechanics Metodi: Torque & Angular Momentum Analysis, Conservation Laws Competenze: Physical Reasoning Objects: String, Rod Fonte: Testo (PDF) — p.10

Puck on a thread

Un piccolo puck può muoversi senza frattura su un tavolo a cuscino d’aria. È attaccato da un filo sottile a un bastone fisso e viene ora dato un push in modo che ruota intorno al bastone, con il filo sempre-taut che ruota intorno al bastone.

Come si comporta la velocità orbitale del puck durante il movimento?

A It sta costante.

B: aumenta.

C diminuisce.

D Questo non può essere risposto come indicato.

The following is the list of the Member States’ official languages of the Union:

A very small puck can move frictionlessly on an air cushion table. It’s attached by a thin thread to a fixed rod and is now given a push so that it rotates around the rod, with the always-taut thread winding around the rod.

How does the orbital speed of the puck behave during motion?

A It stays constant.

B It increases.

C It decreases.

D This cannot be answered as stated.

Fall on an exoplanet

On the surface of an extrasolar planet (exoplanet), the fall time of a body from a small height $h$ , neglecting all friction effects, is exactly twice as long as on Earth.

Which of the following statements is consistent with this, assuming a spherically symmetric structure of the exoplanet?

The exoplanet has …

A … half the Earth’s mass and twice the Earth’s radius.

B … exactly the Earth’s mass and four times the Earth’s radius.

C … twice the Earth’s mass and twice the Earth’s radius.

D … four times the Earth’s mass and four times the Earth’s radius.

Topic: Gravitation, Newtonian Mechanics Metodi: Newton’s Law of Gravitation, Kinematic Equations, Dimensional Analysis Competenze: Physical Reasoning Objects: Planet Fonte: Testo (PDF) — p.10

Fall on an exoplanet

On the surface of an extrasolar planet (exoplanet), the fall time of a body from a small height $h$ , neglecting all friction effects, is exactly twice as long as on Earth.

Quali delle seguenti affermazioni sono coerenti con questo, assumendo una struttura sfericamente simmetrica dell’esoplaneta?

Il pianeta esoplanet ha …

A … half the Earth’s mass and twice the Earth’s radius.

B … esattamente la massa della Terra e quattro volte il raggio della Terra.

C … due volte la massa della Terra e due volte il raggio della Terra.

D … quattro volte la massa della Terra e quattro volte il raggio della Terra.

Fall on an exoplanet

On the surface of an extrasolar planet (exoplanet), the fall time of a body from a small height $h$ , neglecting all friction effects, is exactly twice as long as on Earth.

Which of the following statements is consistent with this, assuming a spherically symmetrical structure of the exoplanet?

The exoplanet has …

A … half the mass of the Earth and twice the radius of the Earth.

B … exactly the Earth’s mass and four times the Earth’s radius.

C … twice the mass of the Earth and twice the radius of the Earth.

D … four times the mass of the Earth and four times the radius of the Earth.

Rotating cube

Let $I$ denote the moment of inertia of a cube rotating about an axis through the centres of two opposite faces. Let the edge length of the cube be $a$ .

What is the corresponding moment of inertia of a cube made of the same material but with twice the edge length?

A $2 I$

B $4 I$

C $16 I$

D $32 I$

Topic: Rotational Dynamics Metodi: Torque & Angular Momentum Analysis, Dimensional Analysis Competenze: Physical Reasoning, Estimation & Approximation Objects: — Fonte: Testo (PDF) — p.10

Rotating cube

Let $I$ indica il momento di inerzia di un cubo che ruota intorno ad un asse attraverso i centri di due facce opposte. Lasciate che il lato lato del cubo sia $a$ .

Qual è il momento corrispondente di inerzia di un cubo fatto dello stesso materiale ma con due volte la lunghezza del bordo?

A $2 I$

B $4 I$

C $16 I$

D $32 I$

The following table shows the results of the calculations:

Let $I$ denote the moment of inertia of a cube rotating about an axis through the centers of two opposite faces. Let the edge length of the cube be $a$ .

What is the corresponding moment of inertia of a cube made of the same material but with twice the edge length?

A $2 I$

B $4 I$

C $16 I$

D $32 I$

Earth and Mars

The following figures are meant to show, from right to left, five snapshots of the orbital positions of Earth and Mars, each taken at equal time intervals. The ratios of the orbital radii are to scale, but the planets are greatly enlarged.

State which of the figures (A–D) is correct, and justify your answer.

Topic: Gravitation, Astrophysics Metodi: Kepler’s Laws, Physical Modeling Competenze: Physical Reasoning, Diagrammatic Reasoning Objects: Planet Fonte: Testo (PDF) — p.11

Earth and Mars

Le seguenti figure sono intese a mostrare, da destra a sinistra, cinque snapshot delle posizioni orbitali di Terra e Marte, ciascuna presa a intervalli di tempo uguali. I rapporti dei raggi orbitali sono scalabili, ma i pianeti sono molto più grandi.

State which of the figures (AD) is correct, and justify your answer.

Topic: Gravitation, Astrophysics Metodi: Kepler’s Laws, Physical Modeling Competenze: Physical Reasoning, Diagrammatic Reasoning Objects: Planet Fonte: Testo (PDF) — p.11

The Commission shall adopt delegated acts in accordance with Article 21 of this Regulation.

State which of the figures (AD) is correct, and justify your answer.

Topic: Gravitation, Astrophysics Metodi: Kepler’s Laws, Physical Modeling Competenze: Physical Reasoning, Diagrammatic Reasoning Objects: Planet Fonte: Testo (PDF) — p.11

Black hole in the Milky Way

The 2020 Nobel Prize in Physics was awarded for the discovery of a very massive, compact object at the centre of our galaxy (the Milky Way). The figure shows the position of a star observed on various dates relative to the presumed position of the centre of the Milky Way. The position is given in astronomical units ( $1 au = 1, 50 \times 1 0^{11} m$ ). For simplicity, assume that the star’s orbit lies in the plane of the drawing and that the orbit is not affected by relativistic effects.

What mass, as a multiple of the solar mass ( $M_{⊙} = 1, 99 \times 1 0^{30} kg$ ), can be estimated from the data for the black hole presumed to be at the centre of the Milky Way?

The mass of the black hole corresponds most closely to …

A … $1 \times 1 0^{5}$ solar masses.

B … $2 \times 1 0^{6}$ solar masses.

C … $4 \times 1 0^{7}$ solar masses.

D … $8 \times 1 0^{8}$ solar masses.

Topic: Astrophysics, Gravitation Metodi: Kepler’s Laws, Order-of-Magnitude Estimation Competenze: Estimation & Approximation, Experimental Data Analysis Objects: Black Hole, Star Fonte: Testo (PDF) — p.12

Il buco nero nella Via Lattea

Il Premio Nobel di Fisica 2020 è stato assegnato per la scoperta di un oggetto molto massiccio e compatto al centro della nostra galassia (la Via Lattea). La figura mostra la posizione di una stella osservata in varie date relative alla presunta posizione del centro della Via Lattea. La posizione è data in unità astronomiche ( $1 au = 1, 50 \times 1 0^{11} m$ ). Per semplicità, supponiamo che l’orbita della stella sia nel piano del disegno e che l’orbita non sia influenzata da effetti relativistici.

Qual è la massa, come multiple della massa solare ( $M_{⊙} = 1, 99 \times 1 0^{30} kg$ ), che si può stimare dai dati per il buco nero presunto essere al centro della Via Lattea?

La massa del buco nero corrisponde più strettamente a …

A … $1 \times 1 0^{5}$ masse solari.

B … $2 \times 1 0^{6}$ masse solari.

C … $4 \times 1 0^{7}$ masse solari.

D … $8 \times 1 0^{8}$ masse solari.

Black hole in the Milky Way

The 2020 Nobel Prize in Physics was awarded for the discovery of a very massive, compact object at the center of our galaxy (the Milky Way). The figure shows the position of a star observed on various dates relative to the presumed position of the center of the Milky Way. The position is given in astronomical units ( $1 au = 1, 50 \times 1 0^{11} m$ ). For simplicity, assume that the star’s orbit lies in the plane of the drawing and that the orbit is not affected by relativistic effects.

What mass, as a multiple of the solar mass ( $M_{⊙} = 1, 99 \times 1 0^{30} kg$ ), can be estimated from the data for the black hole presumed to be at the center of the Milky Way?

The mass of the black hole corresponds most closely to …

A … $1 \times 1 0^{5}$ solar masses.

B … $2 \times 1 0^{6}$ solar masses.

C … $4 \times 1 0^{7}$ solar masses.

D … $8 \times 1 0^{8}$ solar masses.

Pendulum in an elevator

Two elevator cars of masses $m_{A}$ and $m_{B}$ with $m_{A} < m_{B}$ hang from the ends of a long rope that runs over a fixed pulley. A simple pendulum of length $ℓ$ hangs in the left car. With the cars at rest and for small deflections, the period of the pendulum is $T$ .

When the cars are released, they move frictionlessly under the influence of gravity.

How must the length $ℓ^{'}$ of the simple pendulum in the left car be chosen so that, after the car is released, it oscillates with period $T$ ?

$A ℓ^{'} = \frac{m _{A}}{m _{B}} ℓ B ℓ^{'} = \frac{2 m _{A}}{m _{A} + m _{B}} ℓ C ℓ^{'} = \frac{2 m _{B}}{m _{A} + m _{B}} ℓ D ℓ^{'} = \frac{m _{B}}{m _{A}} ℓ$

Topic: Oscillations & Waves, Newtonian Mechanics Metodi: Simple Harmonic Motion Analysis, Free-Body Diagram Competenze: Physical Reasoning, Mathematical Modeling Objects: Pendulum, String, Pulley Fonte: Testo (PDF) — p.13

pendolo in ascensore

Due ascensori di masse $m_{A}$ e $m_{B}$ con $m_{A} < m_{B}$ pendono dalle estremità di una lunga corda che corre sopra un’autolivello fissa. A simple pendulum of length $ℓ$ hangs in the left car. Con le auto a riposo e per piccole deflezioni, il periodo del pendolo è $T$ .

Quando le auto vengono rilasciate, si muovono senza attrito sotto l’influenza della gravità.

How must the length $ℓ^{'}$ of the simple pendulum in the left car be chosen so that, after the car is released, it oscillates with period $T$ ?

$A ℓ^{'} = \frac{m _{A}}{m _{B}} ℓ B ℓ^{'} = \frac{2 m _{A}}{m _{A} + m _{B}} ℓ C ℓ^{'} = \frac{2 m _{B}}{m _{A} + m _{B}} ℓ D ℓ^{'} = \frac{m _{B}}{m _{A}} ℓ$

Pendulum in an elevator

When the cars are released, they move frictionlessly under the influence of gravity.

How must the length $ℓ^{'}$ of the simple pendulum in the left car be chosen so that, after the car is released, it oscillates with period $T$ ?

$A ℓ^{'} = \frac{m _{A}}{m _{B}} ℓ B ℓ^{'} = \frac{2 m _{A}}{m _{A} + m _{B}} ℓ C ℓ^{'} = \frac{2 m _{B}}{m _{A} + m _{B}} ℓ D ℓ^{'} = \frac{m _{B}}{m _{A}} ℓ$

Oscillation with an obstacle

A small metal ball hangs from the ceiling on a thin thread of length $L$ . The simple pendulum swings parallel to the wall with an oscillation period of $T = 1, 0 s$ .

Now a nail is driven firmly into the wall at a distance of $\frac{3}{4} L$ from the ceiling. As it swings to the right, the pendulum’s thread catches on the nail and is obstructed by it. The ball is released from the position shown on the right in the figure.

Which of the following figures (A–D) shows the position of the ball $1, 5 s$ after release?

Topic: Oscillations & Waves Metodi: Simple Harmonic Motion Analysis, Small-Angle Approximation Competenze: Physical Reasoning, Diagrammatic Reasoning Objects: Pendulum, Ball Fonte: Testo (PDF) — p.13

Oscillazione con un ostacolo

Una piccola palla di metallo appesa dal soffitto su un filo sottile di lunghezza $L$ . Il semplice pendolo sguazza parallelo al muro con un periodo di oscillazione di $T = 1, 0 s$ .

