mjc 2010 h2 physics prelim paper 3x

This document consists of 21 printed pages

MERIDIAN JUNIOR COLLEGE

Preliminary Examinations Higher 2

___________________________________________________________________

H2 Physics 9646/3

Paper 3 15 September 2010

2 hours

___________________________________________________________________ READ THESE INSTRUCTIONS FIRST

Class Reg Number

Candidate Name _____________________________ This booklet contains Sections A and B of the Preliminary exam paper 3.

Do not open this booklet until you are told to do so. Section A Answer all questions.

Section B Answer any two questions.

In the event that all 3 questions are attempted, only the first 2 questions will be marked. You are advised to spend about one hour on each section. Write your answers on this question booklet in the blanks provided.

INFORMATION FOR CANDIDATES

The number of marks is given in brackets [ ] at the end of each question or part question. Marks will be deducted if units are not stated where necessary or if answers are not quoted to the appropriate number of significant figures. All working for numerical answers must be shown. You are reminded of the need for good English and clear presentation of your answers.

Examiner’s Use

Section A

Q1 /8

Q2 /10

Q3 /6

Q4 /8

Q5 /8

Section B

Circle the questions you have attempted

Q6 /20

Q7 /20

Q8 /20

Deductions

Total /80

Preliminary Examination Meridian Junior College 15 September 2010 JC2 H2 Physics 2010

2

DATA AND FORMULAE Data speed of light in free space c = 3.00 x 108

m s-1

permeability of free space µo = 4π x 10-7 H m-1 permittivity of free space ε0 = 8.85 x 10-12 F m-1

= (1/(36π)) 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 + 1

2at2

v2 = u2 + 2as

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 = xo sin ωt velocity of particle in s.h.m. v = vo cos ωt

= ± ω 2 2o -x x

resistors in series R = R1 + R2 + …

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

electric potential V = Q/4πεor alternating current/voltage x = xo sin ωt

transmission coefficient T = exp(-2kd)

where k = π −2

2

8 ( )m U E

h

radioactive decay x = xo exp(-λt ) decay constant

λ

= 1

2

0.693

t


3

Section A

Answer all the questions in this section.

1 (a) A charged body falls vertically in a vacuum near the Earth’s surface. The variation with time t of its vertical speed v is shown in Fig. 1.1 below.

Fig. 1.1 An electric field induces a horizontal force on the body that causes the body to accelerate horizontally at 2.25 m s-2. Calculate the displacement of this body after 0.50 s falling from rest.

displacement = ................................m

angle = ........................... [4]

v/ m s-1

t/ s 0


4

(b) Another object moving in a straight line has a graph of the variation with time of its

velocity shown in Fig. 1.2.

Fig. 1.2

(i) Sketch on Fig. 1.2, a graph of the variation of the acceleration with

time for the same object within the same time frame.

[2]

(ii) Explain your sketch in (i) between time t1 and t2.

…………………………………………………………………………………………........

………………………………………………………………………………………….......

……………………………………………………………………………………..... [2]

0 t2 t1

v/ ms-1

t/ s


5

2 (a) It is often assumed that air resistance acting on a moving object will result in the

object slowing down. Air resistance can however indirectly make an object speed up. Consider a 1000 kg satellite orbiting at 280 km above the Earth’s surface. A small force of air resistance makes the satellite descend into a circular orbit with an altitude of 100 km. [Radius of Earth = 6.37 x 106 m, mass of Earth = 5.98 x 1024 kg]

(i) By calculating the speed of the satellite at both orbits, show that the satellite

is indeed travelling faster at the lower orbit. [3]

(ii) Show that the total mechanical energy of the satellite, E can be expressed

as:

E s

o2= −

GM mE

R where ME is the mass of earth, ms is the mass of satellite and, Ro is the

radius of orbit. [2]


6

(iii) Explain the significance of the negative sign in the expression for the total

mechanical energy of the satellite.

…………………………………………………………………………………........

…………………………………………………………………………………........

…………………………………………………………………………….....

