Centre Number 71 Candidate Number

Centre Number 71 Candidate Number

ADVANCED General Certificate of Education 2006

Physics assessing

Module 4: Energy, Oscillations and Fields

A2Y11

Assessment Unit A2 1

[A2Y11] THURSDAY 1 JUNE, MORNING

TIME

1 hour 30 minutes. INSTRUCTIONS TO CANDIDATES

Write your Centre Number and Candidate Number in the spaces provided at the top of this page. Answer all seven questions. Write your answers in the spaces provided in this question paper. INFORMATION FOR CANDIDATES

The total mark for this paper is 90. Quality of written communication will be assessed in questions 2(a)(ii), (c) and 4(b). Figures in brackets printed down the right-hand side of pages indicate the marks awarded to each question. Your attention is drawn to the Data and Formulae Sheet which is inside this question paper. You may use an electronic calculator. Question 7 contributes to the synoptic assessment requirement of the Specification. You are advised to spend about 55 minutes in answering questions 1–6, and about 35 minutes in answering question 7. A2Y1S6

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For Examiner’s use only Question Number

1 2 3 4 5 6 7 Total Marks

Marks

If you need the values of physical constants to answer any questions in this paper, they may be found on the Data and Formulae Sheet.

Examiner Only Marks

Remark

Answer all seven questions

1

(a) (i) State the principle of conservation of energy. _____________________________________________________ __________________________________________________ [1]

(ii) Give a practical example of a case in which kinetic energy is transformed into thermal energy (heat). _____________________________________________________ _____________________________________________________ __________________________________________________ [1]

(b) A ball of mass 0.26 kg is held at rest above a vertical coiled spring of spring constant k. (The spring constant is the constant of proportionality in Hooke’s law.) Initially the bottom of the ball is 0.55 m above the top of the uncompressed spring, as shown in Fig. 1.1.

0.55 m

0.15 m

Fig 1.1

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Fig 1.2

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The ball is then dropped so that it falls on to the spring, compressing it by 0.15 m. Fig. 1.2 shows the spring at the instant of maximum compression, when the ball is again at rest. In the calculations below, air resistance can be neglected.

Examiner Only Marks

Remark

(i) Calculate the loss of gravitational potential energy of the ball between the situations shown in Fig. 1.1 and Fig. 1.2.

Loss of gravitational potential energy = ___________ J

[2]

(ii) State what has happened to this energy. _____________________________________________________ __________________________________________________ [1]

(iii) Hence calculate the spring constant k.

k = ___________ N m–1

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[2]

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2

In parts (a)(ii) and (c) of this question you should answer in continuous prose. You will be assessed on the quality of your written communication.

Examiner Only Marks

Remark

(a) The Formulae Sheet gives the following expression for the product pV of the pressure and volume of a gas: pV =

1 Nm < c 2 > 3

(i) State what the product Nm in this equation represents. __________________________________________________ [1] (ii) The quantity is called the mean-square speed of the molecules. Explain, in words, how you would calculate the mean-square speed from a set of values c1, c2, c3 ... of the speeds c of the molecules. _____________________________________________________ _____________________________________________________ _____________________________________________________ _____________________________________________________ _____________________________________________________ __________________________________________________ [3]

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(b) The Formulae Sheet gives the following expression for the average kinetic energy <Ek> of a molecule:

Examiner Only Marks

Remark

1 3 m < c 2 > = kT 2 2 Fig. 2.1 is a graph of the average kinetic energy <Ek> of a molecule against celsius temperature θ. ▼

<EEk>/J /J k

▼

0

θ /°C

0 Fig. 2.1 (not to scale)

Obtain numerical values for the gradient and energy intercept of this graph.

Gradient = ______________ J °C–1 Energy intercept = ______________ J

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(c) One assumption of the kinetic theory is that the collisions of the molecules of the gas with the walls of the container are perfectly elastic.

Examiner Only Marks

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Describe and explain what would happen to the gas if the collisions were inelastic. _________________________________________________________ _________________________________________________________ _________________________________________________________ ______________________________________________________ [3] Quality of written communication

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[1]

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BLANK PAGE (Questions continue overleaf)

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3

A person is swinging a ball on the end of a string so that it moves with uniform angular velocity in a horizontal circle (Fig. 3.1).

Examiner Only Marks

Remark

Fig. 3.1

(a) Fig. 3.2 shows a plan view of the ball moving in its circular path.