Ora un unghie è spinto saldamente nel muro a una distanza di $\frac{3}{4} L$ dal soffitto. Mentre si svinge a destra, il filo del pendolo si accinge al clavo ed è ostruito da esso. La palla viene rilasciata dalla posizione mostrata sulla destra nella figura.

Quale delle seguenti cifre (AD) mostra la posizione della palla $1, 5 s$ dopo il rilascio?

Oscillation with an obstacle

A small metal ball hangs from the ceiling on a thin thread of length $L$ . The simple pendulum swings parallel to the wall with an oscillation period of $T = 1, 0 s$ .

Which of the following figures (A–D) shows the position of the ball $1, 5 s$ after release?

Double spring pendulum

In each of the two spring pendulums shown, a body of mass $m$ oscillates frictionlessly. The spring constants $D_{1}$ and $D_{2}$ of the two Hookean springs are different, so that the bodies oscillate at different frequencies:

$f_{1} = 1, 2 Hz, f_{2} = 1, 6 Hz$

What is the oscillation frequency (natural frequency) of the system shown below, in which the springs $D_{1}$ and $D_{2}$ are coupled in series with the mass $m$ ?

A $1, 4 Hz$

B $2, 0 Hz$

C $2, 4 Hz$

D $2, 8 Hz$

Topic: Oscillations & Waves Metodi: Simple Harmonic Motion Analysis, Hooke’s Law Competenze: Physical Reasoning, Mathematical Modeling Objects: Spring, Block Fonte: Testo (PDF) — p.14

Double spring pendulum

In each of the two spring pendulums shown, a body of mass $m$ oscillates frictionlessly. Le costanti di primavera $D_{1}$ e $D_{2}$ delle due sorgenti di Hookean sono diverse, in modo che i corpi oscillare a diverse frequenze:

$f_{1} = 1, 2 Hz, f_{2} = 1, 6 Hz$

Qual è la frequenza di oscillazione (natural frequency) del sistema mostrato qui sotto, in cui le springs $D_{1}$ e $D_{2}$ sono accoppiate in serie con la massa $m$ ?

A $1, 4 Hz$

B $2, 0 Hz$

C $2, 4 Hz$

D $2, 8 Hz$

Double spring pendulum

$f_{1} = 1, 2 Hz, f_{2} = 1, 6 Hz$

What is the oscillation frequency (natural frequency) of the system shown below, in which the springs $D_{1}$ and $D_{2}$ are coupled in series with the mass $m$ ?

A $1, 4 Hz$

B $2, 0 Hz$

C $2, 4 Hz$

D $2, 8 Hz$

Coulomb force

Two equally sized charged metal spheres are at a very large distance from each other. The charge of one sphere is three times as large as that of the other. The force the spheres exert on each other is $F$ . The spheres are now brought into contact and then placed at a distance twice as large as the initial one.

What is now approximately the force between them?

A $0, 25 F$

B $0, 33 F$

C $0, 50 F$

D The force stays the same.

Topic: Electrostatics Metodi: Coulomb’s Law Competenze: Physical Reasoning, Mathematical Modeling Objects: Conducting Sphere Fonte: Testo (PDF) — p.15

Coulomb force

Due sfere di metallo cariche di dimensioni uguali sono a una grande distanza l’una dall’altra. La carica di una sfera è tre volte più grande di quella dell’altra. La forza che le sfere esercitano l’una sull’altra è $F$ . Le sfere sono ora messe in contatto e poi posizionate a una distanza due volte più grande dell’inizio.

Cosa c’è ora circa la forza tra loro?

A $0, 25 F$

B $0, 33 F$

C $0, 50 F$

D La forza rimane la stessa.

Topic: Electrostatics Metodi: Coulomb’s Law Competenze: Physical Reasoning, Mathematical Modeling Objects: Conducting Sphere Fonte: Testo (PDF) — p.15

The following is the list of the Member States’ official data protection authorities:

What is now approximately the force between them?

A $0, 25 F$

B $0, 33 F$

C $0, 50 F$

D The force stays the same.

Topic: Electrostatics Metodi: Coulomb’s Law Competenze: Physical Reasoning, Mathematical Modeling Objects: Conducting Sphere Fonte: Testo (PDF) — p.15

Coaxial cable

A coaxial cable consists of a long thin cylinder with resistivity $ρ_{1}$ , surrounded by a hollow cylinder with resistivity $ρ_{2} > ρ_{1}$ . A current of magnitude $I$ flows through the cable.

A second coaxial cable looks the same as the first from the outside, but on the inside consists of only a single material with resistivity $ρ$ , and likewise carries a current $I$ .

At how many of the marked points A, B and C (at different radii in the cross section) do the magnetic fields produced by the respective cables differ?

A 0

B 1

C 2

D 3

Topic: Magnetism, Electromagnetism Metodi: Ampère’s Law, Symmetry Argument Competenze: Physical Reasoning, Mathematical Modeling Objects: Wire, Cylinder Fonte: Testo (PDF) — p.15

Coaxial cable

Un cavo coaxial consiste di un lungo cilindro sottile con resistività $ρ_{1}$ , circondato da un cilindro vuoto con resistività $ρ_{2} > ρ_{1}$ . Un flusso di grandezza $I$ scorre attraverso il cavo.

Un secondo cavo coaxial sembra lo stesso del primo dall’esterno, ma all’interno è costituito da un solo materiale con resistività $ρ$ , e porta allo stesso modo un corrente $I$ .

A quanti dei punti segnati A, B e C (a diversi radii nella sezione trasversale) i campi magnetici prodotti dai rispettivi cavi differiscono?

A 0

B 1

C 2

D 3

Coaxial cable

A coaxial cable consists of a long thin cylinder with resistivity $ρ_{1}$ , surrounded by a hollow cylinder with resistivity $ρ_{2} > ρ_{1}$ . A current of magnitude $I$ flows through the cable.

A second coaxial cable looks the same as the first from the outside, but on the inside consists of only a single material with resistivity $ρ$ , and similarly carries a current $I$ .

At how many of the marked points A, B and C (at different radii in the cross section) do the magnetic fields produced by the respective cables differ?

A 0

B 1

C 2

D 3

Fields

A very light charged particle is accelerated through a voltage $U$ . It then flies into a region permeated by a constant magnetic field perpendicular to its direction of motion. The particle follows a circular arc of radius $r = 1, 50 cm$ .

Now an electric field of constant field strength $E = 4, 40 \times 1 0^{4} V m^{- 1}$ is switched on, oriented perpendicular to both the magnetic field and the particle’s instantaneous direction of motion. As a result, the particle continues to move in a straight line.

What is the voltage $U$ with which the particle was initially accelerated?

A $110 V$

B $220 V$

C $330 V$

D $440 V$

Topic: Electromagnetism, Electrostatics Metodi: Lorentz Force Analysis, Electric Potential Method Competenze: Physical Reasoning, Mathematical Modeling Objects: Point Charge Fonte: Testo (PDF) — p.16

Fields

Una particella molto leggera è accelerata attraverso una tensione $U$ . Poi vola in una regione permeata da un campo magnetico costante perpendicolare alla sua direzione di movimento. La particella segue un arco circolare di radius $r = 1, 50 cm$ .

Now an electric field of constant field strength $E = 4, 40 \times 1 0^{4} V m^{- 1}$ is switched on, oriented perpendicular to both the magnetic field and the particle’s instantaneous direction of motion. Di conseguenza, la particella continua a muoversi in linea retta.

What is the voltage $U$ with which the particle was initially accelerated?

A $110 V$

B $220 V$

C $330 V$

D $440 V$

Fields

What is the voltage $U$ with which the particle was initially accelerated?

A $110 V$

B $220 V$

C $330 V$

D $440 V$

Charged Dust

Six identical, initially at rest dust particles of mass $m = 2, 0 \times 1 0^{- 10} kg$ and charge $q = 2, 0 \times 1 0^{- 12} C$ are arranged in a vacuum at the vertices of a regular hexagon of edge length $a = 10 μ m$ . At the center of the hexagon sits a seventh dust particle, also initially at rest, with the same mass $m$ but opposite charge $- q$ . The particles are now released.

What is the speed of one of the positively charged dust particles relative to the negatively charged dust particle, after the particles have moved far apart from one another?

A about $5, 5 m s^{- 1}$

B about $6, 0 m s^{- 1}$

C about $9, 8 m s^{- 1}$

D about $13 m s^{- 1}$

Topic: Electrostatics, Conservation of Energy Metodi: Coulomb’s Law, Energy Conservation Method, Conservation of Momentum Competenze: Mathematical Modeling, Physical Reasoning Objects: Point Charge Fonte: Testo (PDF) — p.16

Dust caricato

Sei identiche particelle di polvere di massa $m = 2, 0 \times 1 0^{- 10} kg$ e carico $q = 2, 0 \times 1 0^{- 12} C$ sono disposte in un vuoto ai vertici di un hexagono regolare di lunghezza di bordo $a = 10 μ m$ . Al centro dell’esagono si trova una settima particella di polvere, inizialmente a riposo, con la stessa massa $m$ ma carica opposta $- q$ . Le particelle sono state rilasciate.

Qual è la velocità di una delle particelle di polvere cariche positivamente rispetto alla particella di polvere carica negativamente, dopo che le particelle si sono spostate lontano l’una dall’altra?

A about $5, 5 m s^{- 1}$

B about $6, 0 m s^{- 1}$

C about $9, 8 m s^{- 1}$

D about $13 m s^{- 1}$

The following is the list of the types of waste and scrap of waste and scrap of waste and scrap of waste and scrap of waste and scrap of waste and scrap of waste and scrap of waste and scrap of waste and scrap of waste and scrap of waste and scrap of waste and scrap of waste and scrap of waste and scrap of waste and scrap of waste and scrap of waste and scrap of waste and scrap of waste and scrap of waste and scrap of waste and scrap of waste and scrap of waste and scrap of waste and scrap of waste and scrap of waste and scrap of waste and scrap of waste and scrap of waste and scrap of waste and scrap of waste and scrap of waste and scrap of waste and scrap of waste and scrap of waste and scrap of waste and scrap of waste and scrap of waste and scrap of waste and scrap of waste and scrap of waste and scrap of waste and scrap of waste.

What is the speed of one of the positively charged dust particles relative to the negatively charged dust particles, after the particles have moved far apart from each other?

A about $5, 5 m s^{- 1}$

B about $6, 0 m s^{- 1}$

C about $9, 8 m s^{- 1}$

D about $13 m s^{- 1}$

Induction in Conducting Loops

The four conducting loops shown (a through d) each have edge lengths $ℓ$ or $2 ℓ$ . They move with constant velocity $v$ into a sharply bounded region containing a uniform magnetic field of flux density $B$ , oriented into the plane of the drawing.

How do the voltages $U_{a}$ through $U_{d}$ induced in the loops just as they enter the region with the magnetic field compare to one another?

A $∣ U_{a} ∣ = ∣ U_{b} ∣ = ∣ U_{c} ∣ = ∣ U_{d} ∣$

B $∣ U_{a} ∣ < ∣ U_{b} ∣ < ∣ U_{c} ∣ < ∣ U_{d} ∣$

C $∣ U_{a} ∣ = ∣ U_{b} ∣ < ∣ U_{c} ∣ = ∣ U_{d} ∣$

D $∣ U_{a} ∣ < ∣ U_{b} ∣ = ∣ U_{c} ∣ < ∣ U_{d} ∣$

Topic: Electromagnetic Induction Metodi: Faraday’s Law of Induction, Lenz’s Law Competenze: Physical Reasoning, Diagrammatic Reasoning Objects: Wire Fonte: Testo (PDF) — p.17

Induzione in circuiti di condotta

I quattro circuiti che conducono mostrati (a attraverso d) hanno lunghezze di bordo $ℓ$ o $2 ℓ$ . Si muovono con velocità costante $v$ in una regione nettamente limitata contenente un campo magnetico uniforme di densità di flusso $B$ , orientato verso il piano del disegno.

