22
Name: ______( ) PDG: ______/13
2014 JC2 Prelim Examination
PHYSICS Higher 2 9646/03
Paper 3 Longer Structured Questions Monday 15 September 2014
2 hours
Candidates answer on the Question Paper.
No Additional Materials are required.
READ THESE INSTRUCTIONS FIRST
Write your name and PDG in the spaces at the top of this page.
Write in dark blue or black pen on both sides of the paper.
You may use a soft pencil for any diagrams, graphs or rough working.
Do not use staples, paper clips, highlighters, glue or correction fluid.
Section A
Answer all questions.
For Examiner’s UseSection A
1
2
3
4
5
6
Section B
7
8
9
Deduction
Total
Section B
Answer any two questions.
You are advised to spend about one hour on each section.
At the end of the examination, fasten all your work securely together.
The number of marks is given in brackets [ ] at the end of each question or part question.
Data
speed of light in free space, c = 3.00 x 108 m s−1
permeability of free space, m = 4p x 10−7 H m−1
permittivity of free space, e = 8.85 x 10−12 F m−1
(1/(36p)) x 10−9 F m−1
elementary charge, e = 1.60 x 10−19 C
the Planck constant, h = 6.63 x 10−34 J s
unified atomic mass constant, u = 1.66 x 10−27 kg
rest mass of electron, me = 9.11 x 10−31 kg
rest mass of proton, mp = 1.67 x 10−27 kg
molar gas constant, R = 8.31 J K−1 mol−1
the Avogadro constant, NA = 6.02 x 1023 mol−1
the Boltzmann constant, k = 1.38 x 10−23 J K−1
gravitational constant, G = 6.67 x 10−11 N m2 kg−2
acceleration of free fall, g = 9.81 m s−2
Formulae
uniformly accelerated motion, s = ut + at2
v2 = u2 + 2as
work done on/by a gas, W = pDV
hydrostatic pressure, p = r gh
gravitational potential, ϕ = −G
displacement of particle in s.h.m., x = x0 sin wt
velocity of particle in s.h.m., v = v0 cos wt
v = ± ω
mean kinetic energy of a E = kT
molecule of an ideal gas,
resistors in series, R = R1 + R2 + …
resistors in parallel, 1/R = 1/R1 + 1/R2 + …
electric potential, V =
alternating current/voltage, x = x0 sin wt
transmission coefficient, T µ exp(−2kd)
where k =
radioactive decay, x = x0exp(− lt)
decay constant, l =
22
Section A
Answer all the questions in this Section
1 / Fig. 1.1 shows the cross-section of a symmetrical object that is partially submerged in water and displaced from its equilibrium position. The thickness of the object is uniform throughout.Fig. 1.1
The density of the object is uniform and is less than the density of water.
(a) / On Fig. 1.1, draw arrows to show the forces acting on the object. [1]
(b) / Describe the subsequent motion of the object.
…...………………………………………………………………………….………………...... [1]
(c) / On Fig. 1.2, draw the final equilibrium position of the object and indicate the forces acting on the object with arrows.
Fig. 1.2
[2]
(d) / If the amount of water displaced by the object at equilibrium is the same as that shown in Fig. 1.1, determine the density of the object in terms of the density of water, rw.
density of object = ……………………………. [2]
2 / (a) / (i) / State the first law of thermodynamics.
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(ii) / Explain why, for an ideal gas, the internal energy is equal to the total kinetic energy of the molecules of the gas.
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(b) / A cylinder contains 1.0 mol of an ideal gas.
(i) / The volume of the cylinder is constant. Calculate the thermal energy required to raise the temperature of the gas by 1.0 K.
energy = …………………………….J [2]
(ii) / The volume of the cylinder is now allowed to increase so that the gas remains at constant pressure when it is heated. Explain whether the thermal energy required to raise the temperature of the gas by 1.0 K is now different from your answer in (b)(i).
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(c) / In order for an atom to escape completely from the Earth’s gravitational field, it must have a speed of approximately 1.1 x 104 m s-1 at the top of the Earth’s atmosphere.
(i) / Estimate the temperature at the top of the atmosphere such that helium, assumed to be an ideal gas, could escape from the Earth. The mass of a helium atom is 6.6 x 10-27 kg.
temperature = …………………………….K [2]
(ii) / Suggest why some helium atoms will escape at temperatures below that calculated in (c)(i).
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3 / (a) / Explain what is meant by the principle of superposition.