Fig. 3.2

(i) On Fig. 3.2, mark the path the ball would follow if the string were to break when the ball is at the position shown. [1]

(ii) The force acting on the ball as it moves in its circular path with uniform angular velocity is said to be centripetal (towards the centre of the circle). Explain why it must be in this direction. _____________________________________________________ _____________________________________________________ _____________________________________________________ __________________________________________________ [1]

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(b) The ball has mass 0.15 kg and moves in a circle of radius 0.60 m. It makes 2.0 revolutions each second.

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(i) Assume that the ball rotates with the string in the horizontal plane. Calculate the tension T in the string.

Tension = ________ N

[2]

(ii) In fact, the weight W of the ball makes it impossible for the string to be horizontal. The real situation is sketched in Fig. 3.3.

T

θ

W Fig. 3.3

Assume that the horizontal component of the tension has the value calculated in (b)(i). Determine the angle θ.

θ = ________ °

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[3]

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4

In part (b) of this question you should answer in the form of short notes. You will be assessed on the quality of your written communication.

Examiner Only Marks

Remark

(a) A body moves with simple harmonic motion in a straight line. During this motion, the force on the body is proportional to the displacement from the equilibrium position and is in the opposite direction to the displacement. 10 a/m s–2

5

–6 –6

–4 –4

–2 –2

0

2

4

x/mm

6

–5

–10 Fig. 4.1

Fig. 4.1 is a graph of the acceleration a of the body as a function of its displacement x from the equilibrium position. (i) Explain how Fig. 4.1 shows that the force on the body is proportional to the displacement of the body from the equilibrium position, and that the force is in the opposite direction to the displacement. _____________________________________________________ _____________________________________________________ _____________________________________________________ __________________________________________________ [3]

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(ii) Use Fig. 4.1 to find the amplitude and period of the motion.

Examiner Only Marks

Remark

Amplitude = ___________ mm Period = ___________ s

[4]

(b) Write revision notes, suitable for this examination, on the subject of Damping and Resonance. The Specification gives the guidance: “Descriptive treatment of frequency response, resonance and effect of damping.” Bullet point notes, illustrated by sketches and/or graphs, will be sufficient.

_________________________________________________________ _________________________________________________________ _________________________________________________________ _________________________________________________________ _________________________________________________________ _________________________________________________________ _________________________________________________________ _________________________________________________________ ______________________________________________________ [5] Quality of written communication

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5

A student, asked to explain what is meant by a field of force, gave the answer

Examiner Only Marks

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“A field of force is an area where a unit charge experiences a force”. (a) Identify two errors, omissions or irrelevant details in the student’s explanation. 1. _______________________________________________________ _________________________________________________________ 2. _______________________________________________________ ______________________________________________________ [2]

(b) It seems that the student may have been confusing the explanation of a field of force with the definition of electric field strength. Define electric field strength and state how the direction of the electric field is obtained. _________________________________________________________ _________________________________________________________ _________________________________________________________ ______________________________________________________ [2]

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Examiner Only Marks

Remark

BLANK PAGE

QUESTIONS CONTINUE ON PAGE 14 2663

(Questions continue overleaf) 13

[Turn over[Turn over

1313

[Turn [Turn over[Turn over [Turn over

1–10/4/06 ES 2–26 26/4/06 /4/06 GG 1–12/3/06 GG

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(a) (i) State, in words, the law of gravitational force between two point masses.

Examiner Only Marks

Remark

_____________________________________________________ _____________________________________________________ _____________________________________________________ __________________________________________________ [3]

(ii) The laws of force for gravitational and electric fields have similar mathematical forms. However, they differ in some important ways. State one of these differences. _____________________________________________________ __________________________________________________ [1]

(b) Gravitational force has an important role in explaining the orbits of planets and satellites. What is this role? ______________________________________________________ [1]

(c) (i) Kepler’s third law of planetary motion states that, for the simplified case of circular orbits, the square of the period of rotation of the planet in its orbit about the Sun is proportional to the cube of the radius of the orbit. Show that this result is consistent with the law of gravitational force.

[4]

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(ii) The radius of the Earth’s orbit about the Sun is 1.50 × 1011 m. Calculate the mass of the Sun.