How do the voltages $U_{a}$ through $U_{d}$ induced in the loops just as they enter the region with the magnetic field compare to one another?

A $∣ U_{a} ∣ = ∣ U_{b} ∣ = ∣ U_{c} ∣ = ∣ U_{d} ∣$

B $∣ U_{a} ∣ < ∣ U_{b} ∣ < ∣ U_{c} ∣ < ∣ U_{d} ∣$

C $∣ U_{a} ∣ = ∣ U_{b} ∣ < ∣ U_{c} ∣ = ∣ U_{d} ∣$

D $∣ U_{a} ∣ < ∣ U_{b} ∣ = ∣ U_{c} ∣ < ∣ U_{d} ∣$

Induction in Conducting Loops

How do the voltages $U_{a}$ through $U_{d}$ induced in the loops just as they enter the region with the magnetic field compare to one another?

A $∣ U_{a} ∣ = ∣ U_{b} ∣ = ∣ U_{c} ∣ = ∣ U_{d} ∣$

B $∣ U_{a} ∣ < ∣ U_{b} ∣ < ∣ U_{c} ∣ < ∣ U_{d} ∣$

C $∣ U_{a} ∣ = ∣ U_{b} ∣ < ∣ U_{c} ∣ = ∣ U_{d} ∣$

D $∣ U_{a} ∣ < ∣ U_{b} ∣ = ∣ U_{c} ∣ < ∣ U_{d} ∣$

Falling Magnet

A cylindrical magnet is dropped through three different vertically standing tubes. The tubes have identical dimensions but are made of different materials: one of Plexiglas, one of brass, and one of aluminium.

For a fall distance of $L = 1, 0 m$ in the tubes, the following fall times are measured:

Material	Fall time
Plexiglas	$t_{Plexiglas} = 0, 46 s$
Brass	$t_{Messing} = 2, 15 s$
Aluminium	$t_{Aluminium} = 3, 81 s$

The electrical conductivity of the aluminium tube is $σ_{Aluminium} = 3, 7 \times 1 0^{7} A V^{- 1} m^{- 1}$ .

What value for the electrical conductivity $σ_{Messing}$ is obtained as an estimate from the fall times?

A $1, 2 \times 1 0^{7} A V^{- 1} m^{- 1}$

B $2, 1 \times 1 0^{7} A V^{- 1} m^{- 1}$

C $4, 9 \times 1 0^{7} A V^{- 1} m^{- 1}$

D $6, 6 \times 1 0^{7} A V^{- 1} m^{- 1}$

Topic: Electromagnetic Induction, Electromagnetism Metodi: Faraday’s Law of Induction, Experimental Data Analysis Competenze: Estimation & Approximation, Experimental Data Analysis Objects: Magnet, Tube Fonte: Testo (PDF) — p.17

Falling Magnet

Un magnete cilindrico viene scaricato attraverso tre diversi tubi verticalmente stabili. I tubi hanno dimensioni identiche ma sono fatti di materiali diversi: uno di plexiglas, uno di rame e uno di alluminio.

Per una distanza di caduta di $L = 1, 0 m$ nei tubi, i seguenti tempi di caduta sono misurati:

♬ Materiale ♬ Tempo di caso ♬ |---|---| | Plexiglas | $t_{Plexiglas} = 0, 46 s$ | | Brass | $t_{Messing} = 2, 15 s$ | | Aluminium | $t_{Aluminium} = 3, 81 s$ |

La conductività elettrica del tubo di alluminio è $σ_{Aluminium} = 3, 7 \times 1 0^{7} A V^{- 1} m^{- 1}$ .

What value for the electrical conductivity $σ_{Messing}$ is obtained as an estimate from the fall times?

A $1, 2 \times 1 0^{7} A V^{- 1} m^{- 1}$

B $2, 1 \times 1 0^{7} A V^{- 1} m^{- 1}$

C $4, 9 \times 1 0^{7} A V^{- 1} m^{- 1}$

D $6, 6 \times 1 0^{7} A V^{- 1} m^{- 1}$

Falling Magnet

A cylindrical magnet is dropped through three different vertically standing tubes. The tubes have identical dimensions but are made of different materials: one of plexiglass, one of brass, and one of aluminum.

For a fall distance of $L = 1, 0 m$ in the tubes, the following fall times are measured:

♪ The material is fall time ♪ |---|---| | Plexiglas | $t_{Plexiglas} = 0, 46 s$ | | Brass | $t_{Messing} = 2, 15 s$ | | Aluminium | $t_{Aluminium} = 3, 81 s$ |

The electrical conductivity of the aluminium tube is $σ_{Aluminium} = 3, 7 \times 1 0^{7} A V^{- 1} m^{- 1}$ .

What value for the electrical conductivity $σ_{Messing}$ is obtained as an estimate from the fall times?

A $1, 2 \times 1 0^{7} A V^{- 1} m^{- 1}$

B $2, 1 \times 1 0^{7} A V^{- 1} m^{- 1}$

C $4, 9 \times 1 0^{7} A V^{- 1} m^{- 1}$

D $6, 6 \times 1 0^{7} A V^{- 1} m^{- 1}$

Conducting Loop Falling in a Magnetic Field

A square conducting loop of edge length $a$ , resistance $R$ and mass $m$ falls from rest into a sharply bounded region of width $b > a$ containing a uniform magnetic field of flux density $B$ , oriented into the plane of the drawing. Graphs A, B, C and D are intended to represent the velocity of the conducting loop as a function of time for various magnetic field strengths.

Which of the graphs shows a physically possible process?

Topic: Electromagnetic Induction, Newtonian Mechanics Metodi: Faraday’s Law of Induction, Free-Body Diagram, Lenz’s Law Competenze: Physical Reasoning, Diagrammatic Reasoning Objects: Wire Fonte: Testo (PDF) — p.18

Conducting Loop Falling in a Magnetic Field

Un quadrato conduttore loop di lunghezza di bordo $a$ , resistenza $R$ e massa $m$ cade da rest in una regione di larghezza $b > a$ che contiene un campo magnetico uniforme di densità di flusso $B$ , orientato verso il piano del disegno. I grafici A, B, C e D sono destinati a rappresentare la velocità del loop conduttore come funzione di tempo per varie forze di campo magnetico.

Quale dei grafici mostra un processo fisicamente possibile?

Conducting loop falling in a magnetic field

Which of the graphs shows a physically possible process?

Pentagon of Resistors

A battery with a voltage of $9, 0 V$ is connected in series with an ideal ammeter. This series combination can be connected to any two corners of the resistor pentagon shown (with resistances $4, 0 Ω$ , $5, 0 Ω$ , $6, 0 Ω$ , $7, 0 Ω$ , $8, 0 Ω$ ).

What is the smallest current, in magnitude, that flows through the ammeter in this case?

A $0, 30 A$

B $0, 60 A$

C $1, 2 A$

D $2, 3 A$

Topic: Circuits Metodi: Kirchhoff’s Laws, Equivalent Circuit Reduction Competenze: Mathematical Modeling, Physical Reasoning Objects: Battery, Resistor, Galvanometer Fonte: Testo (PDF) — p.19

Pentagon of Resistors

Una batteria con una voltage di $9, 0 V$ è collegata in serie con un ammetro ideale. Questa combinazione di serie può essere collegata a due angoli del pentagono resistente mostrato (con resistenze $4, 0 Ω$ , $5, 0 Ω$ , $6, 0 Ω$ , $7, 0 Ω$ , $8, 0 Ω$ ).

Qual è la corrente più piccola, in magnitudo, che scorre attraverso l’ammetro in questo caso?

A $0, 30 A$

B $0, 60 A$

C $1, 2 A$

D $2, 3 A$

The following table shows the results of the tests:

A battery with a voltage of $9, 0 V$ is connected in series with an ideal amp. This series combination can be connected to any two corners of the resistor pentagon shown (with resistances $4, 0 Ω$ , $5, 0 Ω$ , $6, 0 Ω$ , $7, 0 Ω$ , $8, 0 Ω$ ).

What is the smallest current, in magnitude, that flows through the ammeter in this case?

A $0, 30 A$

B $0, 60 A$

C $1, 2 A$

D $2, 3 A$

Battery Operation

A single battery can keep a light bulb glowing for a time $t$ . For simplicity, assume that the bulb glows with constant brightness until the battery is exhausted, and that the resistance of the light bulb is constant.

Which statement is correct when two of these batteries are used to operate two of the light bulbs?

A If the batteries are connected in series and the bulbs are connected in series, the bulbs can be operated for about a time $t /4$ .

B If the batteries are connected in series and the bulbs are connected in parallel, the bulbs can be operated for about a time $t /2$ .

C If the batteries are connected in parallel and the bulbs are connected in series, the bulbs can be operated for about a time $2 t$ .

D If the batteries are connected in parallel and the bulbs are likewise connected in parallel, the bulbs can be operated for about a time $t$ .

Topic: Circuits Metodi: Kirchhoff’s Laws, Equivalent Circuit Reduction Competenze: Physical Reasoning Objects: Battery Fonte: Testo (PDF) — p.19

Battery Operation

A single battery can keep a light bulb glowing for a time $t$ . Per semplicità, supponiamo che la lampadina brilla con costante luminosità fino a quando la batteria non è esaurita e che la resistenza della lampadina sia costante.

Quale dichiarazione è corretta quando due di queste batterie vengono utilizzate per operare due delle lampadine?

A If the batteries are connected in series and the bulbs are connected in series, the bulbs can be operated for about a time $t /4$ .

B If the batteries are connected in series and the bulbs are connected in parallel, the bulbs can be operated for about a time $t /2$ .

C If the batteries are connected in parallel and the bulbs are connected in series, the bulbs can be operated for about a time $2 t$ .

D Se le batterie sono collegate in parallelo e le lampadine sono collegate in parallelo, le lampadine possono essere utilizzate per circa un tempo $t$ .

Topic: Circuits Metodi: Kirchhoff’s Laws, Equivalent Circuit Reduction Competenze: Physical Reasoning Objects: Battery Fonte: Testo (PDF) — p.19

Battery Operation

Which statement is correct when two of these batteries are used to operate two of the light bulbs?

A If the batteries are connected in series and the bulbs are connected in series, the bulbs can be operated for about a time $t /4$ .

B If the batteries are connected in series and the bulbs are connected in parallel, the bulbs can be operated for about a time $t /2$ .

C If the batteries are connected in parallel and the bulbs are connected in series, the bulbs can be operated for about a time $2 t$ .

D If the batteries are connected in parallel and the bulbs are similarly connected in parallel, the bulbs can be operated for about a time $t$ .

Topic: Circuits Metodi: Kirchhoff’s Laws, Equivalent Circuit Reduction Competenze: Physical Reasoning Objects: Battery Fonte: Testo (PDF) — p.19

Diode and Resistors

A diode is an electronic component that, in simplified terms, acts as a complete insulator in one direction (the reverse direction). In the opposite direction (the forward direction) the diode lets almost no current pass up to a certain voltage; above this voltage, however, it behaves approximately like an ideal conductor.

The circuit shown contains a diode and two resistors with resistance values $R_{1}$ and $R_{2}$ . The graph shows measured values of the current $I$ as a function of the applied voltage $U$ .

Which resistance values best match the measured values shown?

A $R_{1} = 220 Ω$ and $R_{2} = 670 Ω$

B $R_{1} = 220 Ω$ and $R_{2} = 330 Ω$

C $R_{1} = 470 Ω$ and $R_{2} = 220 Ω$

D $R_{1} = 470 Ω$ and $R_{2} = 150 Ω$

Topic: Circuits Metodi: Kirchhoff’s Laws, Experimental Data Analysis Competenze: Experimental Data Analysis, Physical Reasoning Objects: Resistor Fonte: Testo (PDF) — p.20

Diode e resistori

Un diodo è un componente elettronico che, in termini semplificati, agisce come un completo isolante in una direzione (la direzione inversa). In direzione opposta (the forward direction) il diodo lascia quasi nessun corrente passare fino a una certa tensione; above this voltage, however, it behaves approximately like an ideal conductor.