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(b) / Light from a mercury vapour lamp is incident normally on a diffraction grating and the diffraction pattern is observed on a screen placed 30 cm away from the diffraction grating. The positions of the first order orange spectrum of wavelength 580 nm are 20cm apart, as shown in Fig. 3.1 below.
(i) / Show that the diffraction grating has 545 number of lines per mm.
[2]
(ii) / Fig. 3.2 shows some of the energy levels in a mercury atom. Another spectrum that was also emitted from the mercury lamp is shown by the transition A.
Calculate the wavelength of the spectrum associated with the transition A.
wavelength = ……………………………… m [2]
(iii) / Hence, determine the highest order of diffracted beam that can be observed on the screen in Fig. 3.1 for the spectrum calculated in (b)(ii).
highest order = ……………………………… [2]
4 / A short magnet is released and falls straight through a long solenoid as shown in Fig. 4.1.
A voltage sensor and datalogger are used to measure the e.m.f induced in the solenoid.
Fig. 4.1
Fig. 4.2 shows how the induced e.m.f e in the solenoid changes with time, t.
Fig. 4.2
With reference to Fig. 4.2, explain
a) / why the second peak values of the induced e.m.f. is greater than the first peak value.
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b) / the difference in the signs of the induced e.m.f.
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5 / Free neutrons (neutrons not contained within a nucleus) are unstable and decay by b-emission with a half-life of 770 s.
(a) / Explain what is meant by
(i) / the neutrons are unstable.
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(ii) / half-life.
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(b) / Write down a possible nuclear equation for the decay of a free neutron.
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(c) / Using your relationship in (b) and the following data, calculate the energy released in the decay of a free neutron.
rest mass of neutron = 1.008665 u
rest mass of proton = 1.007276 u
rest mass of electron = 0.000549 u
[2]
(d) / Sketch, on the axes of Fig. 5.1, the following graphs to show the variation with time of
(i) / the number of undecayed neutrons and label as N,
(ii) / the number of b-particles and label as B.
[2]
(e) / Label on the axis of Fig. 5.1, the half-life of neutron. [1]
6 / The energy bands in an intrinsic semiconductor are illustrated in Fig. 6.1
Using band theory,
(a) / describe how the electrical resistance of an intrinsic semiconductor material decreases with increase of temperature.
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(b) / suggest and explain a difference in the resistance of an intrinsic semiconductor compared to a p-type semiconductor.
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Section B
Answer two questions from this section
7 / (a) / (i) / State Newton’s first law of motion.…………………………………………………………………………………......
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(ii) / State Newton’s second law of motion.
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(iii) / With a suitable definition of the unit of force, Newton’s second law can be written in the following relationship
force = mass x acceleration
for a body of constant mass.
Hence, together with Newton’s third law, derive the principle of conservation of momentum.
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(b) / An alpha particle collides head-on with a stationary nitrogen-14 atom. The nitrogen atom moves off in the same direction as the approaching alpha particle with a speed of 0.005 c where c is the speed of light.
(i) / Calculate the change in momentum of the alpha particle.
change in momentum = …………………………….N s [2]
(ii) / Show quantitatively whether the interaction described in (b) is elastic in nature if the initial speed of the alpha particle is 0.02 c.
[3]
(c) / Alpha particles of speed 4.41x106m s-1 enter a region of uniform electric field at an angle 25 ° with the horizontal. The region of field is set up by two plates P and Q in a horizontal plane as shown in Fig. 7.1.
Fig. 7.1
(i) / State and explain how the horizontal component of the velocity of the alpha particles would vary along the length of the plates.
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(ii) / Fig. 7.2 shows how the vertical displacement of an alpha particle varies with time as it passed through the plates.
Fig. 7.2
1. / With reference to the features of the graph in Fig. 7.2, state and explain the direction of the resultant force acting on the alpha particle. Ignoring the effect of gravity.
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2. / Sketch on Fig. 7.3 how the vertical displacement of the alpha particles would vary with position along the length of plate Q as they travel between the plates. You may assume that the vertical displacement above plate Q to be positive.
Fig. 7.3
[2]
(iii) / Using Fig. 7.2, determine the resultant force experienced by an alpha particle.
resultant force = …………………………….N [3]
(iv) / The stream of alpha particles entering the region between PQ is replaced with a stream of protons with the same entry speed and angle of projection.
On Fig. 7.2, sketch the variation of vertical displacement with time for a proton.
[2]
8 / A toy car’s wheel is set up as a pendulum by hanging it vertically from a fixed support. The wheel oscillates about the fixed support as illustrated in Fig. 8.1.
The variation with displacement x of the acceleration a of the wheel is shown in Fig.8.2.