Mass of Sun = ________ kg

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Examiner Only Marks

Remark

[3]

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7

Data analysis question

Examiner Only Marks

Remark

This question contributes to the synoptic assessment requirements of the Specification. In your answer, you will be expected to use the ideas and skills of physics in the particular situations described. You are advised to spend about 35 minutes in answering this question. Work functions of metals (a) Nearly ninety years ago Robert Millikan carried out classic experiments which provided quantitative proof of Einstein’s photoelectric emission equation (which is quoted in your Data and Formulae Sheet). A clean metal surface in an evacuated tube was illuminated with monochromatic light. If the light was of a suitable wavelength, photoelectrons were emitted. When these electrons reached the collecting electrode and passed round the circuit, a measurable photocurrent I was produced. A stopping potential was applied to the collecting electrode so that the photoelectrons were just prevented from reaching the collector. Typical current-voltage (I-V) characteristics were as shown in Fig. 7.1. These characteristics were obtained when the metal was illuminated, separately, with light of wavelength 546 nm and 365 nm.

3 I/ µ A

–2.0

–1.5

–1.0

2

λ = 365 nm

1

λ = 546 nm

– 0.5

0

0.5

1.0 V/V

Fig. 7.1

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(i) Fig. 7.2 shows part of a circuit which could be used to find the stopping potential and measure it.

Examiner Only Marks

Remark

radiation

collector

clean metal surface

insert battery symbol here

label meter appropriately

Fig. 7.2

Insert appropriate symbols to complete the circuit. This circuit should include a potential divider. Make sure that the battery symbol shows the correct polarity for obtaining the stopping potential part of the I-V characteristic. [4]

(ii) The two characteristics in Fig. 7.1 show steady values of photocurrent I, that differ in value. Suggest a reason why there might be this difference. _____________________________________________________ _____________________________________________________ __________________________________________________ [1]

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(iii) In another experiment the stopping potentials were measured to a greater degree of precision than in this experiment. Table 7.1 gives the values of the stopping potentials Vs required when the metal was illuminated by light of different wavelengths λ.

Examiner Only Marks

Remark

Table 7.1

λ/nm

Vs/V

365

1.430

436

0.875

496

0.530

546

0.300

hf/J

(1) To how many significant figures is the 0.300 V value of the stopping potential quoted? _______________________________________________ [1] (2) Show that a formula for converting wavelengths λ in nm to photon energies hf in J is hf (in J ) =

1.99 × 10 –16 λ (in nm )

Equation 7.1

[2] (3) Use Equation 7.1 to convert the values of λ in Table 7.1 to corresponding values of hf. Insert these values in the third column of the Table. [2]

(iv) (1) You are to plot a graph of Vs against hf on the graph grid of Fig. 7.3. Label the horizontal axis, select a suitable scale, plot the values from Table 7.1 and draw the best straight line through the points. [5]

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Examiner Only Marks

Remark

1.5 Vs /V

1.0

0.5

0 Fig. 7.3

(2) Find the gradient of your graph. Give an appropriate unit.

Gradient = ___________________ Unit:

___________________

[4]

(3) Read off the intercept on the hf-axis.

Intercept on hf-axis = ___________ J

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(v) The Einstein photoelectric equation is

Examiner Only Marks

hf = hf0 +

1 2 mvmax 2

Remark

Equation 7.2

1 2 2 mvmax represents the maximum kinetic energy of the 2 photoelectron. This quantity is measured using the stopping potential, and is given by The term+

1 2 = eVs mvmax 2

Equation 7.3

(1) Making reference to Equation 7.2, explain how the work function of the metal can be obtained from your graph. __________________________________________________ __________________________________________________ Calculate its value in electron volts (eV).

Work function = ___________ eV

[2]

(2) Making reference to Equations 7.2 and 7.3, state how the elementary charge e is related to the gradient of your graph. _______________________________________________ [1]

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(b) Another way of measuring the work function of a metal is to study the thermionic emission from it. As the temperature of the metal is increased, more and more electrons are emitted from it. This emission is called the thermionic emission current, and the current per unit area of the metal is the thermionic emission current density. The equation giving the thermionic emission current density J at a kelvin temperature T is J = A0T 2e– φ/kT

Examiner Only Marks

Remark

Equation 7.4

where A0 is a constant, φ is the work function and k is the Boltzmann constant. To obtain the work function, the current density J is measured at a number of temperatures T.

(i) A simplified picture of thermionic emission is to suppose that the free electrons in the metal behave like the molecules of an ideal gas. Use this picture and the idea of the work function of a metal to suggest why, as the temperature of the metal is raised, more and more electrons are emitted from it. _____________________________________________________ _____________________________________________________ _____________________________________________________ _____________________________________________________ _____________________________________________________ __________________________________________________ [3]

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(ii) (1) The emission current density J is the current per unit surface area of the emitter. State its unit.