Il circuito mostrato contiene un diodo e due resistori con valori di resistenza $R_{1}$ e $R_{2}$ . Il grafico mostra i valori misurati della corrente $I$ come funzione della tensione applicata $U$ .

Quali valori di resistenza corrispondono meglio ai valori misurati mostrati?

A $R_{1} = 220 Ω$ e $R_{2} = 670 Ω$

B $R_{1} = 220 Ω$ e $R_{2} = 330 Ω$

C $R_{1} = 470 Ω$ e $R_{2} = 220 Ω$

D $R_{1} = 470 Ω$ e $R_{2} = 150 Ω$

Topic: Circuits Metodi: Kirchhoff’s Laws, Experimental Data Analysis Competenze: Experimental Data Analysis, Physical Reasoning Objects: Resistor Fonte: Testo (PDF) — p.20

Diode and resistors

The circuit shown contains a diode and two resistors with resistance values $R_{1}$ and $R_{2}$ . The graph shows measured values of the current $I$ as a function of the applied voltage $U$ .

Which resistance values best match the measured values shown?

A $R_{1} = 220 Ω$ and $R_{2} = 670 Ω$

B $R_{1} = 220 Ω$ and $R_{2} = 330 Ω$

C $R_{1} = 470 Ω$ and $R_{2} = 220 Ω$

D $R_{1} = 470 Ω$ and $R_{2} = 150 Ω$

Topic: Circuits Metodi: Kirchhoff’s Laws, Experimental Data Analysis Competenze: Experimental Data Analysis, Physical Reasoning Objects: Resistor Fonte: Testo (PDF) — p.20

Resonant Circuits

A circuit consisting of an ideal coil and an ideal capacitor is called a resonant circuit. The two electrical resonant circuits shown above, with the same inductance $L$ but different capacitances $C_{i}$ , oscillate without resistance at the following frequencies:

$f_{1} = f (C_{1}, L), f_{2} = \frac{4}{3} f (C_{2}, L)$

What is the oscillation frequency $f_{12}$ (natural frequency) of the following coupled system, in which $C_{1}$ and $C_{2}$ are connected in series with $L$ ?

$A \frac{2}{3} f B \frac{3}{4} f C \frac{4}{5} f D \frac{5}{4} f$

Topic: Circuits, Oscillations & Waves Metodi: Simple Harmonic Motion Analysis, Equivalent Circuit Reduction Competenze: Mathematical Modeling, Physical Reasoning Objects: Inductor, Capacitor Fonte: Testo (PDF) — p.21

**Ressonanti **

Un circuito composto da una bobina ideale e da un condensatore ideale è chiamato circuito risonante. I due circuiti elettrici risonanti mostrati sopra, con la stessa induttanza $L$ ma diverse capacità $C_{i}$ , oscillate senza resistenza alle seguenti frequenze:

$f_{1} = f (C_{1}, L), f_{2} = \frac{4}{3} f (C_{2}, L)$

Qual è la frequenza di oscillazione $f_{12}$ (natural frequency) del seguente sistema accoppiato, in cui $C_{1}$ e $C_{2}$ sono collegati in serie con $L$ ?

$A \frac{2}{3} f B \frac{3}{4} f C \frac{4}{5} f D \frac{5}{4} f$

The following table shows the results of the calculations:

$f_{1} = f (C_{1}, L), f_{2} = \frac{4}{3} f (C_{2}, L)$

What is the oscillation frequency $f_{12}$ (natural frequency) of the following coupled system, in which $C_{1}$ and $C_{2}$ are connected in series with $L$ ?

$A \frac{2}{3} f B \frac{3}{4} f C \frac{4}{5} f D \frac{5}{4} f$

Alternating-Current Circuit

A resistor with resistance value $R$ , a capacitor of capacitance $C$ and a coil of inductance $L$ are connected to an alternating-voltage source with amplitude $U$ . The following graph shows the amplitude $I$ of the current in the circuit as a function of the frequency $f$ of the sinusoidal alternating voltage.

Which of the following circuit diagrams (A–D) correctly represents the circuit used?

Topic: Circuits, Oscillations & Waves Metodi: Kirchhoff’s Laws, Simple Harmonic Motion Analysis Competenze: Physical Reasoning, Diagrammatic Reasoning Objects: Resistor, Capacitor, Inductor Fonte: Testo (PDF) — p.22

Alternating current circuit

Un resistore con valore di resistenza $R$ , un condensatore di capacità $C$ e una bobina di induttanza $L$ sono collegati a una fonte di voltaggio alternato con amplitudine $U$ . Il grafico seguente mostra l’amplitudine $I$ del corrente nel circuito come funzione della frequenza $f$ del sinusoidal alternating voltage.

Quale dei seguenti diagrammi di circuito (AD) rappresenta correttamente il circuito utilizzato?

The following information shall be provided:

Which of the following circuit diagrams (AD) correctly represents the circuit used?

Hot Disc

A metal disc with a hole in its center is heated.

What happens upon heating?

A The hole becomes larger.

B The hole becomes smaller.

C The hole stays the same size.

D This question cannot be answered without further information.

Topic: Thermodynamics, Elasticity & Materials Metodi: Physical Modeling Competenze: Physical Reasoning Objects: Disk Fonte: Testo (PDF) — p.23

Hot Disc

Un disco metallico con un buco al centro è riscaldato.

Cosa succede quando si riscaldano?

Un buco diventa più grande.

B Il buco diventa più piccolo.

C. Il buco rimane della stessa dimensione.

D Questa domanda non può essere risolta senza ulteriori informazioni.

Topic: Thermodynamics, Elasticity & Materials Metodi: Physical Modeling Competenze: Physical Reasoning Objects: Disk Fonte: Testo (PDF) — p.23

The following table shows the information available:

A metal disc with a hole in its center is heated.

What happens upon heating?

A hole gets bigger.

B The hole gets smaller.

C. The hole stays the same size.

D This question cannot be answered without further information.

Topic: Thermodynamics, Elasticity & Materials Metodi: Physical Modeling Competenze: Physical Reasoning Objects: Disk Fonte: Testo (PDF) — p.23

Temperature Units

The fictitious temperature unit Nups is defined by setting $0 K = 1000 Nups$ , $0^{\circ} C = 400 Nups$ and a linear variation with temperature.

Which temperature in $^{\circ} C$ most closely corresponds to $0 Nups$ ?

A $120^{\circ} C$

B $150^{\circ} C$

C $180^{\circ} C$

D $210^{\circ} C$

Topic: Thermodynamics Metodi: Dimensional Analysis, Physical Modeling Competenze: Unit Conversion, Mathematical Modeling Objects: — Fonte: Testo (PDF) — p.23

Unità di temperatura

Il fictitious temperature unit Nups is defined by setting $0 K = 1000 Nups$ , $0^{\circ} C = 400 Nups$ and a linear variation with temperature.

Which temperature in $^{\circ} C$ most closely corresponds to $0 Nups$ ?

A $120^{\circ} C$

B $150^{\circ} C$

C $180^{\circ} C$

D $210^{\circ} C$

Topic: Thermodynamics Metodi: Dimensional Analysis, Physical Modeling Competenze: Unit Conversion, Mathematical Modeling Objects: — Fonte: Testo (PDF) — p.23

The following table shows the results of the calculations:

The fictitious temperature unit Nups is defined by setting $0 K = 1000 Nups$ , $0^{\circ} C = 400 Nups$ and a linear variation with temperature.

Which temperature in $^{\circ} C$ most closely corresponds to $0 Nups$ ?

A $120^{\circ} C$

B $150^{\circ} C$

C $180^{\circ} C$

D $210^{\circ} C$

Topic: Thermodynamics Metodi: Dimensional Analysis, Physical Modeling Competenze: Unit Conversion, Mathematical Modeling Objects: — Fonte: Testo (PDF) — p.23

Heat Capacity

The same amount of thermal energy is supplied to four samples of different substances. The temperature of $3 g$ of substance A thereby increases by $8 K$ , the temperature of $4 g$ of substance B by $5 K$ , the temperature of $6 g$ of substance C by $9 K$ , and the temperature of $7 g$ of substance D by $4 K$ .

Which substance has the highest specific heat capacity?

A B C D

Topic: Thermodynamics Metodi: First Law of Thermodynamics Competenze: Physical Reasoning, Mathematical Modeling Objects: — Fonte: Testo (PDF) — p.23

Capacità di calore

La stessa quantità di energia termica viene fornita a quattro campioni di sostanze diverse. La temperatura di $3 g$ di sostanza A aumenta quindi di $8 K$ , la temperatura di $4 g$ di sostanza B di $5 K$ , la temperatura di $6 g$ di sostanza C di $9 K$ , e la temperatura di $7 g$ di sostanza D di $4 K$ .

Quale sostanza ha la più alta capacità di calore specifica?

A B C D

Topic: Thermodynamics Metodi: First Law of Thermodynamics Competenze: Physical Reasoning, Mathematical Modeling Objects: — Fonte: Testo (PDF) — p.23

The heat capacity of the heat source shall be measured at the temperature of the heat source.

Which substance has the highest specific heat capacity?

A B C D

Topic: Thermodynamics Metodi: First Law of Thermodynamics Competenze: Physical Reasoning, Mathematical Modeling Objects: — Fonte: Testo (PDF) — p.23

Kettle with Ice Cube

Water is heated in a kettle. During heating, an ice cube at temperature $ϑ_{0} = 0^{\circ} C$ is thrown into the water. The figure shows the temperature of the water as a function of time. The temperature of the water is initially equal to room temperature and can be assumed to be the same throughout the entire kettle at any given time.

The heating power of the kettle is $900 W$ . For the specific heat capacity of water, $c = 4, 2 kJ k g^{- 1} K^{- 1}$ , and for the specific heat of fusion (enthalpy of fusion) of ice, $h = 335 kJ k g^{- 1}$ .

What was the mass of the ice cube when it was thrown into the water?

A $16 g$

B $26 g$

C $56 g$

D $145 g$

Topic: Thermodynamics Metodi: First Law of Thermodynamics, Experimental Data Analysis Competenze: Experimental Data Analysis, Mathematical Modeling Objects: Container Fonte: Testo (PDF) — p.24

Kettle with Ice Cube

L’acqua è riscaldata in una bombola. Durante il riscaldamento, un ice cube a temperatura $ϑ_{0} = 0^{\circ} C$ viene gettato nell’acqua. La figura mostra la temperatura dell’acqua in funzione del tempo. La temperatura dell’acqua è inizialmente pari a temperatura ambiente e può essere presunta essere la stessa in tutto il cottello in qualsiasi momento.

Il potere di riscaldamento del pozzolo è $900 W$ . Per la specific heat capacity of water, $c = 4, 2 kJ k g^{- 1} K^{- 1}$ , and for the specific heat of fusion (enthalpy of fusion) of ice, $h = 335 kJ k g^{- 1}$ .

Qual era la massa del cubo di ghiaccio quando fu gettato in acqua?

A $16 g$

B $26 g$

C $56 g$

D $145 g$

Kettle with Ice Cube

The heating power of the kettle is $900 W$ . For the specific heat capacity of water, $c = 4, 2 kJ k g^{- 1} K^{- 1}$ , and for the specific heat of fusion of ice, $h = 335 kJ k g^{- 1}$ .

What was the mass of the ice cube when it was thrown into the water?

A $16 g$

B $26 g$

C $56 g$

D $145 g$

Melting Ice

On a cold winter day, three identical, non-insulated wooden boxes stand outside the house, each filled with the same amount of ice at temperature $0, 0^{\circ} C$ . To melt the ice, an electric heating element is placed in each of the boxes. The heating elements are identical but are operated at different voltages.

In the first box the heating element is operated at a voltage of $80 V$ — all the ice melts in $20, 0 min$ . A voltage of $120 V$ is applied to the heating element of the second box — the ice melts in $4, 0 min$ . In the third box a voltage of $40 V$ is used.

Which of the following statements is then correct for the melting of the ice in the third box?

A About $80 min$ are needed to melt all the ice.

B About $100 min$ are needed to melt all the ice.

C About $130 min$ are needed to melt all the ice.

D With the voltage used, it is not possible to melt all the ice.

