Name: ……………………….…………………. HT group: …………... CATHOLIC JUNIOR COLLEGE JC1 PROMOTIONAL EXAMINATION 2008 0800 – 1100 hrs PHYSICS 9745 Higher 2 Thursday 2 nd October 2008 3 hours Additional materials: MCQ answer sheet for Section A Writing paper for Section B READ THESE INSTRUCTIONS FIRST There are 20 questions in Section A. Answer all questions. Record your answer in soft 2B pencil on the MCQ answer sheet. Each correct answer will score two marks. Marks will not be deducted for a wrong answer. Any rough working should be done in this booklet. There are 9 questions in Section B. Answer all questions. Begin each new question on a fresh sheet of writing paper. Write in dark blue or black pen on the writing paper provided. You may use a soft pencil for any diagrams, graphs or rough working. The number of marks is given in brackets [ ] at the end of each question or part question. Total marks for Section B is 100 marks. Do not use staples, paper clips, highlighters, glue or correction fluid. Write your name and tutorial group on all the work you hand in. Total marks for Section A and B is 140 marks. A maximum of 2 marks will be deducted for mistakes made in units and significant figures. This question paper consists of 17 printed pages
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Name: ……………………….…………………. HT group : …………...
CATHOLIC JUNIOR COLLEGE JC1 PROMOTIONAL EXAMINATION 2008
0800 – 1100 hrs
PHYSICS 9745 Higher 2
Thursday 2nd October 2008 3 hours
Additional materials: MCQ answer sheet for Section A Writing paper for Section B
READ THESE INSTRUCTIONS FIRST
There are 20 questions in Section A . Answer all questions.
Record your answer in soft 2B pencil on the MCQ answer sheet.
Each correct answer will score two marks. Marks will not be deducted for a wrong
answer.
Any rough working should be done in this booklet.
There are 9 questions in Section B . Answer all questions.
Begin each new question on a fresh sheet of writing paper.
Write in dark blue or black pen on the writing paper provided. You may use a soft
pencil for any diagrams, graphs or rough working.
The number of marks is given in brackets [ ] at the end of each question or part
question.
Total marks for Section B is 100 marks.
Do not use staples, paper clips, highlighters, glue or correction fluid.
Write your name and tutorial group on all the work you hand in.
Total marks for Section A and B is 140 marks.
A maximum of 2 marks will be deducted for mistakes made in units and
1 The Stefan-Boltzmann law states that R, the total energy radiated by a blackbody per unit surface area
per unit time is given by R = σT4, where σ is the Stefan-Boltzmann constant, and T is the
thermodynamic temperature of the blackbody. What is the base unit of σ?
A kg s-3 K-4 B kg s-3 K4 C kg m2 s-2 K-4 D kg m2 s-2 K4
[ ] [ ][ ] [ ]
4-3-4
2
22
44
4
K s kg==
==
=−
K
sm
smkg
T
At
E
T
R
TR
σ
σ
2 Four students A to D measured and calculated the electronic charge, e. The table shows the results
obtained. Which student obtained a set of results that could be described as accurate but not precise?
Student Electron charge, e / 10-19 C
A 1.62 1.59 1.59 1.61 1.60
B 1.57 1.63 1.64 1.58 1.59
C 1.59 1.60 1.58 1.57 1.57
D 1.58 1.62 1.65 1.59 1.66
Student Electron charge, e / 10-19 C Average / 10-19 C
Conclusion
A 1.62 1.59 1.59 1.61 1.60 1.60 P, A B 1.57 1.63 1.64 1.58 1.59 1.60 NP, A C 1.59 1.60 1.58 1.57 1.57 1.58 P, NA D 1.58 1.62 1.65 1.59 1.66 1.62 NP, NA
3 A ball rolls off the top of a flight of steps. Assuming elastic collisions with the steps, which graph
shows the variation of the resultant vertical force, F acting on it with respect to time, t?
1 (a) During a laboratory class, Christopher used the vernier callipers to measure the diameter of a Styrofoam ball. He recorded the ball’s diameter as (5.28 ± 0.01) cm. Looking up the density table of materials, he found that the density of Styrofoam is 150 kg m-3.
(i) Calculate the mass, in kg, of the Styrofoam ball.
[2]
( )]1A[kg1016.1
1028.515061
]1M[d61
2d
34
r34
m
2
32
3
3
3
−
−
×=
×××π=
πρ=
πρ=
πρ=
(ii) Calculate the fractional uncertainty in the mass of the Styrofoam ball.