Unit: _________________________

Examiner Only Marks

Remark

[1]

kT in Equation 7.4. (2) State the unit, if any, of the quantity e–φφ//kT

Unit: _________________________

Hence obtain the unit, if any, of the constant A0. Unit: _________________________

[2]

(iii) It is possible to use a graphical method to find the value of φ from a set of values of J and T. (1) Equation 7.4 can be rewritten in the form J – φ /kT 2 = A0 e T

Equation 7.5

Take natural logarithms (logarithms to the base e) of both sides of Equation 7.5. Equation in logarithmic form:

[1]

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(2) Compare your equation in (b)(iii)(1) with the standard linear form

Examiner Only Marks

Remark

y = mx + c

and hence state the axes you would use to obtain a linear graph from which φ could be determined.

y-axis (vertical): __________________ x-axis (horizontal): __________________

(3) On Fig. 7.4, sketch the graph you would expect to obtain.

[2]

[1]

Fig. 7.4

(4) State how you would use the graph to determine the value of φ. __________________________________________________ __________________________________________________ __________________________________________________ _______________________________________________ [2]

THIS IS THE END OF THE QUESTION PAPER

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S – 4/06 – 4000 – 302507(177)

GCE Physics (Advanced Subsidiary and Advanced) Data and Formulae Sheet

Values of constants speed of light in a vacuum

c = 3.00 × 108 m s –1

permeability of a vacuum

µ 0 = 4π × 10–7 H m–1

permittivity of a vacuum

ε 0 = 8.85 × 10–12 F m–1 1 –––– = 8.99 × 109 F –1 m 4π ε 0

(

)

elementary charge

e = 1.60 × 10–19 C

the Planck constant

h = 6.63 × 10–34 J s

unified atomic mass unit

1 u = 1.66 × 10–27 kg

mass of electron

me = 9.11 × 10–31 kg

mass of proton

mp = 1.67 × 10–27 kg

molar gas constant

R = 8.31 J K–1 mol–1

the Avogadro constant

NA = 6.02 × 1023 mol–1

the Boltzmann constant

k = 1.38 × 10–23 J K–1

gravitational constant

G = 6.67 × 10–11 N m2 kg–2

acceleration of free fall on the Earth’s surface

g = 9.81 m s–2

electron volt

1 eV = 1.60 × 10–19 J

A2Y11INS A2Y1S6

2663.02

USEFUL FORMULAE The following equations may be useful in answering some of the questions in the examination: Thermal physics

Mechanics Momentum-impulse relation

mv – mu = Ft for a constant force

Average kinetic energy of a molecule

1 –2 m

Power

P = Fv

Kinetic theory

pV = 1–3 Nm

Conservation of energy

1 –2 mv 2

– 1–2 mu 2 = Fs for a constant force

Simple harmonic motion Displacement

x = x0 cos ω t or x = x0 sin ω t

Capacitors

Capacitors in parallel

1 1 1 1 = + + C C1 C 2 C 3 C = C1 + C2 + C3

Time constant

τ = RC

Capacitors in series

Velocity

v = ±ω x 0 2 − x 2

Simple pendulum

T = 2π l / g

Magnetic flux density due to current in

Loaded helical spring

T = 2π m / k

(i)i long straight (i)i solenoid

B=

(ii) long straight (i)i conductor

B=

Medical physics Sound intensity level/dB

= 10 lg10(I/I0)

Sound intensity difference/dB

= 10 lg10(I2/I1)

Resolving power

sin θ = λ/ D

Waves

Electromagnetism

µ0NI l

µ0I 2πa

Alternating currents A.c. generator

E = E0 sin ω t = BANω sin ω t

Particles and photons

Two-slit interference

λ = ay/d

Diffraction grating

d sin θ = nλ

Light Lens formula

1/u + 1/v = 1/f

Stress and Strain Hooke’s law

F = kx

Strain energy

E = x (= 1–2 Fx = 1–2 kx 2 if Hooke’s law is obeyed)

Electricity Potential divider A2Y1S6

= 3–2 kT

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Vout = R1Vin/(R1 + R2)

Radioactive decay

A = λN A = A0e–λt

Half life

t1–2 = 0.693/λ

Photoelectric effect

1 –2 mv2max =

de Broglie equation

λ = h /p

Particle Physics Nuclear radius

1–

r = r0 A3

hf – hf0