Topic: Thermodynamics, Circuits Metodi: First Law of Thermodynamics, Physical Modeling Competenze: Physical Reasoning, Mathematical Modeling Objects: Container, Resistor Fonte: Testo (PDF) — p.25

Melting Ice

In un giorno di inverno freddo, tre scatole di legno identiche e non isolate erano fuori casa, ciascuna piena della stessa quantità di ghiaccio a temperatura $0, 0^{\circ} C$ . Per fondere il ghiaccio, un elemento di riscaldamento elettrico viene posto in ciascuna delle scatole. I calori sono identici ma operano a tensioni diverse.

In the first box the heating element is operated at a voltage of $80 V$ all the ice melts in $20, 0 min$ . Un voltage di $120 V$ è applicato all’elemento di riscaldamento della seconda scatola il ghiaccio si melta in $4, 0 min$ . In the third box a voltage of $40 V$ is used.

Quale delle seguenti affermazioni è corretta per il melting of the ice in the third box?

A About $80 min$ sono necessari per melting all the ice.

B About $100 min$ sono necessari per melt all the ice.

C About $130 min$ sono necessari per melting all the ice.

D Con la tensione utilizzata, non è possibile fondere tutto il ghiaccio.

The following table shows the results of the calculation of the Melting Ice

On a cold winter day, three identical, non-insulated wooden boxes stood outside the house, each filled with the same amount of ice at temperature $0, 0^{\circ} C$ . To melt the ice, an electric heating element is placed in each of the boxes. The heating elements are identical but are operated at different voltages.

In the first box the heating element is operated at a voltage of $80 V$ all the ice melts in $20, 0 min$ . A voltage of $120 V$ is applied to the heating element of the second box the ice melts in $4, 0 min$ . In the third box a voltage of $40 V$ is used.

Which of the following statements is correct for the melting of the ice in the third box?

A About $80 min$ are needed to melt all the ice.

B About $100 min$ are needed to melt all the ice.

C About $130 min$ are needed to melt all the ice.

D With the voltage used, it’s not possible to melt all the ice.

Heat Conduction

The ends of three round metal rods made of identical material are each held at constant temperatures:

Rod I: diameter $2, 0 cm$ , length $20 cm$ , rod ends: $50^{\circ} C$ and $20^{\circ} C$
Rod II: diameter $3, 0 cm$ , length $50 cm$ , rod ends: $60^{\circ} C$ and $30^{\circ} C$
Rod III: diameter $4, 0 cm$ , length $80 cm$ , rod ends: $70^{\circ} C$ and $40^{\circ} C$

How do the heat powers $P_{I}$ , $P_{II}$ and $P_{III}$ transferred through the rods by heat conduction compare to one another?

A $P_{I} < P_{II} = P_{III}$

B $P_{I} = P_{II} < P_{III}$

C $P_{II} < P_{I} = P_{III}$

D $P_{III} < P_{II} < P_{I}$

Topic: Thermodynamics Metodi: Physical Modeling, Dimensional Analysis Competenze: Mathematical Modeling, Physical Reasoning Objects: Rod Fonte: Testo (PDF) — p.26

Heat conduction

Le estremità di tre barre di metallo rotondo fatte di materiale identico sono ciascuna tenuta a temperature costanti:

Rod I: diametro $2, 0 cm$ , lunghezza $20 cm$ , estremità di rod: $50^{\circ} C$ e $20^{\circ} C$
Rod II: diametro $3, 0 cm$ , lunghezza $50 cm$ , estremità del rod: $60^{\circ} C$ e $30^{\circ} C$
Rod III: diametro $4, 0 cm$ , lunghezza $80 cm$ , estremità del rod: $70^{\circ} C$ e $40^{\circ} C$

How do the heat powers $P_{I}$ , $P_{II}$ and $P_{III}$ transferred through the rods by heat conduction compare to one another?

A $P_{I} < P_{II} = P_{III}$

B $P_{I} = P_{II} < P_{III}$

C $P_{II} < P_{I} = P_{III}$

D $P_{III} < P_{II} < P_{I}$

Topic: Thermodynamics Metodi: Physical Modeling, Dimensional Analysis Competenze: Mathematical Modeling, Physical Reasoning Objects: Rod Fonte: Testo (PDF) — p.26

Heat Conduction

The ends of three round metal rods made of identical material are each held at constant temperatures:

Rod I: diameter $2, 0 cm$ , length $20 cm$ , end of rod: $50^{\circ} C$ and $20^{\circ} C$
Rod II: diameter $3, 0 cm$ , length $50 cm$ , end of rod: $60^{\circ} C$ and $30^{\circ} C$
Rod III: diameter $4, 0 cm$ , length $80 cm$ , rod ends: $70^{\circ} C$ and $40^{\circ} C$

How do the heat powers $P_{I}$ , $P_{II}$ and $P_{III}$ transferred through the rods by heat conduction compare to one another?

A $P_{I} < P_{II} = P_{III}$

B $P_{I} = P_{II} < P_{III}$

C $P_{II} < P_{I} = P_{III}$

D $P_{III} < P_{II} < P_{I}$

Topic: Thermodynamics Metodi: Physical Modeling, Dimensional Analysis Competenze: Mathematical Modeling, Physical Reasoning Objects: Rod Fonte: Testo (PDF) — p.26

Resistor Heating

Two resistors of the same design are connected in parallel to a voltage source of $2, 6 V$ . A total current of $310 mA$ flows. An image of the circuit is taken with an infrared camera. After calibration, the camera can also determine the surface temperatures of the two resistors: they are $33^{\circ} C$ and $67^{\circ} C$ . The ambient temperature is $21^{\circ} C$ .

What are the approximate values of the two resistors?

A $1, 7 Ω$ and $6, 7 Ω$

B $12 Ω$ and $30 Ω$

C $10 Ω$ and $45 Ω$

D $20 Ω$ and $80 Ω$

Topic: Circuits, Thermodynamics Metodi: Kirchhoff’s Laws, Experimental Data Analysis Competenze: Experimental Data Analysis, Physical Reasoning Objects: Resistor Fonte: Testo (PDF) — p.26

Resistor Heating

Due resistori dello stesso design sono collegati in parallelo a una fonte di tensione di $2, 6 V$ . A total current of $310 mA$ flows. Un’immagine del circuito è stata scattata con una fotocamera infrarossa. Dopo la calibrazione, la fotocamera può anche determinare le temperature di superficie dei due resistori: $33^{\circ} C$ e $67^{\circ} C$ . La temperatura ambiente è $21^{\circ} C$ .

Quali sono i valori approssimativi dei due resistori?

A $1, 7 Ω$ e $6, 7 Ω$

B $12 Ω$ e $30 Ω$

C $10 Ω$ e $45 Ω$

D $20 Ω$ e $80 Ω$

The following is the list of the types of heating systems used:

What are the approximate values of the two resistors?

A $1, 7 Ω$ and $6, 7 Ω$

B $12 Ω$ and $30 Ω$

C $10 Ω$ and $45 Ω$

D $20 Ω$ and $80 Ω$

Thermal Radiation

A piece of metal at a temperature of $550^{\circ} C$ emits thermal radiation with a power $P$ .

What is the radiated power when the temperature of the metal is raised to $1100^{\circ} C$ ?

A about $1, 7 P$

B about $2, 0 P$

C about $7, 7 P$

D about $16 P$

Topic: Thermodynamics Metodi: Physical Modeling, Dimensional Analysis Competenze: Physical Reasoning, Mathematical Modeling Objects: — Fonte: Testo (PDF) — p.27

Radiamento termico

Un pezzo di metallo a una temperatura di $550^{\circ} C$ emette radiazioni termiche con una potenza $P$ .

Qual è la potenza irradiata quando la temperatura del metallo è sollevata a $1100^{\circ} C$ ?

A about $1, 7 P$

B about $2, 0 P$

C about $7, 7 P$

D about $16 P$

Topic: Thermodynamics Metodi: Physical Modeling, Dimensional Analysis Competenze: Physical Reasoning, Mathematical Modeling Objects: — Fonte: Testo (PDF) — p.27

The following conditions are met:

A piece of metal at a temperature of $550^{\circ} C$ emits thermal radiation with a power $P$ .

What is the radiated power when the temperature of the metal is raised to $1100^{\circ} C$ ?

A about $1, 7 P$

B about $2, 0 P$

C about $7, 7 P$

D about $16 P$

Topic: Thermodynamics Metodi: Physical Modeling, Dimensional Analysis Competenze: Physical Reasoning, Mathematical Modeling Objects: — Fonte: Testo (PDF) — p.27

Stopping global warming

The mad scientist Knox has found a method to stop global warming. To do so, he wants to increase the radius $r$ of the Earth’s orbit, assumed to be circular, by $1, 0 %$ .

By approximately how much could the mean temperature $T$ at the Earth’s surface (currently about $15^{\circ} C$ ) thereby drop?

A about $0, 7 K$

B about $1, 4 K$

C about $2, 8 K$

D about $5, 6 K$

Topic: Thermodynamics, Astrophysics Metodi: Physical Modeling, Approximation & Series Expansion Competenze: Estimation & Approximation, Mathematical Modeling Objects: Planet Fonte: Testo (PDF) — p.27

Stopping global warming

Il scienziato pazzo Knox ha trovato un metodo per fermare il riscaldamento globale. To do so, he wants to increase the radius $r$ of the Earth’s orbit, assumed to be circular, by $1, 0 %$ .

By approximately how much could the mean temperature $T$ at the Earth’s surface (currently about $15^{\circ} C$ ) thereby drop?

A about $0, 7 K$

B about $1, 4 K$

C about $2, 8 K$

D about $5, 6 K$

Stopping global warming

The mad scientist Knox has found a method to stop global warming. To do so, he wants to increase the radius $r$ of the Earth’s orbit, assumed to be circular, by $1, 0 %$ .

By approximately how much could the mean temperature $T$ at the Earth’s surface (currently about $15^{\circ} C$ ) thereby drop?

A about $0, 7 K$

B about $1, 4 K$

C about $2, 8 K$

D about $5, 6 K$

Cyclic process

An ideal gas undergoes a cyclic process. Starting from state A, it is first heated at constant volume up to state B, then it expands without a change in temperature (isothermally) up to state C, and is finally compressed isobarically back to the initial state A.

Let $p$ , $V$ and $T$ denote the pressure, volume and temperature of the gas.

Which of the following graphs (I: $p$ - $V$ diagram; II: $p$ - $T$ diagram; III: $T$ - $V$ diagram) correctly represent the cyclic process?

A Only graphs I and II.

B Only graphs I and III.

C Only graphs II and III.

D All three graphs.

Topic: Thermodynamics Metodi: Thermodynamic Cycle Analysis, Ideal Gas Law Competenze: Physical Reasoning, Diagrammatic Reasoning Objects: Gas Fonte: Testo (PDF) — p.28

processo ciclico

Il gas ideale subisce un processo ciclico. Partendo dallo stato A, viene riscaldato a volume costante fino allo stato B, poi si espandono senza un cambiamento di temperatura (isotermicamente) fino allo stato C, e finalmente viene compresso isobaricamente indietro allo stato iniziale A.

Let $p$ , $V$ and $T$ denotano la pressione, volume e temperatura del gas.

Quali dei seguenti grafici (I: $p$ - $V$ diagramma; II: $p$ - $T$ diagramma; III: $T$ - $V$ diagramma) rappresentano correttamente il processo ciclico?

A Only grafici I e II.

B Only grafici I e III.

C Only grafici II e III.

D Tutti e tre i grafici.

Topic: Thermodynamics Metodi: Thermodynamic Cycle Analysis, Ideal Gas Law Competenze: Physical Reasoning, Diagrammatic Reasoning Objects: Gas Fonte: Testo (PDF) — p.28

The following table shows the results of the calculation of the risk of the risk of a risk:

The ideal gas undergoes a cyclic process. Starting from state A, it is first heated at constant volume up to state B, then it expands without a change in temperature (isothermally) up to state C, and is finally compressed isobarically back to the initial state A.

Let $p$ , $V$ and $T$ denote the pressure, volume and temperature of the gas.