[2]
]1A[1068.528.501.0
3
]1M[dd
3mm
d61
m
3
3
−×=
×=
∆=∆
πρ=
(iii) Hence express the mass of the Styrofoam ball, together with its uncertainty, to an
appropriate number of significant figures.
[2]
]1M[kg1056.6
1016.11068.5m
1068.5mm
5
23
3
−
−−
−
×=×××=∆
×=∆
( ) kgmm 51071160 −×±=∆± [A1]
(b) Christopher then put the Styrofoam ball in a basin of water of density 1000 kg m-3 and observed
that the ball is floating on water.
(i) State the condition which must be satisfied in order for the Styrofoam ball to float on water.
[1]
Upthrust on Styrofoam ball = Weight of Styrofoam ball (Principle of Flotation) [B1]
(ii) Hence calculate the fraction of the Styrofoam ball submerged in water. [2]
]1A[15.01000150
f
]1M[gVgfV
WU
water
ball
ballwater
=
=
ρρ
=
××ρ=××ρ=
(iii) Describe what will happen when the Styrofoam ball is transferred into a basin of sea water.
[1]
Since density of sea water is greater than the density of fresh water, the fraction of Styrofoam ball submerged in water is less. [B1]
2 An C-130 transport aeroplane is flying horizontally at an altitude of 20 metres and it flies at a constant velocity of 50 ms-1. A supply package is dropped out of the the plane at the instant shown in the diagram below. Assume air resistance is negligible.
Figure 2
(i) What is the time taken for the package to reach the ground? [2]
stt
atuts
02.2)81.9(2
120
2
1
2
2
=⇒=
+=
M1
A1
(ii) What is the speed of the package just before hitting the ground? [2]
12222
1
77.538.1950
8.19)02.2(81.9
−
−
=+=+=
==+=
msvvv
msatuv
yx
y
M1
A1
(iii) What is the angle to the horizontal at which the package hits the ground? [2]
(iv) Ignoring the effect due to air resistance sketch on the same graph showing how the horizontal and vertical velocities vary with time.
[2]
Assume downward direction is positive and left direction is positive as well.
B2 for shape.
(v) If the package was pushed backwards out of the plane at 2 ms-1 relative to the
plane, explain qualitatively how would your answer in part (i) and part (ii) be
affected?
[2]
Actual initial speed of package reduced to 48.
No change to part (i),
but reduces the resultant velocity in part (ii)
B1
B1
3 A red ball, of mass 0.3 kg and velocity 10 m s–1, collides elastically and head-on with a blue ball, of mass 0.2 kg and velocity 15 m s–1, moving in the opposite direction
(a) (i) State the law of conservation of momentum. [2] In an isolated system
Total momentum is conserved. B1 B1
(ii) State the condition for a collision to be considered elastic. [1] Kinetic energy is conserved. B1 (iii) What do you expect to see in the subsequent motion if the collision is head on. [1] Velocities before and after collision are in a straight line B1 (b) Find the relative velocity of separation of the two vehicles after the collision [2] 1
1221 25)15(10 −=−−=−=− msvvuu
(c) Hence, or otherwise, find the respective magnitude of the final velocities of the two balls [4]
(d) Extra energy is required from the engine to maintain constant speed in the loop.
Suggest two possible reasons.
[2]
Work done against air resistance
Work done against gravity
B1
B1
5 (a) Explain the term simple harmonic motion. [2] Oscillatory motion such
that the acceleration is always proportional to (x0), the displacement from a fixed point. and it is directed always toward the fixed point.
B1 B1
(b) (i) State the defining equation for simple harmonic motion [1]
0
2xa ω−= A1
(ii) Write down a solution to the equation giving the displacement x in terms of the amplitude of oscillation x0, the angular frequency ω and the time t
[1]
txx ωcos0= A1
(c) The velocity v of a body of mass m undergoing simple harmonic motion is given by, 22 xxv o −±= ω
Find the kinetic energy of the body in terms of its displacement x, and ω and x0
[1]
)(
2
1
2
1 220
22 xxmmvKE −== ω A1
(d) Sketch two separate graphs, to show how the velocity and kinetic energy vary with the displacement of a body undergoing simple harmonic motion.
6 This question is about the physics of seismic waves. When an earthquake occurs, two kinds of seismic wave travel from their source through the body of the earth. Primary or P waves have the greater speed and are longitudinal. The slower Secondary or S waves are transverse.
(a) The diagram shows a Secondary wave approaching a tall building from underneath. Copy and indicate, with a double-headed arrow, in which direction you would expect the building to vibrate when the wave reaches it.