Fig. 8.2
(a) / (i) / Use Fig. 8.2 to explain why the motion of the wheel is simple harmonic.
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(ii) / State a condition that must be satisfied for the oscillation of the wheel to be simple harmonic.
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(b) / The wheel in Fig. 8.1 is displaced and released at time t = 0. The oscillations of the wheel have amplitude 14.7 cm and angular frequency 2.40 rad s-1.
(i) / Define angular frequency.
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(ii) / State an expression for the displacement x of the wheel in terms of time t.
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(iii) / Use your expression in (b)(ii) to sketch the variation of the kinetic energy of the wheel EK with time t for one complete oscillation in Fig 8.3. [2]
Fig. 8.3
(c) / The angular frequency value stated in (b) is calculated from the period of the simple harmonic motion. An accurate value for the period is found by timing a large number of oscillations.
(i) / Explain why a large number of oscillations would help to achieve a more accurate value for the period.
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(ii) / Calculate the number of oscillations that are measured in a total time of 83.8 s.
number of oscillations = ………………………… [2]
(iii) / A stopwatch with display provides timing to 1/100th of a second over a range of 9 hours, 59 minutes and 59.99 seconds was used to record the duration of the oscillations in (c)(ii).
Explain why the duration of the oscillations in (c)(ii) is recorded to 0.1 seconds.
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(d) / In order to time the oscillations of the wheel in Fig. 8.1, a stopwatch is started when the centre of the wheel passes a marker. This marker is 2.7 cm from the equilibrium position as shown in Fig.8.4.
Fig. 8.4
(i) / The wheel has a mass of 0.165 kg. Calculate the restoring force acting on the wheel as it passes the marker.
restoring force = ………………………… N [2]
(ii) / Calculate the speed of the wheel at the instant it passes the marker.
speed …………………………m s-1 [2]
(e) / In an experiment to demonstrate resonance, the wheel in Fig. 8.1 is made to oscillate by an external periodic driving force of frequency f. Fig. 8.5 shows the variation with frequency f of the amplitude of the forced oscillations of the wheel.
Fig. 8.5
(i) / Describe how the amplitude of oscillation depends on the forcing frequency.
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(ii) / Sketch in Fig. 8.5 the shape of the graph if the forced oscillations of the wheel were repeated in a vacuum. Label your sketch as A.
[2]
9 / (a) / Two small charged metal spheres A and B are situated in a vacuum. The distance between the centres of the spheres is 12.0 cm, as shown in Fig. 9.1.
/
Fig 9.1 (not to scale)
The charge on each sphere may be assumed to be a point charge at the centre of the sphere.
Point P is a movable point that lies on the line joining the centres of the spheres and is distance x from the centre of sphere A.
The variation with distance x of the electric field strength E at point P is shown in Fig.9.2.
Fig 9.2
(i) / Define electric field strength.
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(ii) / State the evidence provided by Fig. 9.2 for the statements that
1. / the spheres are conductors,
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2. / the charges on the spheres are both positive.
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(iii) / An a-particle is placed at x = 4.0 cm on the line joining the centres of the spheres.
Describe what will happen to the a-particle?
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(b) / Fig. 9.3 shows two charged parallel plates which are 12.0 cm apart. A flame probe connected to an electroscope or electrostatic voltmeter can be used to measure the electric potential in the space between the plates. The probe is a tiny gas flame which makes the air near the probe conduct. By moving the probe about, between the plates, the equipotential surfaces can be mapped out. The dashed lines A, B, C, D and E represent some equipotential surfaces. (Not to scale)
Fig. 9.3
(i) / Define electric potential.
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(ii) / Suggest how the flame probe enables air between the plates to conduct electricity.
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(iii) / On Fig. 9.3, draw lines to show the electric field between the plates. [2]
(iv) / On Fig. 9.4, sketch the variation of the electric potential, V, at different points along the line XY where X and Y are midpoints of the parallel plates.
Label the positions of equipotential lines A, B, C, D and E clearly on your graph.
Fig. 9.4
[2]
(v) / 1. / A proton, which is initially at rest at P as shown in Fig 9.5, is moved within the electric field. Complete the table below by stating the work done in moving the proton along each of the following path.
Fig 9.5
Path taken / Work done / eV
P → Q
Q → R
P → Q → R → P
[3]
2. / The proton, back at position P, is released from rest.
Describe the motion of the proton.
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3. / Give a quantitative explanation as to why gravitational force due to Earth is not considered when predicting the motion of the proton between the plates.
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