Centre Number Index Number Name Class

RAFFLES INSTITUTION 2009 Preliminary Examination

PHYSICS Higher 2 Paper 2

9745 / 02

17 September 2009 1 hour 15 minutes

Candidates answer on the Question Paper. No Additional Materials are required.

READ THESE INSTRUCTIONS FIRST Write your Centre number, index number, name and class in the spaces provided at the top of this page. Write in dark blue or black pen. You may use a soft pencil for any diagrams, graphs or rough working. Do not use staples, paper clips, highlighters, glue or correction fluid. Answer all questions. Write your answers in the spaces provided in this booklet. The number of marks is given in brackets [ ] at the end of each question or part question.

For Examiner’s Use

1 / 12

2 / 6

3 / 12

4 / 6

5 / 8

6 / 16

Total / 60

This booklet consists of 14 printed pages including the cover page.

2

Data

speed of light in free space, c = 3.00 x 108 m s−1

permeability of free space, µ0 = 4π x 10−7 H m−1

permittivity of free space, ε0 = 8.85 x 10−12 F m−1

(1 / (36 π)) 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

3

Formulae

uniformly accelerated motion, s = 212ut at+

2v = 2 2u as+

work done on/by a gas, W = p∆V

hydrostatic pressure, p = ρgh

gravitational potential, φ = Gm

r−−−−

displacement of particle in s.h.m., x = x0 sin ω t

velocity of particle in s.h.m., v = v0 cos ω t

= ( )2 20x xω± −

resistors in series, R = R1 + R2 + …

resistors in parallel, 1/R = 1/R1 + 1/R2 + …

electric potential, V = 4

Qrε0π

alternating current/voltage, x = x0 sin ω t

transmission coefficient, T = exp(−2kd)

where k =

(((( ))))2

2

8 m U E

h

π −−−−

radioactive decay, x = x0 exp (−λt)

decay constant, λ = 12

0.693t

4

1 A toy rocket of initial mass 0.92 kg is fired vertically into the air. Its mass decreases at a constant rate of 0.18 kg s−1 as the fuel burns and is ejected out as exhaust gas. The final mass of the rocket is 0.20 kg. The rocket rises to a height such that, during the flight, the gravitational field strength of the Earth may be considered to have the constant value of 9.81 N kg−1.

(a) Use appropriate physics law(s) to explain how the toy rocket works.

[2]

(b) Calculate

(i) the initial weight of the rocket,

Initial weight = N [1] (ii) the final weight of the rocket,

Final weight = N [1]

(iii) the time taken for the fuel to be burned.

Time taken = s [1]

5

(c) The variation with time t of the upward force on the rocket during the first 4.0 s after firing is shown in Fig. 1.1.

(i) On Fig.1.1, use the same scales to draw a graph showing the variation with time t of the total weight of the rocket during the first 5.0 s after firing.

[1]

(ii) Hence read off from Fig. 1.1 the time delay between firing the rocket and lift-off.

Time delay = s [1] (d) (i) On Fig. 1.1, shade the area of the graph which represents the change in

momentum of the rocket during the first 4.0 s after the rocket is fired.

[1]

(ii) Estimate the change in momentum of the rocket during the first 4.0 s.

Change in momentum = N s [2] (iii) Hence, deduce the time when the rocket will reach the highest point of its

journey.

Time = s [2]

Fig. 1.1

0 1.0 2.0 3.0 4.0 5.0 t / s

20.0

15.0

upward force / N

10.0

5.0

0

6

2 An object of mass 0.050 kg is placed on a horizontal platform and the platform is made to oscillate vertically in simple harmonic motion with an amplitude of 40 mm. The frequency of oscillation is increased gradually until the object begins to lose contact with the platform.

(a) State at what point in the motion of the platform the object first loses contact with the platform.

[1]

(b) Find the lowest frequency at which this occurs.

Frequency = Hz [2] (c) Calculate the maximum speed of the platform.

Maximum speed = m s−1 [1] (d) Hence, or otherwise, determine the total energy of the object at any point of the motion,

assuming there is no damping.

Total energy = J [2]

7

3 (a) State what is meant by an electric field of force.

[1]

(b) A wooden rod with a negatively charged metal tip is situated near a thin metal plate

carrying positive charge. An uncharged metal sphere is introduced in the region between the rod and the metal plate.

On Fig. 3.1, sketch the electric field pattern around the objects. [3]

Fig. 3.1

(c) Fig. 3.2 shows two long parallel conducting plates with potentials 50 V and –50 V respectively. The plates are 2.0 mm apart. An electron enters the region at an angle θ = 45° with a speed v = 5.6 x 106 m s−1 at a point mid-way between the plates as shown.

x

θ v

50 V − 50 V

2.0 mm

Displacement d along plates

Fig. 3.2

electron

+

+

+

+

+

- - - - -

8

(i) Describe the energy changes of the electron as it moves between the plates.

