Carmel Divine Grace Foundation Secondary School

PHYSICS(A-LEVEL)

PAPER I

Name: ______( ) Date: 25-2-98

Time: 3 hours

Class: S.7 B No. of pages: 18

i. This paper carries 120 marks.

ii. Answer ALL questions.

iii. Write your answers in the spaces provided in this question/answer paper. In calculations you should show all the main steps in your working.

iv. Assume : velocity of light in air = 3 x 108 ms-1

acceleration due to gravity = 10 m s-2

1. Figure 1.1 shows a small block of mass m is connected vertically to the ceiling and the floor by two identical springs.

ceiling ceiling

Figure 1.1

floor floor

Initially, the upper spring and the lower spring are stretched with amounts e1 and e2 respectively. The force constant of each spring is 5 N m-1. The block is now slightly displaced vertically from the equilibrium position and is released from rest. (Assume that both springs are always in tensions.)

(a) Write down the expressions

(i) relating e1 and e2. (1 mark)

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(ii) for the tensions T1 and T2 in the spring when the block is at a upward displacement y from the equilibrium position. (1 mark)

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(b) Show that the motion of the block is simple harmonic. (3 marks)

______

gravitational potential energy

Figure 1.2

time /s

(i) Using crosses, indicate on the graph the points corresponding to the time at which the block is at its extreme positions. (1 mark)

(ii) Find the period of oscillation and the mass of the block. (4 marks)

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(d) State the changes, if any, in the period of oscillation if

(i) the height of the ceiling increases; (1 mark)

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(ii) the lower spring is removed. (1 mark)

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2. In Figure 2, a uniform magnetic field B pointing into the paper and a uniform electric field E pointing upwards are applied on the left-hand side and the right-hand side of positive y-axis respectively. The region below x-axis is field free. Neglect the gravitational effect.

Suppose a charged particle of mass m and charge q enters the magnetic field with an initial velocity v0 at point P. After leaving the magnetic field, it moves into the electric field and leaves it at point S.

Figure 2

field free region

(a) What is the sign of the charge carried by the particle? (1 mark)

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(b) Find the radius of curvature of its motion in the region of the magnetic field B in terms of m, q, B and v0. (2 marks)

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(d) If the uniform magnetic field is also applied to the region with the uniform electric field, how would the speed vS of the charged particle at point S be affected? Explain briefly. (2 marks)

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3. Figure 3.1 shows three of the characteristics of an n-p-n transistor.

IB / mA IC / mA

1.2

0 VBE / V 0 IB / mA

0.8 10

IC / mA

7.2 IB = 60 mA

4.8 IB = 40 mA

2.4 IB = 20 mA

0 0.2 VCE / V

Figure 3.1

The following circuit is connected to investigate the input/output voltage characteristics of the transistor.

6 V

RL=2.2 kW

Vout

IB RB=15 kW

Vin

0 V

(a) Find the values of IC , IB and Vin when the transistor is just saturated. (3 marks)

______

(b) Sketch the input/output voltage characteristics of the transistor on the following diagram, inserting the results in part (a) and their corresponding values of Vout.

(3 marks)

Vout/ V

0 Vin/ V

______

(d) The voltage amplification of the above transistor circuit depends on the current amplification factor b. Unfortunately, b varies greatly even among the same model of transistors. The following circuit design overcomes this drawback.

Vout

Vin

0 V

(i) Express IC in terms of Vout and RC. (1 mark)

______

(ii) Express IE in terms of Vin and VBE. (1 mark)

______

(iii) Show that the voltage amplification of the circuit is given by

(3 marks)

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(iv) State one assumption in your calculation. (1 mark)

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Figure 4.1

Figure 4.1 shows a metal wire of mass per unit length 2 g m-1. Two bridges are separated by a distance of 0.8 m and a large magnet is placed mid-way between them. A 0.50 kg mass is suspended to provide tension to the wire. When an alternating current supplied by a signal generator is made to flow through the wire, it oscillates.

(a) Explain why the wire oscillates when an alternating current flows through it.

(2 marks)

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(b) Suggest TWO ways to increase the amplitude of the oscillation of the wire without varying the frequency of the signal generator. (2 marks)

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(d) As the wire oscillates, sound is emitted. State THREE differences between the waves in the wire and the sound emitted. (3 marks)

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Figure 5.1

Figure 5.1 shows a conducting disc which can rotate freely about its axle. When a horseshoe magnet is made to rotate in front of the disc, it starts to rotate in the same direction as the magnet.

(a) Explain the rotation of the disc. (2 marks)

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(b) Should the disc rotate at a higher or lower angular velocity than the horseshoe magnet ? (1 mark)

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The horseshoe magnet is replaced by a uniform magnetic field B . B is perpendicular to the plane of the disc, as shown in Figure 5.2. The disc is spinning about its axle. The angular velocity w of the disc is kept constant by a torque t (not shown) acting on the disc. The disc is connected to an external circuit.

Figure 5.2

voltage output

(d) Deduce an expression for the e.m.f. e generated between the centre and the rim

of the disc in terms of B, w and the radius of the disc r. (2 marks)

______

(e) Given the following information of the disc generator:

radius r = 0.82 m

internal resistance = 2 W

current output = 2 A

voltage output = 1.5 V

strength of magnetic field B = 1.2 T

Find

(i) the e.m.f. e,

(ii) the angular velocity w,

(iii) and the torque t . (6 marks)

______

(f) Figure 5.3 shows a braking system of a motor. A conducting disc is attached to the axle of the motor and passes between the poles of an electromagnet. When a circuit in the electromagnet is switched on, the motor slows down.