Figure 6.1
[1]
B1
(b) The centre of an earthquake produces both longitudinal waves (P waves) and transverse waves (S waves). The graph below shows the variation with time t of the distance d moved by the two types of wave. d / km
(c) The waves from an earthquake close to the Earth’s surface are detected at three laboratories L1, L2 and L3. The laboratories are at the corners of a triangle so that each is separated from the others by a distance of 900 km, as shown in the diagram below.
L L
L
1 2
3
900 km
Figure 6.2
The records of the variation with time of the vibrations produced by the earthquake as detected at the three laboratories are shown below. All three records were started at the same time.
time
start of trace
L
L
L
1
2
3
Figure 6.3
On each record, one pulse is made by the S wave and the other by the P wave. The separation of the two pulses is referred to as the S-P time interval. The S-P time intervals are 68 s, 42 s and 27 s for laboratories L1, L2 and L3 respectively.
(i) Use the formula “speed = distance / time” to write an expression for the distance, in m, traveled by the P waves, dp, from the source to station L1.
[1]
ttspeedd Pp 9600==
(ii) Hence write an expression for the distance traveled by the S waves, ds, from the source to the L1 seismological station.
[1]
)68(5818)( +=+= tttspeedd SPSS
(iii) Given that dp = ds, calculate the time taken for the P waves to travel from the source to the L1 seismological station.
[1]
st
tt
6.104
)68(58189600
=+=
(iv) Hence determine the distance from the source to L1. [1]
(v) Hence, derive a formula that you can use to determine the distance from the source to L1, in terms of vP (the speed of the P wave), vS (the speed of the S wave), and tSP (the S-P time interval).
[1]
kmtt
vv
tvvtvd
vv
tvt
ttvtv
SPSP
sp
SPSPpp
sp
SPS
SPsp
768.1458189600
)5818)(9600(
)(
=−
=
−==
−=
+=
(vi) Determine the distance from the source to the seismological station for L2 and L3. [2]
kmd
kmd
L
L
398)27(768.14
620)42(768.14
3
2
====
(vii) Copy diagram A and show how you could determine a possible site of the epicenter of the earthquake. (label the point E)
[2]
L L
L
1 2
3
900 km
(B1 for arcs drawn)
B1 for correct location (rough)
(viii) State one assumption made in this method of calculation that might lead to inaccurate results.
[1]
The calculation assumes the earthquake originates at the surface of the Earth instead of below the surface.
B1
7 (a) State what is meant by
(i) an electric field of force, [1]
(ii) a gravitational field of force. [1]
[(a)(i) An electric field of force is a region around an electric charge in which an electric force is exerted on another electric charge. [B1] (a)(ii) A gravitational field of force is a region around a body of finite mass in which a gravitational force is exerted on another body of finite mass. [B1]
(b) Two ions A and B are separated by a distance of 0.80 nm in a vacuum, as shown in Figure
7.1. A has a charge of +3.2 x 10-19 C and B has a charge of -1.6 x 10-19 C. A point X is positioned vertically above B, at a distance 0.50 nm. Copy Figure 7.1 and draw labeled arrows to represent
(i) the electric field EA at the point X due to A only,
[1]
(ii) the electric field EB at the point X due to B only.
[(i) arrow points away from A; arrow should be along the line joining A and X. [B1] (ii) arrow points towards B; arrow should be along the line joining B and X. [B1]
(iii) the resultant field E at the point X.
[1]
[Completes vector diagram to show magnitude and direction of E. Makes use of answer in d(i) for direction. [B1] ]
(c) (i) Sketch on the diagram in (b), lines representing the electric field between the two ions. Include the field line passing through X.
[4]
[no. of field lines leaving A is twice that terminating at B. [B1] Shape of field lines. [B1] Direction of field lines. [B1 ] Field line at point X is tangential to E drawn in (d)(ii). [B1 ]
(ii) Indicate clearly on the diagram in (b), the position of the null point (where electric field is zero, other than at infinity).
[1]
Null point is to the right of charge -q B1
(iii) Explain why the null point exists at this position [1]
Null point exists because at this point, the Electric force from +2q and that of –q cancel
each other out.
B1
(d) (i) Find the magnitude of the electric force that A exerts on B. [2]
(ii) Explain quantitatively why the gravitational force is usually not considered at the atomic scale. mass of A, mA = 5.81 x 10-26 kg mass of B, mB =3.98 x 10-26 kg
[3]
[FG = GmAmB / r2 [M1] = 2.41 x 10-43 N [A1] Ratio FE/FG = 2.98 x 1033 The electric force is about 33 orders of magnitude stronger than the gravitational force. Hence the gravitational force is negligible compared to the electric force. [B1 – for comparing] (e) Figure 7.2 shows two identical conducting spheres of uniform density. Each sphere has mass
M and carries an overall charge +Q. They are placed in a vacuum with their centres distance
d apart. When the two conductors are brought into this set up, the charges redistribute as
shown in the diagram.
