h2 physics exam set g p2

7/27/2019 H2 Physics Exam Set G P2

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H2 Physics Set G Paper 2

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INSTRUCTION TO CANDIDATES

This booklet contains 5 questions.

Do not open this booklet until you are told to do so.

Answerall questions.

Write your answers on this question booklet in the blanks provided.

INFORMATION FOR CANDIDATES

The number of marks is given in brackets [ ] at the endof each question or part question. Marks will bededucted if units are not stated where necessary or ifanswers are not quoted to the appropriate number ofsignificant figures.

All working for numerical answers must be shown.You are reminded of the need for good English andclear presentation of your answers.

Examiners Use

Q1 /10

Q2 /10

Q3 /9

Q4 /16

Q5 /15

Deductions

Total /60


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DATA AND FORMULAE

Dataspeed of light in free space c = 3.00 x 108m s-1

permeability of free space o = 4 x 10-7 H m-1

permittivity of free space 0 = 8.85 x 10-12 F m-1

= (1/(36)) x 10-9 F m-1

elementary charge e = 1.60 x 10- C

the Planck constant h = 6.63 x 10-34 J s

unified atomic mass constant u = 1.66 x 10- kg

rest mass of electron me = 9.11 x 10- kg

rest mass of proton mp = 1.67 x 10- 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

Formulaeuniformly accelerated motion

s = ut +1

2at2

v2 = u2+ 2as

work done on/by a gas W = pV

hydrostatic pressure p = gh

gravitational potential = -Gm/r

displacement of particle in s.h.m. x = xo sin t

velocity of particle in s.h.m. v = vo cos t

= 2 2

o-x x

resistors in series R = R1 + R2+

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

electric potential V = Q/4or

alternating current/voltage x = xo sin t

transmission coefficient T = exp(-2kd)

where k =

2

2

8 ( )m U E

h

radioactive decay x = xo exp(-t)

decay constant

=1

2

0.693

t


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ice cube

d

Answer all the questions in the spaces provided.

1 A glass of water containing an ice cube as shown in Fig. 1.1 is placed in astationary lift.

Fig. 1.1

(a) Express the depth, d, at which the ice cube floats in equilibrium in terms of the density of

ice, ice, density of water, water, and the height of the ice cube, h.

d= ____________ m [2]

(b) The lift now moves upwards with a uniform acceleration a. Show that the ratio of the

depth at which the ice cube now floats, d', to the equilibrium depth, d, from (a), is givenby

'1

d a

d g . [3]

ice cube

dh


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(c) Given that ice = 0.90 g cm-3 and water= 1.0 g cm

-3, determine the acceleration of the liftsuch that the ice cube is just completely submerged.

Acceleration = ________________ m s-2 [3]

(d) State and explain what would happen to the ice cube if the lift were to move upward withacceleration greater than that found in (c).

.

.

.

.

. [2]


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2 (a) A fixed mass of a monatomic ideal gas undergoes a cycle of changes of pressure p,volume Vand temperature Tas shown in Figure 2.1 below.

Figure 2.1

(i) The temperature of the gas at F is 87 C and the process E to F is anadiabatic process. Calculate the temperature of the gas at E.

Temperature of gas at E = ______________ K [2]

(ii) For the process FG, work is done on the gas. Calculate the change inthe internal energy of the gas

Change in internal energy = _________________ J

F

28.320.3

E

G

p /10-

Pa

8.2

15.1

20.2

11.5V/10

-m

-


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[2]

(iii) The gas undergoes a whole cyclic process, EFGE. State and

explain whether heat is absorbed or liberated from the gas.

.

.

.

.

.. [2]

(b) Two students in Dr. Randys class attempt an experiment to find how air pressure varieswith temperature.

They heat identical sealed glass flasks of air, to be considered as an ideal gas, in an oilbath. The flasks are heated from 300 K to 450 K. The pressure in flask A rises fromatmospheric pressure,po, as expected, but the pressure in flask B remains at po becausethe rubber bung is defective and air leaks out of the flask.

Calculate the fraction, f, of gas molecules in flask B compared to flask A at 430 K.

Fraction f= ____________________ [2]

(c) The temperatures of three identical objects A, B and C are TA, TB and TC, and TA


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3 (a) An electron microscope is often used to study the structure of crystals. One of the mainbenefits of using an electron microscope is that it uses electrons to attain resolutions ofup to 1.0 nm.

(i) Determine the accelerating potential required to obtain electrons with wavelengthsof 1.0 nm.

Accelerating potential = _________ V [3]

(ii) Calculate the energy of a photon required to attain the same resolution.

Photon energy = ______________ eV [2]

(iii) The energy of the bonds between typical crystal molecules is about 6.0 eV. Stateand explain if it would be suitable to use photons to study the structure of thecrystals.

.

.

.

.

.. [2]


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..

.. [1]

(c) Free neutrons have a characteristic half-life of 10.4 min. A group of free neutrons hasaverage thermal energy of 0.0400 eV.

(i) Show that the time taken for the neutrons to travel a distance of 10.0 km is 3.61 s.

[2]

(ii) Determine the fraction at which the group of free neutrons with thermal energy0.0400 eV will decay before traveling a distance of 10.0 km.

Fraction = _________________ [2]

(d) State 1 advantage and 1 disadvantage of nuclear fission.

Advantage:

..

..

..

Disadvantage: ...


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..

..