[3]

(ii) Hence, or otherwise, determine the electron’s closest distance of approach, x, to

the −50 V plate.

x = m [3] (iii) On Fig. 3.3 below, sketch the variation with the displacement d along the

plates of the electric potential energy, Ep, of the electron.

[2]

Fig. 3.3

Ep

Displacement, d 0

9

4 (a) Define magnetic flux.

[1]

(b) A rectangular loop of wire, of length 8.0 cm and width 5.0 cm, has a resistance of 2.0 Ω.

It is moved towards the right at a constant speed of 2.5 cm s−1 through a region in which there is a uniform magnetic field of flux density 3.5 × 10−2 T. Fig. 4.1 shows the loop just entering the magnetic field at time t = 0.

Fig. 4.1

(i) On Fig. 4.2, sketch a graph to show the variation with time t of the magnetic flux φ through the loop from t = 0 till the loop is completely out of the magnetic field. Indicate relevant values on both axes. [3]

(ii)

On Fig. 4.3, sketch a graph to show the variation with time t of the induced current Ι in the loop from t = 0 till the loop is completely out of the magnetic field. Indicate relevant values on both axes. [2]

5.0 cm

8.0 cm

2.5 cm s−1 20 cm × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × ×

Magnetic field into the paper

t / s

φ / Wb

0

Fig. 4.2

t / s

I / A

0

Fig. 4.3

10

5 (a) Explain using band theory, the difference in the resistivities of semiconductors and insulators. Include a diagram in your answer.

[4]

(b) A single semiconductor crystal can be selectively doped so that one region is n-type

material and the adjacent region is p-type material. Explain how a depletion region is formed at the p-n junction.

[4]

11

6 A simple automatic sliding door consists of the steel door frame, sliding glass panels and infra-red sensors as shown in Fig. 6.1.

Each infra-red sensor consists of an infra-red laser pointer, a photocell and a processing unit as shown in Fig. 6.2.

Fig. 6.2

The light from the laser pointer emerges from an aperture in a continuous infra-red beam and enters through an aperture in the casing of the photocell. The aperture of the laser pointer and that of the photocell are of the same size and perfectly aligned. As the beam of light strikes the emitter of the photocell, photoelectric effect takes place and causes the current through the processing unit to fall to zero. If a person walks through the door frame, he will momentarily block the laser beam from reaching the photocell. This interruption will be interpreted by the processing unit as a signal to open the sliding door. Once the person moves out of the sensor range, the beam is again transmitted to the photocell.

sliding glass panels

Infra-red laser pointers

photocells

Fig. 6.1

Processing unit

laser pointer

metal plates

emitter

A

B

C

D

high resistance

photocell casing

12

(a) Explain what is meant by photoelectric effect.

[2]

(b) On Fig. 6.2,

(i) label the polarities of the metal plates. [1] (ii) trace the complete path of the current when photoelectric effect takes place in the

photocell, indicating clearly the direction of the current. [1] (c) Explain why no current flows through the processing unit when photoelectric effect takes

place.

[2]

The general design specifications of the automatic sliding door are shown in Fig. 6.3.

Width of door frame 3000 mm

Opening speed of each glass panel 0.70 m s−1

Closing speed of each glass panel 0.50 m s−1

Duration for which the door remains open 10.0 s

Wavelength of the infra-red beam 750 nm

Power of the infra-red laser pointer 4.0 mW

(d) A man is moving slowly towards the door at 0.50 m s−1. At a distance of 5.8 m away from the door, the door just begins to open. Using the data given in Fig. 6.3, determine if the door will start closing before he reaches the sensor. [2]

Fig. 6.3.

13

The fall in intensity of the laser beam is measured by α, where

intensity of the beam at distance from the laser pointerintensity of the beam at the aperture of the laser pointer

dα =

Fig. 6.4 shows the variation with d of α.

(e) (i) From the graph, state the value of α when the beam reaches the photocell. α =

[1] (ii) If one in five of the incident photons ejects a photoelectron in the photocell,

calculate the current generated in the circuit.

Current = A [4]

(iii) What property of laser light makes it suitable for use in this design?

[1]

d / m

Fig. 6.4

0.50 1.00 1.50 2.00 2.50 3.00

1.00

0.98

0.96

0.94

0.92

α

14

************ END OF PAPER ************

The automatic sliding door design in Fig. 6.1 is impractical. A more practical design has an additional microwave sensor at the top of the door frame as shown in Fig. 6.5.

Fig. 6.5

(f) Suggest a reason why the additional sensor is needed.

[1]

(g) Name one other application that uses the photoelectric effect.

[1]

microwave sensor