(i) Explain why the electric force FE between them the two conductors cannot be found using the equation below.
2
2
4 d
QF
oE πε
=
[1]
The net effect of the charges does not act through the center of the spheres. The expression above can be used only to find the electric force between point charges or between bodies with a spherically symmetric charge distribution. [B1]
(ii) Suggest a condition under which the electric force FE between them may be
approximated by the expression in (e)(i).
[1]
When the spheres are separated by an infinitely large distance. [B1] OR when the distance between the conductors is infinitely larger than the diameter of the conductors. (iii) Explain whether the expression below can be used to calculate the gravitational force
between the spheres.
2
2
dGM
FG =
[2]
[Yes. This expression is valid for point masses or bodies with a spherically symmetric mass distribution. The gravitational force exerted by a body with a spherically symmetric mass distribution on a particle outside is the same as if the entire mass were concentrated at the centre. [B1] The redistribution of the electrons on the spheres does not cause a significant change in the mass distribution since electrons are of negligible mass. Hence the expression can be used. [B1] ]
8 (a) In a Young’s double-slit experiment, coherent light from two slits 1S and 2S falls on a screen 800 mm beyond the slits. The distance between the centres of the slits is 0.600 mm. There is a central bright fringe at O and the third bright fringe is formed at P, 2.00 mm away from O.
Figure 8.1
(i) Show that the distance S1P is 800.0018 mm
[1]
Using Pythagoras’ theorem, mm0018.800PS,80070.1PS 1222
1 =+= [A1]
(ii) Show that the distance S2P is 800.0033 mm
[1]
Using Pythagoras’ theorem, mm0033.800PS,80030.2PS 2222
2 =+= [A1]
(iii) By considering the path difference S2P - S1P, hence calculate the wavelength of light used.
(b) A spectrometer and diffraction grating were set up to study the Balmer series of the hydrogen spectrum. The emission spectrum of an element was viewed in the second order and visible lines were observed. The angular positions of these lines measured against the scale on the spectrometer are shown in the table. Angular position of the zero order = 126.4O Number of rulings per unit length = 450 000 lines per m
Figure 8.2
(i) Calculate the wavelength of the violet line from the angular position given.
[2]
O
OO
67.21
4.12607.148
=−=θ
15 m105.4N −×=
]1A[m1010.4
]1M[2105.4
67.21sinNnsind
nN
sin
nsind
7
5
O
−×=××
=
θ=λ
λ=θλ=θ
(ii) Calculate the maximum number of violet lines possible. [2]
For highest order, θ = 90O
]1M[51010.4
90sin1022.2
sindn
nsind
7
O7
=×
××=
λθ=
λ=θ
−
−
Maximum number of violet lines observed = 2 x 5 + 1 = 11 [A1]
(iii) State one advantage and one disadvantage of using the larger order spectrum instead of the first order spectrum.
[2]
Advantage: The angle of diffraction for the larger order spectrum is larger than that of the first order spectrum, therefore there is less percentage uncertainty in the measurement of the angle for a given precision of the measuring instrument. [B1] Disdvantage: The intensity of the larger order spectrum is lower than that of the first order spectrum. [B1]
9 (a) State the difference between e.m.f. and potential difference. [2]
Rate of energy converted from non-electrical to electrical when 1 C of charge is delivered a circuit while the potential difference is the energy dissipated when 1 C of charge flows between two points.
B1 B1
(b) How many electrons pass a point in 3 minutes when the current flowing is 3 A? [2] Q=It = 3(3)(60) = 540 C
540 = Ne
N= 2119
1038.3106.1
540540 ×=×
= −e
M1
A1
(c) A 5 V rated battery is connected with a switch in series with a component that has an effective resistance of 2 Ω. If the battery has an internal resistance of 0.5 Ω,
(i) State the electromotive force delivered by the battery? [1]
Emf = 5V A1
(ii) Calculate the terminal potential difference when the switch is closed? [1]
VV 45
5
45
5.02
2 ==+
=
A1
(iii) Calculate the power dissipated at the component? [2]
Total resistance = Ω=+ 5.25.02
I= AR
V2
5.2
5 ==
Power = WRI 8)2(222 ==
M1
A1 (iv) Calculate the power loss in the battery? [2]