[1]

(iv) Hence, calculate the change in mechanical energy due to air resistance.

change in mechanical energy = ……………….. J [2] (c) Black holes are formed when massive stars collapse towards a singularity i.e. a

point mass. There exist a boundary, known as the event horizon, surrounding a black hole where a even body travelling at the speed of light (if it is possible) can barely escape. Consider the gravitational potential energy of the body at the event horizon, deduce an expression for the radius of the event horizon, event horizonR in terms of

the mass of the black hole, M and speed of light c.

event horizonR = ……………….. [2]


7

3

(a) A thin layer of copper is deposited uniformly on the surface of an iron wire of radius 0.60 mm and length 3.0 m shown in Fig. 3.1.

Fig. 3.1 (Not to scale) Determine the effective resistance between the ends of the copper-plated wire, given that the thickness of the copper is 1.78 x 10-5 m. [Resistivity of iron = 8.90 x 10-8 Ω m; resistivity of copper = 1.60 x 10-8 Ω m]

effective resistance = .......................... Ω [3]

iron wire

thin layer of copper

I


8

(b) Fig. 3.2 shows a system in which an unmodulated audio frequency signal is

transmitted from the transmitter to the receiver through a cable. The cable consists of two strands of insulated copper wire.

Fig. 3.2 The power output of the transmitter is 12.5 mW and the corresponding current in each wire is 2.5 mA. Power is lost to the surroundings due to the rise in temperature produced by this current. For transmitted signal to be detected the power input to the receiver must be at least 1.5 mW. The resistance of each 1.0 m of the copper wire used in the cable is 0.27 Ω.

Calculate the maximum distance between the transmitter and receiver at which the

transmission can be detected successfully. maximum distance = ……………………m [3] 4 (a) State Faraday’s law of electromagnetic induction.

………………………………………………………………………………………….......

………………………………………………………………………………………….......

……………………………………………………………………………………...... [1]

I

insulation

transmitter 12.5 mW

receiver

copper wire


9

(b) A long straight wire carries a direct current. A rigid loop of conducting wire is

placed near the wire such that the wire is in the plane of the loop. The loop is moved at constant speed away from the wire as shown in Fig. 4.1.

(i) Explain why an e.m.f. is induced in the loop.

…………………………………………………………………………………………........

…………………………………………………………………………………………........

…………………………………………………………………………………………........

……………………………………………………………………………………...... [2]

(ii) On Fig. 4.1, draw an arrow to indicate the direction of the current induced in

the loop and explain your answer below.

…………………………………………………………………………………………........

…………………………………………………………………………………………........

…………………………………………………………………………………………........

……………………………………………………………………………………...... [2]

(iii) It was found that energy is dissipated in the wire loop. Explain how the

movement of the loop gives rise to energy dissipation.

………………………………………………………………………………………….........

…………………………………………………………………………………………........

………………………………………………………………………………………….......

………………………………………………………………………………………….......

……………………………………………………………………………………...... [3]

wire

current

conducting loop

direction of motion of loop

Fig. 4.1


10

5 (a) Explain what is meant by internal energy of a system.

…………………………………………………………………………………………........

…………………………………………………………………………………………........

……………………………………………………………………………………...... [2]

(b) The temperature, T of an ideal gas at pressure p is defined by the equation

p = nkT

(i) Identify the quantity n.

……………………………………………………………………………………...... [1]

(ii) State an equation relating k and R, molar gas constant.

……………………………………………………………………………………...... [1]

(c) State the process and give one practical example of each of the following : (i) a process in which heat is supplied to a system without causing an increase

in temperature.

…………………………………………………………………………………………........

…………………………………………………………………………………………........

……………………………………………………………………………………...... [2]

(ii) a process in which no heat enters or leaves a system but the temperature

changes.

…………………………………………………………………………………………........

…………………………………………………………………………………………........

……………………………………………………………………………………...... [2]


11

Section B

Answer two questions in this section. 6 (a) (i) State Newton’s 1st law of motion and show it leads to the concept of force.

…………………………………………………………………………………………........

…………………………………………………………………………………………........

…………………………………………………………………………………………........

……………………………………………………………………………………....... [2]

(a) (ii) Express the unit of force in terms of S.I. base units.