.. [2]

(e) (i) Uranium nuclei may undergo nuclear fission when bombarded by neutron. One

such reaction is 235 1 140 92 192 0 54 38 0U n Xe Sr 2 n .Calculate the energy released per fission event.

The binding energy per nucleon of 23592U is 7.59 MeV,140

54 Xe is 8.29 MeV and that of92

38Sr is 8.65 MeV.

Energy Released = __________________ J [2]

(ii) Suppose enriched uranium containing 3.40% of the fissionable isotope 23592

U is used

as fuel for a ship. The water exerts an average frictional drag of 1.00 x 105 N onthe ship. Calculate the distance which the ship can travel per kilogram of fuel.Assume that the ships engine has an efficiency of 20.0%.


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Distance traveled per kilogram of fuel = ___________________ m [4]

5 Carbon nanotubes have been one of the most exciting new materials discovered in the 1990s.The structure of these cylindrical carbon molecules essentially can be conceptualized to beformed by wrapping a single atomic layer of graphite into a seamless hollow cylinder. Theseare known as single-walled nanotubes, as shown in Fig. 5.1 and Fig. 5.2. Carbon nanotubeshave many interesting properties that make them potentially useful in many applications innanotechnology, electronics, optics and other fields of materials science. They exhibitextraordinary mechanical properties and unique electrical properties, and are efficientconductors of heat.

Mechanical propertiesCarbon nanotubes are among the stiffest and strongest materials known. This is essentiallydue to the strong covalent bonds formed between the carbon atoms. Fig. 5.3 shows a table

which gives the Youngs modulus and breaking strength of three extremely strong materialsknown today.

Material Young's modulus (GPa) breaking strength (GPa)

Single-walled carbon nanotubes ~1000 ~ 53

Stainless Steel ~200 ~0.65

Kevlar ~150 ~3.5

Fig. 5.3

Breaking strength can be defined as force per unit cross-sectional area.

The Youngs modulus of a material is given by the equation

Fig. 5.1 Fig. 5.2


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0

stress applied on object

strain on object

F AE

L L

Eis the Young's modulus (modulus of elasticity)Fis the force applied to the object;A is the original cross-sectional area through which the force is applied;

L is the amount by which the length of the object changes;L0 is the original length of the object.

Electrical conductivityStudies have shown that carbon nanotubes have excellent electrical conductivity, surpassingthat of even silver. This can be attributed to the large amounts of free electrons that arepresent in the structure. Carbon nanotubes have a high electrical current density of4.0 109 A cm-2, a value that is about 1000 times greater than copper.

Thermal ConductivityCarbon nanotubes are very efficient conductors of heat, even much more so than copper ordiamond. It is predicted that the thermal conductivity of carbon nanotubes can reach values of6000 W m-1 K-1 as compared to coppers thermal conductivity of 385 W m-1 K-1. They arethermally stable up to about 3000 K in vacuum and 1000 K in air.

(a) (i) Determine the maximum weight that can be hung from the end of a single-wallcarbon nanotube of cross sectional area of 10 nm2.

Maximum wieght = _______________ N [2]

(ii) Calculate the work done required to extend a carbon nanotube of length 100 nmand cross-sectional area of 100 nm2 by 1% of its original length.


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Work Done = ______________ J [3]

(iii) While carbon nanotubes are very resistant to tensional forces, they are not asstrong when compressional forces are applied. Give a reason for this.

..

..

.. [1]

(b) Thermal conductivity is a measure of how well an object is able to conduct heat energyper unit time. It is dependent on three main factors. Two of the factors are: (i) the powerof the heat incident on the object and, (ii) difference in temperature per unit length of theobject (also known as temperature gradient). By using dimensional analysis or otherwise,suggest an equation for thermal conductivity. Show your workings clearly.

[3]


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(c) With the invention of lasers and its development, there is an increasing need to protectboth the human eye and sensitive optical equipment from laser damage. Currentmaterials used to make protective goggles essentially work like filters. Filters work byblocking out certain wavelengths while allowing other wavelengths to pass through. For

example, a scientist working with red laser would wear safety goggles with red filters,while another scientist working with a blue laser would require a different type of goggleswith a blue filter. This not only means that different goggles are required for protectionagainst different wavelengths of lasers, but it is quite an uncomfortable experience towear such goggles for long periods of time. The filters dramatically reduce the intensity ofambient light entering the eyes, which will reduce visibility and the scientists will seeeverything in the same shade of colour.

Carbon nanotubes offer an exciting prospect as a solution to this problem, with itsexcellent optical limiting properties. Carbon nanotubes are currently being researched toinvestigate these properties. The experiments involve passing high powered lasersthrough a suspension of carbon nanotubes in different solutions and then measuring the

output power. Fig. 5.4 below shows the experiemental results from one such experiment.

Fig. 5.4(i) State which of the three suspensions provides the greatest protection against

lasers.

.. [1]

Suspension A

Suspension B

Suspension C


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(ii) Estimate the percentage reduction in output energy density when the input energydensity is 8.0 J cm-2 when using Suspension C.

Percentage reduction = ________________ [2]

(iii) Using Fig. 5.4, and considering the low light intensity region, deduce why carbonnanotubes are ideal materials for making laser safety goggles.

..

..

..

..

.. [2]

(d) Give 1 possible reason why carbon nanotubes are not widely used commercially.

..

. [1]

End of Paper

h2 physics exam set g p2

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