Which of the following graphs (I: $p$ - $V$ diagram; II: $p$ - $T$ diagram; III: $T$ - $V$ diagram) correctly represent the cyclic process?

A only graphs I and II.

B Only graphs I and III.

C Only graphs II and III.

D all three graphs.

Topic: Thermodynamics Metodi: Thermodynamic Cycle Analysis, Ideal Gas Law Competenze: Physical Reasoning, Diagrammatic Reasoning Objects: Gas Fonte: Testo (PDF) — p.28

Humid bathroom air

After a long shower, the temperature in the bathroom is $28^{\circ} C$ and the relative humidity is $80 %$ .

The saturation vapour pressure curve for water vapour gives the maximum water vapour pressure $p_{sat}$ possible at a temperature $ϑ$ before the water vapour condenses.

How much water vapour (in $g m^{- 3}$ ) is present in the air in the bathroom? Use $M_{Wasser} = 18, 0 g mo l^{- 1}$ .

A about $22 g m^{- 3}$

B about $27 g m^{- 3}$

C about $2, 3 \times 1 0^{2} g m^{- 3}$

D about $3, 0 \times 1 0^{3} g m^{- 3}$

Topic: Thermodynamics, Kinetic Theory Metodi: Ideal Gas Law, Experimental Data Analysis Competenze: Experimental Data Analysis, Mathematical Modeling Objects: Gas Fonte: Testo (PDF) — p.29

Humid bathroom air

Dopo un lungo bagno, la temperatura in bagno è $28^{\circ} C$ e l’umidità relativa è $80 %$ .

La saturation vapour pressure curve for water vapour gives the maximum water vapour pressure $p_{sat}$ possible at a temperature $ϑ$ before the water vapour condenses.

Quanto vapore d’acqua (in $g m^{- 3}$ ) è presente nell’aria del bagno? Usare $M_{Wasser} = 18, 0 g mo l^{- 1}$ .

A about $22 g m^{- 3}$

B about $27 g m^{- 3}$

C about $2, 3 \times 1 0^{2} g m^{- 3}$

D about $3, 0 \times 1 0^{3} g m^{- 3}$

Humid bathroom air

After a long shower, the temperature in the bathroom is $28^{\circ} C$ and the relative humidity is $80 %$ .

The saturation vapour pressure curve for water vapour gives the maximum water vapour pressure $p_{sat}$ possible at a temperature $ϑ$ before the water vapour condenses.

How much water vapour (in $g m^{- 3}$ ) is present in the air in the bathroom? Use $M_{Wasser} = 18, 0 g mo l^{- 1}$ .

A about $22 g m^{- 3}$

B about $27 g m^{- 3}$

C about $2, 3 \times 1 0^{2} g m^{- 3}$

D about $3, 0 \times 1 0^{3} g m^{- 3}$

Refraction of light

A light ray strikes an arrangement of two equally large glass blocks set up perpendicular to each other and is refracted upon entering the first block. The refractive index of the glass is $1, 5$ ; outside the blocks there is air. The angle of incidence is $4 5^{\circ}$ .

Which of the following image excerpts (A–D) shows the path of the refracted light ray after it exits the second block?

Topic: Geometric Optics Metodi: Snell’s Law, Ray Tracing Competenze: Physical Reasoning, Diagrammatic Reasoning Objects: — Fonte: Testo (PDF) — p.30

Refrazione di luce

Un raggio di luce colpisce un’arrangamento di due blocchi di vetro uguali dimensioni, montati perpendicolare l’uno all’altro, e si refracta all’entrata nel primo blocco. L’indice di refraczione del vetro è $1, 5$ ; fuori dai blocchi c’è aria. L’angolo di incidenza è $4 5^{\circ}$ .

Quale delle seguenti immagini mostra il percorso del raggio di luce refratto dopo che esce dal secondo blocco?

Topic: Geometric Optics Metodi: Snell’s Law, Ray Tracing Competenze: Physical Reasoning, Diagrammatic Reasoning Objects: — Fonte: Testo (PDF) — p.30

Refraction of light

Which of the following image excerpts (AD) shows the path of the refracted light ray after it exits the second block?

Topic: Geometric Optics Metodi: Snell’s Law, Ray Tracing Competenze: Physical Reasoning, Diagrammatic Reasoning Objects: — Fonte: Testo (PDF) — p.30

Glass block

A laser beam running in the plane of the drawing strikes a glass block (refractive index $n = 1, 5$ ) with side lengths $a$ and $4 a$ from the left at an angle of incidence $α = 3 0^{\circ}$ . As indicated in the sketch, within the glass block it finally hits exactly the lower right corner.

What is the distance $x$ of the entry point from the upper boundary surface of the block?

$A a (2 - 1) B a (2 - 3) C a (1 - \frac{2}{2}) D a (1 - \frac{3}{3})$

Topic: Geometric Optics Metodi: Snell’s Law, Ray Tracing Competenze: Mathematical Modeling, Physical Reasoning Objects: — Fonte: Testo (PDF) — p.31

Glass block

Un laser beam running in the plane of the drawing strikes a glass block (refractive index $n = 1, 5$ ) with side lengths $a$ and $4 a$ from the left at an angle of incidence $α = 3 0^{\circ}$ . Come indicato nello schizzo, all’interno del blocco di vetro, finalmente colpisce esattamente l’angolo inferiore destro.

Qual è la distanza $x$ del punto di entrata dalla superficie di confine superiore del blocco?

$A a (2 - 1) B a (2 - 3) C a (1 - \frac{2}{2}) D a (1 - \frac{3}{3})$

Topic: Geometric Optics Metodi: Snell’s Law, Ray Tracing Competenze: Mathematical Modeling, Physical Reasoning Objects: — Fonte: Testo (PDF) — p.31

The following table shows the results of the calculations:

What is the distance $x$ of the entry point from the upper boundary surface of the block?

$A a (2 - 1) B a (2 - 3) C a (1 - \frac{2}{2}) D a (1 - \frac{3}{3})$

Topic: Geometric Optics Metodi: Snell’s Law, Ray Tracing Competenze: Mathematical Modeling, Physical Reasoning Objects: — Fonte: Testo (PDF) — p.31

Converging lens

A thin converging lens produces, from an object at a distance $d$ from the lens, an image whose distance from the lens is also $d$ .

At what distance from the lens is the image formed when the distance between object and lens is doubled?

A about $\frac{1}{2} d$

B about $\frac{2}{3} d$

C about $\frac{3}{2} d$

D about $2 d$

Topic: Geometric Optics Metodi: Thin Lens & Mirror Equation Competenze: Mathematical Modeling, Physical Reasoning Objects: Lens Fonte: Testo (PDF) — p.31

Lens di conversione

Un thin converging lens produce, da un oggetto a distanza $d$ dalla lente, un’immagine la cui distanza dalla lente è anche $d$ .

A che distanza dalla lente si forma l’immagine quando la distanza tra oggetto e lente è raddoppiata?

A about $\frac{1}{2} d$

B about $\frac{2}{3} d$

C about $\frac{3}{2} d$

D about $2 d$

Topic: Geometric Optics Metodi: Thin Lens & Mirror Equation Competenze: Mathematical Modeling, Physical Reasoning Objects: Lens Fonte: Testo (PDF) — p.31

The following table shows the results of the tests:

A thin converging lens produces, from an object at a distance $d$ from the lens, an image whose distance from the lens is also $d$ .

At what distance from the lens is the image formed when the distance between object and lens is doubled?

A about $\frac{1}{2} d$

B about $\frac{2}{3} d$

C about $\frac{3}{2} d$

D about $2 d$

Topic: Geometric Optics Metodi: Thin Lens & Mirror Equation Competenze: Mathematical Modeling, Physical Reasoning Objects: Lens Fonte: Testo (PDF) — p.31

Lens collection

From the depths of the physics collection your physics teacher has dug out a box with three thin lenses, labelled I, II and III. Lenses I and II are biconvex, lens III is concave on both sides.

An object is positioned at a distance of $50, 0 cm$ from one of the lenses or from a combination of two lenses placed closely one behind the other, and the image distance is measured:

Experiment	Lens(es)	Image distance
1	I	$21, 4 cm$
2	?	$50, 2 cm$
3	?	$11, 6 cm$
4	?	$30, 9 cm$
5	?	$175, 0 cm$

Which of the lenses was (were) used in each of the individual experiments 2–5?

A Experiment 2: I & III · Experiment 3: I & II · Experiment 4: II · Experiment 5: II & III

B Experiment 2: I & III · Experiment 3: II · Experiment 4: II & III · Experiment 5: I & II

C Experiment 2: II · Experiment 3: I & II · Experiment 4: I & III · Experiment 5: II & III

D Experiment 2: II & III · Experiment 3: II · Experiment 4: I & II · Experiment 5: I & III

Topic: Geometric Optics Metodi: Thin Lens & Mirror Equation, Experimental Data Analysis Competenze: Experimental Data Analysis, Mathematical Modeling Objects: Lens Fonte: Testo (PDF) — p.32

Lens collection

Dal depths of the physics collection il vostro insegnante di fisica ha trovato una scatola con tre lenti sottili, etichettate I, II e III. I e II sono biconvex, il III è concavo su entrambi i lati.

Un oggetto è posizionato a una distanza di $50, 0 cm$ da una delle lenti o da una combinazione di due lenti posizionate vicino all’altra, e la distanza dell’immagine è misurata:

♬ esperimento ♬ lente ♬ immagine distance ♬ |---|---|---| | 1 | I | $21, 4 cm$ | | 2 | ? | $50, 2 cm$ | | 3 | ? | $11, 6 cm$ | | 4 | ? | $30, 9 cm$ | | 5 | ? | $175, 0 cm$ |

Quale delle lenti è stato usato in ogni esperimento individuale?

A esperimento 2: I & III · esperimento 3: I & II · esperimento 4: II · esperimento 5: II & III

B esperimento 2: I & III · esperimento 3: II · esperimento 4: II & III · esperimento 5: I & II

C esperimento 2: II · esperimento 3: I & II · esperimento 4: I & III · esperimento 5: II & III

D Esperimento 2: II & III · Sperimento 3: II · Sperimento 4: I & II · Sperimento 5: I & III

The following table shows the results of the study:

From the depths of the physics collection your physics teacher has dug out a box with three thin lenses, labeled I, II and III. Lenses I and II are biconvex, lens III is concave on both sides.

An object is positioned at a distance of $50, 0 cm$ from one of the lenses or from a combination of two lenses placed closely one behind the other, and the image distance is measured:

♪ experiment ♪ Lens ♪ It’s the distance of the image ♪ |---|---|---| | 1 | I | $21, 4 cm$ | | 2 | ? | $50, 2 cm$ | | 3 | ? | $11, 6 cm$ | | 4 | ? | $30, 9 cm$ | | 5 | ? | $175, 0 cm$ |

Which of the lenses were used in each of the individual experiments?

A experiment 2: I & III · experiment 3: I & II · experiment 4: II · experiment 5: II & III

B Experiment 2: I & III · Experiment 3: II · Experiment 4: II & III · Experiment 5: I & II

C Experiment 2: II · Experiment 3: I & II · Experiment 4: I & III · Experiment 5: II & III

D Experiment 2: II & III · Experiment 3: II · Experiment 4: I & II · Experiment 5: I & III

Two images

A photo of a drinking bottle located at a distance of about $35 cm$ from the camera is taken with a mobile phone camera. In the photo, the background, about $5, 8 m$ away, appears blurred. If a lens is now positioned directly in front of the camera, the background appears sharp in the photo through the lens.

What is the focal length of the lens? (Positive focal lengths denote converging lenses, negative ones diverging lenses.)

A about $- 35 cm$

B about $- 18 cm$

C about $35 cm$

D about $58 cm$

Topic: Geometric Optics Metodi: Thin Lens & Mirror Equation, Ray Tracing Competenze: Physical Reasoning, Mathematical Modeling Objects: Lens Fonte: Testo (PDF) — p.33

Two images

Una foto di una bottiglia da bere situata a una distanza di circa $35 cm$ dalla fotocamera è stata scattata con una fotocamera del telefono cellulare. In foto, il background, about $5, 8 m$ away, appare sfocato. Se un obiettivo è ora posizionato direttamente davanti alla fotocamera, il fondo appare acuto nella foto attraverso il obiettivo.