S.I. base units of force is ….....……………

[1] (b) Michael drove a car of mass 1200 kg which had a maximum speed of 150 km h-1.

During a driving test, it was found that the average retarding force from the air and ground added up to 1200 N when the car was accelerating uniformly.

(i) Calculate the forward driving force when the car accelerated uniformly from rest to the maximum speed in 11.0 s under driving test conditions.

forward driving force= ……………… N [3]


12

(ii) Hence, find the maximum power delivered by the engine.

maximum power = ……………… W [2] (c) Michael wishes to find out how his car will fare during a car crash. He visited a

laboratory where several cars like his own were used in controlled car crash testing. The magnitude F of the force required to crush the barrels was shown below in Fig. 6.1 as a function of the distance x the automobile had moved into the cushion. In a particular crash test, the car was travelling at 100 km h-1 before it struck a crash cushion in which the car was brought to rest by successively crushing steel barrels.

(i) Neglecting friction, predict by using the Work Energy Theorem the distance the car would move into the cushion of steel barrels before coming to rest.

distance = ……………… m [4]

y

x

Fig. 6.1

170

130

90

0.0 1.5 4.0

F / kN

x/ m


13

(ii) State and explain in terms of energy considerations whether the actual

distance will be longer or shorter than the value in (c)(i).

…………………………………………………………………………………………........

…………………………………………………………………………………………........

…………………………………………………………………………………………........

……………………………………………………………………………………....... [2]

(d) Michael parked his 1200 kg car at an underground carpark in Orchard Road. It

started to rain very heavily and rainwater quickly entered and filled the underground carpark such that Michael’s car is floating in the water as shown in Fig. 6.2. The total volume of the car is 6.43 m3 and the volume of air space in the car is 5.50 m3. [Density of rainwater = 1000 kg m-3]

(i) State Archimedes’ principle.

…………………………………………………………………………………………........

……………………………………………………………………………………...... [1]

(ii) Initially, no water enters the passenger compartment. Determine the volume

of car below the water surface when the car is floating as shown in Fig. 6.2.

volume of car = …………………….. m3 [2]

Fig. 6.2


14

(iii) Water slowly enters the car. Determine the volume of water in the car at the

point when it first disappears completely below the water surface. (Assuming that the car remains horizontal throughout the sinking process)

volume of water = …………………… m3 [3]


15

7 (a) Define the Tesla.

………………………………………………………………………………………….......

………………………………………………………………………………………….......

……………………………………………………………………………………...... [2]

(b) Fig. 7.1 shows an arrangement used to accelerate an initially stationary alpha

particle and make it travel in a uniform magnetic field.

Fig. 7.1

(i) On Fig. 7.1, draw a possible trajectory of the alpha particle in the uniform

magnetic field. [1] (ii) Explain whether the force experienced by the alpha particle due to the

magnetic field changes its kinetic energy.

………………………………………………………………………………….........

…………………………………………………………………………………........

………………………………………………………………………………….........

…………………………………………………………………………………........

……………………………………………………………………………........ [3]

Vacuum

B

alpha emitter

A

4.0 kV Uniform magnetic field of 2.00 T directed into the

plane of the paper

Path of alpha particle

Region W


16

(iii) Show that the alpha particle will attain a speed of 6.21 x 105 m s-1 when it

reaches the slit opening of plate B. [ 27Mass of alpha particle 6.644 10 kg−= × ] [1]

(iv) Calculate the electric field that needs to be applied in Region W for the

alpha particle to pass through the uniform magnetic field undeflected.

Magnitude of electric field = ………………..

[2]

Direction of Electric Field = ………………..

[1]

(c) Suppose that the arrangement in Fig. 7.1 is now modified so that the alpha particle

enters the uniform magnetic field at an angle of o30 to the horizontal as shown in Fig. 7.2 below.

Fig 7.2

Uniform magnetic field of 2.00 T directed along the

plane of the paper

Vacuum

B

alpha emitter

A

4.0 kV

300


17

The motion of the alpha particle can be described as a helix as shown on Fig. 7.3 below.