Briefly explain the principle of the braking system. (2 marks)

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6. Figure 6.1 shows the essential structure of an X-ray tube. The electrons from the heated cathode are accelerated by an accelerating voltage of 100 kV. X-rays are produced when the target in the anode is bombarded by the electrons. The spectrum of the X-rays emitted is shown in Figure 6.2.

Figure 6.1 Figure 6.2

Given : Planck constant = 6.6 x 10-34 J s

Electronic charge = 1.6 x 10-19 C

velocity of light = 3 x 108 m s-1

(a) Suppose the power supplied to the X-ray tube is 600 W. Calculate the number of electrons bombarding the target per second. (2 marks)

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(b) Find the minimum wavelength l0 of the X-ray photons. (2 marks)

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Label the discrete lines on Figure 6.2. (6 marks)

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7. fluorescent tube

Figure 7.1

line switch 220 V 50 Hz inductor (ballast)

Figure 7.1 shows a simplified circuit of a florescent tube. An inductor acting as a ballast is connected in series with the fluorescent tube and an a.c. supply.

(a) After being switched on, the current in the circuit is 0.5 A r.m.s. and the power delivered to the circuit is 60 W.

(i) Find the power factor of the circuit. (2 marks)

______

(ii) What is the phase angle between the current in the ballast and p.d. across it ? (Assume that when the fluorescent tube conducts, its resistance is negligible). (1 mark)

______

(iii) Calculate the resistance and the inductance of the ballast. (4 marks)

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(b) Figure 7.2 shows a detail diagram of the fluorescent tube circuit with an automatic starter. The starter is a neon-filled glass bulb, containing a bi-metallic strip and a fixed, normally open contact.

electrodes

filled with inert gas and small droplets of mercury

Figure 7.2

When the line switch is closed, the bi-metallic strip of the starter bends towards the contact . As the strip touches the contact, it restores to its original position at once.

(i) Explain this phenomenon. (2 marks)

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(ii) Explain how the starter help to initiate the discharging process in the tube.

(2 marks)

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(iii) Explain why a layer of fluorescent material is coated inside the fluorescent tube. (1 mark)

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8. Figure 8.1 shows a hydroelectric power station. The inlet pipe of cross sectional area 1 m2 is located at a depth of 100 m below the water surface, with one end inside a reservoir and the other end joined to a water turbine. The pressure P1 in the inlet pipe is 3 x 105 Pa. The atmosphere pressure is 1 x 105 Pa. The density of water is 1000 kg m-3.

Figure 8.1

(a) Find the average flow speed v1 of the water in the inlet pipe. (2 marks)

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Water passing through the turbine flows out through the outlet pipe which has a cross-sectional area of 2 m-3 . The pressure P2 in the outlet is 1.2 x 105 Pa.

P1 = 3 x 105 Pa P2 = 1.2 x 105 Pa

1 m2 v1 ® 2 m2 v2 ®

inlet pipe turbine outlet pipe

(b) Find the average flow speed v2 of the water in the outlet pipe. State one assumption of your calculation. (3 marks)

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(d) By considering the work done per unit mass of water at the inlet and the outlet pipe , find the work done on the turbine by a unit mass of water. (4 marks)

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(e) Find the mechanical power delivered to the turbine. (2 marks)

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9. A student investigate the optical spectrum of hydrogen. A low pressure hydrogen discharge tube is connected to an E.H.T. supply. A spectrometer is then adjusted. Finally, a diffraction grating is placed on the platform of the spectrometer.

(a) Briefly explain how an line emission spectrum is produced by a discharge tube.

(3 marks)

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(b) Figure 9.1 shows the essential feature of a spectrometer. Necessary adjustments on the collimator and the telescope have already been made.

Figure 9.1

Draw on Figure 9.1 two rays from the discharge tube to the eye of the student through the spectrometer. (2 marks)

(c) To observe the spectrum of hydrogen, the student places the diffraction grating on the platform of the spectrometer such that the incident light falls normally on the grating. He records the angular position readings of a particular bright coloured line on each side of the central image as follows:

Left-hand side
(Second-order) / Right-hand side
(Second-order)
angular position reading / 550 20' / 1250 40'

(i) Given the grating constant (i.e. the slit separation) to be 1684 nm, calculate the wavelength of that coloured line.

State its colour. (4 marks)

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(ii) Suggest ONE reason for making measurements by using the second-order images instead of the first-order ones. (1 mark)

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(d) The student recalls from the textbook that the energy levels of a hydrogen atom are given by -13.6/n2 eV, where n is an integer.

Identify the transition which probably given rise to the bright line in (c). Show clearly any calculations you make.

Given : Planck constant = 6.6 x 10-34 J s

Electronic charge = 1.6 x 10-19 C

velocity of light = 3 x 108 m s-1 (3 marks)

______

10. / (a) / A capacitor C1 is given an initial charge Q . It is then shares its charge with an uncharged capacitor C2 as shown in Figure 10.1.

+Q1 C1 +Q2 C2

Figure 10.1

-Q1 -Q2

(i) Find the final charges Q1 and Q2 on the capacitors in terms of C1 , C2 and Q. (4 marks)

______

(ii) Hence, find the final charge Q2 on C2 if the capacitance of C2 is much greater than that of C1 . (1 mark)

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(b) A voltmeter V, a 10 mF capacitor C, a switch S and an operational amplifier are connected as shown in Figure 10.2. The circuit called a coulomb-meter is used to measure the charge on an unknown capacitor which has a capacitance much smaller than 10 mF.

Vin Vout