Qual è la lunghezza focale della lente? (Lenti focali positive indicano lenti convergenti, quelle negative divergenti.)

A about $- 35 cm$

B about $- 18 cm$

C about $35 cm$

D about $58 cm$

Topic: Geometric Optics Metodi: Thin Lens & Mirror Equation, Ray Tracing Competenze: Physical Reasoning, Mathematical Modeling Objects: Lens Fonte: Testo (PDF) — p.33

The following table shows the results of the evaluation:

What is the focal length of the lens? (Positive focal lengths denote converging lenses, negative ones diverging lenses.)

A about $- 35 cm$

B about $- 18 cm$

C about $35 cm$

D about $58 cm$

Topic: Geometric Optics Metodi: Thin Lens & Mirror Equation, Ray Tracing Competenze: Physical Reasoning, Mathematical Modeling Objects: Lens Fonte: Testo (PDF) — p.33

Interference

In an experiment, monochromatic laser light falls perpendicularly onto an optical grating with $300 Linien m m^{- 1}$ . Behind the grating, the interference pattern is observed on a screen (screen distance very large compared to the extent of the pattern).

The wavelength of the first laser is $650 nm$ . A second laser with an unknown wavelength produces a different interference pattern with an otherwise identical setup.

What is the wavelength of the light emitted by the second laser?

A about $450 nm$

B about $530 nm$

C about $610 nm$

D about $690 nm$

Topic: Wave Optics Metodi: Interference & Diffraction Analysis, Experimental Data Analysis Competenze: Experimental Data Analysis, Physical Reasoning Objects: Diffraction Grating, Screen Fonte: Testo (PDF) — p.34

interferenza

In un esperimento, la luce laser monocromatica cade perpendicularmente su una griglia ottica con $300 Linien m m^{- 1}$ . Behind the grating, the interference pattern is observed on a screen (screen distance very large compared to the extent of the pattern).

La lunghezza d’onda del primo laser è $650 nm$ . Un secondo laser con una lunghezza d’onda sconosciuta produce un diverso pattern di interferenza con un setup altrimenti identico.

Qual è la lunghezza d’onda della luce emessa dal secondo laser?

A about $450 nm$

B about $530 nm$

C about $610 nm$

D about $690 nm$

The following information is provided by the Commission:

The wavelength of the first laser is $650 nm$ . A second laser with an unknown wavelength produces a different interference pattern with an otherwise identical setup.

What is the wavelength of the light emitted by the second laser?

A about $450 nm$

B about $530 nm$

C about $610 nm$

D about $690 nm$

Water-layer reflection

The surface of a smooth, horizontal glass plate is covered with a thin, flat layer of water. From above, monochromatic light of wavelength $680 nm$ falls on the water surface at an angle $α = 3 0^{\circ}$ to the surface normal. The refractive index of the glass plate is $1, 50$ and that of the water is $1, 33$ .

Owing to the evaporation of the water, the intensity of the reflected light changes periodically. A time of $15 min$ elapses between the occurrence of two intensity maxima.

At what rate does the thickness $d$ of the water layer decrease?

A about $0, 3 μ m h^{- 1}$

B about $1 μ m h^{- 1}$

C about $3 μ m h^{- 1}$

D about $9 μ m h^{- 1}$

Topic: Wave Optics Metodi: Interference & Diffraction Analysis, Snell’s Law Competenze: Physical Reasoning, Mathematical Modeling Objects: — Fonte: Testo (PDF) — p.34

Reflessione a livello di acqua

La superficie di una piastra di vetro liscia e orizzontale è coperta da un sottile e piatto strato d’acqua. Da sopra, la luce monocromatica di lunghezza d’onda $680 nm$ cade sulla superficie dell’acqua ad un angolo $α = 3 0^{\circ}$ alla superficie normale. L’indice di refraczione della piastra è $1, 50$ e quello dell’acqua è $1, 33$ .

A causa dell’evaporazione dell’acqua, l’intensità della luce riflessa cambia periodicamente. A time of $15 min$ elapses between the occurrence of two intensity maxima.

At what rate does the thickness $d$ of the water layer decrease?

A about $0, 3 μ m h^{- 1}$

B about $1 μ m h^{- 1}$

C about $3 μ m h^{- 1}$

D about $9 μ m h^{- 1}$

Topic: Wave Optics Metodi: Interference & Diffraction Analysis, Snell’s Law Competenze: Physical Reasoning, Mathematical Modeling Objects: — Fonte: Testo (PDF) — p.34

Water-layer reflection

The surface of a smooth horizontal glass plate is covered with a thin, flat layer of water. From above, monochromatic light of wavelength $680 nm$ falls on the water surface at an angle $α = 3 0^{\circ}$ to the surface normal. The refractive index of the glass plate is $1, 50$ and that of the water is $1, 33$ .

Due to the evaporation of the water, the intensity of the reflected light changes periodically. A time of $15 min$ elapses between the occurrence of two intensity maxima.

At what rate does the thickness $d$ of the water layer decrease?

A about $0, 3 μ m h^{- 1}$

B about $1 μ m h^{- 1}$

C about $3 μ m h^{- 1}$

D about $9 μ m h^{- 1}$

Topic: Wave Optics Metodi: Interference & Diffraction Analysis, Snell’s Law Competenze: Physical Reasoning, Mathematical Modeling Objects: — Fonte: Testo (PDF) — p.34

Two transmitters

Two identical electric transmitting dipoles, oriented perpendicular to the plane of the drawing, radiate into space in phase with frequency $f$ from the points $S_{1}$ and $S_{2}$ . A receiver E is moved, starting from $S_{2}$ , along a circle around $S_{1}$ . The distance $S_{1} S_{2} = 20 cm$ . The measured intensity as a function of the angle $α$ shows clear maxima and minima.

What is the frequency $f$ of the radiation?

A $1, 5 GHz$

B $3, 0 GHz$

C $4, 5 GHz$

D $6, 0 GHz$

Topic: Wave Optics, Oscillations & Waves Metodi: Interference & Diffraction Analysis, Experimental Data Analysis Competenze: Experimental Data Analysis, Mathematical Modeling Objects: — Fonte: Testo (PDF) — p.35

Two transmitters

Due identici dipoli elettrici trasmettenti, orientati perpendicolare al piano del disegno, irradiano nello spazio in fase con frequenza $f$ dai punti $S_{1}$ e $S_{2}$ . Un ricevitore E è spostato, partendo da $S_{2}$ , lungo un cerchio intorno a $S_{1}$ . La distanza $S_{1} S_{2} = 20 cm$ . L’intensità misurata come funzione dell’angolo $α$ mostra clear maxima e minima.

Qual è la frequenza $f$ della radiazione?

A $1, 5 GHz$

B $3, 0 GHz$

C $4, 5 GHz$

D $6, 0 GHz$

Two transmitters

What is the frequency $f$ of the radiation?

A $1, 5 GHz$

B $3, 0 GHz$

C $4, 5 GHz$

D $6, 0 GHz$

Lead-glass window

Rooms with X-ray devices are shielded by thick walls and windows made of lead glass. A lead-glass window with a thickness of $2, 0 cm$ can already shield $75 %$ of the intensity of X-radiation.

How thick must the lead-glass window be so that the intensity of the radiation behind the window is only $1 %$ of the intensity in front of the window?

A about $2, 7 cm$

B about $4, 0 cm$

C about $6, 6 cm$

D about $9, 2 cm$

Topic: Modern-Quantum Physics, Nuclear & Particle Physics Metodi: Radioactive Decay Law, Physical Modeling Competenze: Mathematical Modeling, Physical Reasoning Objects: — Fonte: Testo (PDF) — p.35

Lead glass window

Le camere con dispositivi a raggi X sono protette da pareti e finestre spesse di vetro di piombo. Un lead-glass window with a thickness of $2, 0 cm$ può già proteggere $75 %$ dell’intensità di radiazioni X.

Quanto deve essere spessa la finestra di vetro di piombo in modo che l’intensità della radiazione dietro la finestra sia solo $1 %$ dell’intensità di fronte alla finestra?

A about $2, 7 cm$

B about $4, 0 cm$

C about $6, 6 cm$

D about $9, 2 cm$

The following table shows the results of the calculations:

Rooms with X-ray devices are shielded by thick walls and windows made of lead glass. A lead-glass window with a thickness of $2, 0 cm$ can already shield $75 %$ of the intensity of X-rays.

How thick must the lead-glass window be so that the intensity of the radiation behind the window is only $1 %$ of the intensity in front of the window?

A about $2, 7 cm$

B about $4, 0 cm$

C about $6, 6 cm$

D about $9, 2 cm$

Spectra

The atoms of a fictitious element occupy states on the energy levels

$E_{n} = - \frac{C}{n ^{2}}, n = 1, 2, \dots$

where $C$ is a constant. Only the lines of the series of transitions to the ground state $n = 1$ lie in the optical range, but these do so completely.

Which of the spectra shown below (A–D), scaled linearly in wavelength, correctly represents the emission lines of the described element?

Topic: Modern-Quantum Physics Metodi: Bohr Model & Quantization, Photon Energy Relation Competenze: Physical Reasoning, Diagrammatic Reasoning Objects: Atom Fonte: Testo (PDF) — p.36

Spectra

The atoms of a fictitious element occupy states on the energy levels

$E_{n} = - \frac{C}{n ^{2}}, n = 1, 2, \dots$

dove $C$ è una costante. Only the lines of the series of transitions to the ground state $n = 1$ lie in the optical range, but these do so completely.

Quale dei specteri mostrati di seguito (AD), scalato linearmente in lunghezza d’onda, rappresenta correttamente le linee di emissione dell’elemento descritto?

Spectra

The atoms of a fictitious element occupy states on the energy levels

$E_{n} = - \frac{C}{n ^{2}}, n = 1, 2, \dots$

where $C$ is a constant. Only the lines of the series of transitions to the ground state $n = 1$ lie in the optical range, but these do so completely.

Which of the spectra shown below (AD), scaled linearly in wavelength, correctly represents the emission lines of the described element?

Radioactive decay

In the following, three radioactive samples are considered. Initially, at time $t = 0$ , they consist $100 %$ of a single radioactive isotope (parent nuclide) with initial activity $A_{0}$ . The direct decay products (daughter nuclides) are also radioactive. The parent and daughter nuclides of the three samples are:

Sample	Parent nuclide	$T_{Mutter}$	Daughter nuclide	$T_{Tochter}$
1	$^{226} Ra$	$1600 a$	$^{222} Rn$	$3, 8 d$
2	$^{211} Pb$	$36, 1 min$	$^{211} Bi$	$2, 14 min$
3	$^{214} Pb$	$26, 8 min$	$^{214} Bi$	$19, 9 min$

The graphs I, II, III represent the time evolution of the activities $A$ of the parent nuclide, the daughter nuclide and the total activity (time axis scaled in multiples of $T_{Tochter}$ ).

Which of the three nuclide pairs belongs to which diagram?

A $1 \to I$ , $2 \to II$ , $3 \to III$

B $1 \to II$ , $2 \to III$ , $3 \to I$

C $1 \to III$ , $2 \to II$ , $3 \to I$

D $1 \to III$ , $2 \to I$ , $3 \to II$

Topic: Nuclear & Particle Physics Metodi: Radioactive Decay Law, Experimental Data Analysis Competenze: Physical Reasoning, Diagrammatic Reasoning Objects: Nucleus Fonte: Testo (PDF) — p.37

Radioactive decay

In seguito, tre campioni radioattivi sono considerati. Inizialmente, a tempo $t = 0$ , consistono $100 %$ di un singolo isotopo radioattivo (nucleide madre) con attività iniziale $A_{0}$ . I prodotti di decomposizione diretta (nuclidi figli) sono quindi radioattivi. I nuclidi genitori e figli dei tre campioni sono:

Sample	Parent nuclide	$T_{Mutter}$	Daughter nuclide	$T_{Tochter}$
1	$^{226} Ra$	$1600 a$	$^{222} Rn$	$3, 8 d$
2	$^{211} Pb$	$36, 1 min$	$^{211} Bi$	$2, 14 min$
3	$^{214} Pb$	$26, 8 min$	$^{214} Bi$	$19, 9 min$

I grafici I, II, III rappresentano l’evoluzione del tempo delle attività $A$ del nuclide genitore, del nuclide figlia e dell’attività totale (asse del tempo scalata in multipli di $T_{Tochter}$ ).