Fig. 7.3

(i) Calculate the radius r of the helical path.

radius r = ………………..m [2]

B field

v

300

Helical path of alpha particle in uniform B Field

+qα

Pitch, p

Cross – section of helical path

r Radius, r

B field


18

(ii) Show that the period, T of the helical path can be expressed as:

2 m

Tq B

α

α

π=

where mα and qα is the mass and charge of the alpha particle respectively.

[1]

(iii) Calculate the pitch, p.

pitch, p = ………………..m [3]

(iv) Describe and explain how the helical path will change if a positron, 01e

++ (i.e.

a particle with the mass of an electron and charge 191.6 10 C−+ × ) with the same initial velocity was to be used in the experiment instead. You may quote relevant equations to substantiate your answer.

.......……………………….……………………………………………………….….

.......……………………….……………………………………………………….….

.......……………………….……………………………………………………….….

….………………………………………………………………………………........

........………………………………………………………………………………......

..........…………………………………………………………………………………

……………………………………………………………………………........

[4]


19

8 (a) The X-ray spectrum is first produced by an X-ray tube with tungsten (atomic

number, Z = 74) anode. Another X-ray spectrum is then produced using barium (atomic number, Z =56).

Fig. 8.1

(i) Describe how the characteristic X-ray spectrum is formed.

………………………………………………………………………………..…........

………………………………………………………………………………..…........

………………………………………………………………………………..….......

………………………………………………………………………………..…........

………………………………………………………………………………..…........

……………………………………………………………………………........ [4]

(ii) The accelerating potential used to produce the X-ray spectra using tungsten

and barium are the same. Explain how this can be deduced from Fig. 8.1.

…………………………………………………………………………………..........

……………………………………………………………………………........ [1]


20

(iii) Hence calculate the accelerating voltage for the barium spectrum.

accelerating voltage = …………....…. V

[2]

(iv) Explain the difference between the intensity of the Kα- line of the tungsten

and barium spectrum.

…………………………………………………………………………………..........

………………………………………………………………………………….........

……………………………………………………………………………........ [2]

(v) Calculate the minimum accelerating potential to produce Kα – line for

tungsten. Hence sketch on Fig. 8.1 without any additional numerical labels, the spectrum for tungsten if the accelerating potential is reduced to 50 kV.

minimum accelerating potential = …………....…. V

[3]

(b) An X-ray machine is accelerating electrons through a p.d. of 200 kV. The current is 25 mA. The target is a heavy metal mass 1.0 kg, and specific heat capacity 300 J kg K-1 and has a melting point of 3000 K. The machine is at 300 K when it is first started. While the machine is operating, the cooling fails and its temperature increases by 16.5 K within a second.

(i) Calculate efficiency of X-ray production.

efficiency of X-ray production = .....................%

[2]


21

(c) Fig. 8.2 below shows portions of the energy-level diagrams of the helium (He) and

neon (Ne) atoms. The He atom is excited from its ground state to state of 20.61 eV. The excited level of helium at 20.61 eV is very close to a level in neon at 20.66 eV. Upon collision with a neon atom, the energy can be transferred from the helium to the neon atom. This excites the Ne atoms to the E3 state at 20.66 eV. Lasing action takes place for electron transitions from E3 to E2 in the Ne atoms.

(i) State any two unique characteristics of laser light.

………………..………………………………………………………………….......

…………………………………………………………………………….......

[1]

(ii) Explain what is meant by population inversion and how energy state E3 in Ne enables lasing to occur.

………………..………………………………………………………………….......

………………..………………………………………………………………….......

………………..………………………………………………………………….......

………………..………………………………………………………………….......

…………………………………………………………………………….......

[3]

(iii) Explain why direct optical pumping (the supply of photons) excitation method using photons of energy ∆ E = E3 - E1 on Neon atom, in the absence of He atom, is generally not used.

………………..…………………………………………………………………......

………………..…………………………………………………………………......

………………..………………………………………………………………….......

…………………………………………………………………………….......

[2]

End of Paper

Ene

rgy

20.61 eV

Ground state

E3

Collision

18.70 eV Lasing

Helium Atom Neon Atom

E2

E1

Fig. 8.2

mjc 2010 h2 physics prelim paper 3x

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