Quale delle tre coppie di nuclidi appartiene a quale diagramma?

A $1 \to I$ , $2 \to II$ , $3 \to III$

B $1 \to II$ , $2 \to III$ , $3 \to I$

C $1 \to III$ , $2 \to II$ , $3 \to I$

D $1 \to III$ , $2 \to I$ , $3 \to II$

Radioactive decay

In the following, three radioactive samples are considered. Initially, at time $t = 0$ , they consist $100 %$ of a single radioactive isotope (parent nuclide) with initial activity $A_{0}$ . The direct decay products (daughter nuclides) are therefore radioactive. The parent and daughter nuclides of the three samples are:

Sample	Parent nuclide	$T_{Mutter}$	Daughter nuclide	$T_{Tochter}$
1	$^{226} Ra$	$1600 a$	$^{222} Rn$	$3, 8 d$
2	$^{211} Pb$	$36, 1 min$	$^{211} Bi$	$2, 14 min$
3	$^{214} Pb$	$26, 8 min$	$^{214} Bi$	$19, 9 min$

The graphs I, II, III represent the time evolution of the activities $A$ of the parent nuclide, the daughter nuclide and the total activity (time axis scaled in multiples of $T_{Tochter}$ ).

Which of the three nuclide pairs belongs to which diagram?

A $1 \to I$ , $2 \to II$ , $3 \to III$

B $1 \to II$ , $2 \to III$ , $3 \to I$

C $1 \to III$ , $2 \to II$ , $3 \to I$

D $1 \to III$ , $2 \to I$ , $3 \to II$

Galactic message in a bottle

A spaceship leaves the Earth at the constant speed $0, 6 c$ , where $c$ denotes the speed of light in vacuum. After $100 h$ on board, the space travellers throw a message in a bottle towards the Earth at a speed of $0, 8 c$ relative to the spaceship.

How long must the inhabitants of the Earth wait between the launch of the spaceship and the arrival of the message in a bottle?

A about $256 h$

B about $320 h$

C about $400 h$

D about $525 h$

Topic: Special Relativity Metodi: Lorentz Transformation, Relativistic Energy-Momentum Competenze: Mathematical Modeling, Physical Reasoning Objects: — Fonte: Testo (PDF) — p.37

Galactic message in a bottle

Una nave spaziale lascia la Terra alla velocità costante $0, 6 c$ , dove $c$ indica la velocità della luce in vuoto. Dopo $100 h$ a bordo, i viaggiatori spaziali gettano un messaggio in una bottiglia verso la Terra a una velocità di $0, 8 c$ relativa alla nave spaziale.

Quanto tempo dovranno aspettare gli abitanti della Terra tra il lancio della nave spaziale e l’arrivo del messaggio in bottiglia?

A about $256 h$

B about $320 h$

C about $400 h$

D about $525 h$

The first is the “Galactic message in a bottle”.

A spacecraft leaves the Earth at the constant speed $0, 6 c$ , where $c$ denotes the speed of light in vacuum. After $100 h$ on board, the space travelers throw a message in a bottle towards the Earth at a speed of $0, 8 c$ relative to the spacecraft.

How long must the inhabitants of the Earth wait between the launch of the spacecraft and the arrival of the message in a bottle?

A about $256 h$

B about $320 h$

C about $400 h$

D about $525 h$

Power of wind turbines

Wind turbines generate electrical power by using energy from wind to drive generators. At a moderate wind speed, the power made available by the wind of a turbine, and thus theoretically the maximum usable power, is $P$ .

What power made available by the wind of the turbine results from a doubling of the wind speed?

A $2 P$

B $3 P$

C $4 P$

D $8 P$

Topic: Order-of-Magnitude Estimation, Newtonian Mechanics Metodi: Dimensional Analysis, Order-of-Magnitude Estimation Competenze: Estimation & Approximation, Physical Reasoning Objects: — Fonte: Testo (PDF) — p.38

Power of wind turbines

Le turbine eoliche generano energia elettrica utilizzando energia da vento a generatori di guida. A moderata velocità del vento, la potenza resa disponibile dal vento di una turbina, e quindi teoricamente la massima potenza utilizzabile, è $P$ .

Che potenza resa disponibile dal vento della turbina risulta da un raddoppio della velocità del vento?

A $2 P$

B $3 P$

C $4 P$

D $8 P$

Power of wind turbines

What power made available by the wind of the turbine results from a doubling of the wind speed?

A $2 P$

B $3 P$

C $4 P$

D $8 P$

Power of gravitational waves

The general theory of relativity predicts the existence of gravitational waves (waves in the fabric of spacetime). For two bodies of equal mass $m$ orbiting each other at a distance $r$ , the power $P$ radiated by gravitational waves can be expressed with the help of the gravitational constant $G$ and the speed of light in vacuum $c$ .

Which of the following expressions could represent a suitable expression for the power $P$ ?

$A P = \frac{32}{5} \frac{G ^{5} m ^{5}}{c ^{5} r ^{4}} B P = \frac{32}{5} \frac{G ^{5} m ^{5}}{c ^{4} r ^{5}} C P = \frac{32}{5} \frac{G ^{5} m ^{4}}{c ^{5} r ^{5}} D P = \frac{32}{5} \frac{G ^{4} m ^{5}}{c ^{5} r ^{5}}$

Topic: Order-of-Magnitude Estimation, Gravitation Metodi: Dimensional Analysis Competenze: Estimation & Approximation, Mathematical Modeling Objects: — Fonte: Testo (PDF) — p.38

Power of gravitational waves

La teoria generale della relatività predice l’esistenza di onde gravitazionali. For two bodies of equal mass $m$ orbiting each other at a distance $r$ , the power $P$ radiated by gravitational waves can be expressed with the help of the gravitational constant $G$ and the speed of light in vacuum $c$ .

Quali delle seguenti espressioni potrebbero rappresentare un’espressione adatta per la potenza $P$ ?

The power of gravitational waves

The general theory of relativity predicts the existence of gravitational waves. For two bodies of equal mass $m$ orbiting each other at a distance $r$ , the power $P$ radiated by gravitational waves can be expressed with the help of the gravitational constant $G$ and the speed of light in vacuum $c$ .

Which of the following expressions could represent a suitable expression for the power $P$ ?

Tidal Heating

Although a thick layer of ice reflects most of the sunlight reaching Saturn’s moon Enceladus, the Cassini space probe was able to photograph water fountains several hundred kilometres high on its surface. The moon obtains the energy required for this from tidal forces, which heat it up as they are converted into frictional work.

Consider a celestial body of radius $r$ orbiting a planet of mass $M_{P}$ on an orbit with semi-major axis $a$ and eccentricity $e$ ( $0 \leq e < 1$ ). The heating power can be expressed as:

$P \approx \frac{21}{100} r^{5} e^{2} G^{α} M_{P}^{β} a^{γ}$

What are the values of the exponents $α$ , $β$ and $γ$ ?

A $α = - 3/2$ , $β = 5/2$ , $γ = - 15/2$

B $α = 3/2$ , $β = 5/2$ , $γ = - 15/2$

C $α = 3/2$ , $β = - 5/2$ , $γ = 15/2$

D $α = - 3/2$ , $β = 5/2$ , $γ = 15/2$

Topic: Order-of-Magnitude Estimation, Astrophysics Metodi: Dimensional Analysis, Kepler’s Laws Competenze: Estimation & Approximation, Mathematical Modeling Objects: Planet, Satellite Fonte: Testo (PDF) — p.39

Tidal Heating

Sebbene un’épace strata di ghiaccio rifletta la maggior parte della luce solare che raggiunge la luna di Saturno, Enceladus, la sonda spaziale Cassini è stata in grado di fotografare fonti d’acqua a diverse centinaia di chilometri di altezza sulla sua superficie. La luna ottiene l’energia necessaria per questo dalle forze di marea, che lo riscaldano quando vengono convertite in lavoro di attrito.

Considerare un corpo celeste di radius $r$ orbitando un pianeta di massa $M_{P}$ in un’orbita con semi-asse maggiore $a$ e eccentricità $e$ ( $0 \leq e < 1$ ). Il potere di riscaldamento può essere espresso come:

$P \approx \frac{21}{100} r^{5} e^{2} G^{α} M_{P}^{β} a^{γ}$

Quali sono i valori degli esponenti $α$ , $β$ e $γ$ ?

A $α = - 3/2$ , $β = 5/2$ , $γ = - 15/2$

B $α = 3/2$ , $β = 5/2$ , $γ = - 15/2$

C $α = 3/2$ , $β = - 5/2$ , $γ = 15/2$

D $α = - 3/2$ , $β = 5/2$ , $γ = 15/2$

The following table shows the results of the calculations:

Although a thick layer of ice reflects most of the sunlight reaching Saturn’s moon Enceladus, the Cassini space probe was able to photograph water fountains several hundred kilometers high on its surface. The moon gets the energy required for this from tidal forces, which heat it up as they are converted into frictional work.

Consider a celestial body of radius $r$ orbiting a planet of mass $M_{P}$ on an orbit with semi-major axis $a$ and eccentricity $e$ ( $0 \leq e < 1$ ). The heating power can be expressed as:

$P \approx \frac{21}{100} r^{5} e^{2} G^{α} M_{P}^{β} a^{γ}$

What are the values of the exponents $α$ , $β$ and $γ$ ?

A $α = - 3/2$ , $β = 5/2$ , $γ = - 15/2$

B $α = 3/2$ , $β = 5/2$ , $γ = - 15/2$

C $α = 3/2$ , $β = - 5/2$ , $γ = 15/2$

D $α = - 3/2$ , $β = 5/2$ , $γ = 15/2$

Two Plates in Vacuum

Two conducting, parallel plates of area $A$ are placed a distance $d$ apart in vacuum. Owing to the quantum-mechanical Casimir effect, a force acts between the plates that depends on the speed of light $c$ in vacuum and on the reduced Planck constant $ℏ = \frac{h}{2 π}$ .

Which of the following could be a suitable expression for the force $F$ with which the plates are pushed together?

$A F = \frac{π ^{2} ℏ c}{240 d ^{3}} A B F = \frac{π ^{2} ℏ c}{240 d ^{3}} A^{2} C F = \frac{π ^{2} ℏ c}{240 d ^{4}} A D F = \frac{π ^{2} ℏ c}{240 d ^{4}} A^{2}$

Topic: Modern-Quantum Physics, Order-of-Magnitude Estimation Metodi: Dimensional Analysis Competenze: Estimation & Approximation, Physical Reasoning Objects: Capacitor Fonte: Testo (PDF) — p.39

Two platte in vacuum

Due conducenti, plates parallele di area $A$ sono posizionate a distanza $d$ separate in vuoto. A causa dell’effetto quantomeccanico di Casimir, una forza agisce tra le piastre che dipende dalla velocità di luce $c$ in vuoto e sulla costante di Planck ridotta $ℏ = \frac{h}{2 π}$ .

Which of the following could be a suitable expression for the force $F$ with which the plates are pushed together?

$A F = \frac{π ^{2} ℏ c}{240 d ^{3}} A B F = \frac{π ^{2} ℏ c}{240 d ^{3}} A^{2} C F = \frac{π ^{2} ℏ c}{240 d ^{4}} A D F = \frac{π ^{2} ℏ c}{240 d ^{4}} A^{2}$

Two plates in vacuum

Which of the following could be a suitable expression for the force $F$ with which the plates are pushed together?

$A F = \frac{π ^{2} ℏ c}{240 d ^{3}} A B F = \frac{π ^{2} ℏ c}{240 d ^{3}} A^{2} C F = \frac{π ^{2} ℏ c}{240 d ^{4}} A D F = \frac{π ^{2} ℏ c}{240 d ^{4}} A^{2}$

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