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98 AL Physics/Essay Marking Scheme/P.1
PLK VICWOOD K.T. CHONG SIXTH FORM COLLEGE
98’ AL Physics: Essay
Marking Scheme
1.
(a) A body is said to describe s.h.m. if its acceleration (or the net force on it) is
always in opposite direction and proportional to its displacement from the
equilibrium position.
Isochronous oscillation - period (or frequency) of an s.h.m. is independent of
the amplitude of oscillation.
(b) (i) At equilibrium, mg sin  = ke0
When the block is displaced x from the equilibrium position
mg sin  - k(x + e0) = mx
mg sin  - kx - ke0 = mx
k
k

x and 2 =
x =
m
m
2
Therefore the motion is s.h.m. with period T =
which is

independent of .
1
1
½
½
½+½
½ 2½
(ii) A is the amplitude of oscillation (i.e. greatest displacement) which
depends on the total mechanical energy (½kA2) imparted to the system
initially. (It depends on the initial displacement of the block when it is
initially released from rest.)
½
f is the frequency of oscillation
which depends on the intrinsic properties (elasticity and inertia such as k
and m) of the system.
½
½
1 2½
(iii)
x
½
0
T
t
T
t
T
t
v
½
0
a
½
0
Velocity leads displacement by ½ (quarter cycle).
2
½+½
98 AL Physics/Essay Marking Scheme/P.2
Acceleration is in opposite phase to displacement.
(c) (i) The (tangential component of the) weight of the bob (i.e. mg sin )
provides the restoring force.
(ii) - The centre of mass of the spherical bob can be easily located
(same as its geometrical centre) so that the effective length L can
be measured more accurately.
- The bob is small/heavy so that the effect due to air resistance is
minimized.
- The bob is heavy so that the mass of the string can be neglected.
Hence g =
2
2
½
4 2
.
slope
½
Precautions
- Ensure the pendulum oscillates with small amplitude (less than 10).
- Make sure the pendulum oscillates on the same vertical plane.
- In measuring period T, at least 20 oscillations should be counted.
2.
½
½
4 2 L
L
, we have T2 =
g
g
4 2
.
g
½
1
A graph of T2 against L should be plotted which is a straight line passing
through the origin.
Using the slope of the graph =
3
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(iii) Measure the period T of the simple pendulum using a stop watch for
different values of L.
Using the formula T = 2
½
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@½
(a) The telescope is in normal adjustment if the final image is at infinity, so that the
eye is in a fully relaxed state and the observer can view for long periods of time
without undue strain. (or so that the final image is at the position where the
observer expects to see it.)
1 3½
1
1
2
(b) (i)
Objective
L1
Parallel rays
from point at
top of distant
object

fo

Eyepiece
L2
fe
Fe
Fo

h1
I1
Construction line
To top of final virtual
image at infinity
2½
Objective lens is used to collect large amount of light from distant object
and to form a real intermediate image at its focal plane acting as an
object for the eyepiece.
½
½
Eyepiece acts as a magnifying glass for magnifying the intermediate real
image formed by the objective and produce a virtual image.
½
4
98 AL Physics/Essay Marking Scheme/P.3
(ii) Magnifying power M is defined as M = / where
 = angle subtended at the eye by the final image at infinity
(i.e. visual angle of object with aided eye)
 = angle subtended at the eye by the object without the telescope
(i.e. visual angle of the object with unaided eye)
1
Magnifying power can be increased by:- using objective lens of longer focal length f0
- use eyepiece of shorter focal length fe
½
½
Limitations on magnifying power:- f0 cannot be too long as long tube length (f0 + fe) will cause
inconvenience.
- fe cannot be too short as too curved lens causes spherical/
chromatic aberration.
1
1
(iii) One major disadvantage is that the final image observed is inverted.
Use an erecting lens (convex, focal length f) for an additional inversion
by placing it between the intermediate image and the eyepiece as shown.
The final image observed is erect and not laterally inverted.
To top of final virtual
image at infinity
Objective
Parallel rays
from point at
top of distant
object
4
½
½
Eyepiece
Erecting
lens
I1
1
I
2
fo
2f
2f
fe
or (Arrange two totally reflecting prisms (45 - 90 - 45) between the
objective and eyepiece.)
2
(c)
 
Air
t
(nF)
1
Film
Glass
The amount of light reflected can be reduced by coating the lens surface with a
thin film of transparent material (e.g. a fluoride salt) with suitable thickness t
and refractive index nF so that
destructive interference from the reflected light rays  and  from the
interfaces can occur.
1
½
98 AL Physics/Essay Marking Scheme/P.4
3.
Since complete interference is not possible simultaneously for every
wavelength of white light, an average wavelength for , such as green-yellow is
usually chosen since it is most sensitive to the eye.
1
Thus for red and blue (violet) light, the reflection is weakened but not
completely eliminated, so a coated lens appears purple in white light.
½
(a) (i) Lenz’s law states that induced current always flows in such a direction
to oppose the change causing it.
1
When the loop ABCD is leaving the field, the magnetic flux entering the
paper through the loop is decreasing.
By Lenz’s law, an induced current should flow in clockwise direction
(ADCBA) since this produces a flux entering the paper
so as to maintain the original flux.
4
½
½
½ 2½
(ii) Energy may be transformed from one form to another, but it cannot be
created nor destroyed. (i.e. the total energy of a closed system is
constant).
1
As the induced current (clockwise) flows from B to A along the part BA
inside the magnetic field, by Fleming’s Left-hand Rule, a magnetic
force directed to the left will act on BA (opposing the loop’s motion).
1
½
Thus external mechanical work has to be done by an external agent
against this opposing force and converted into electrical energy and
dissipated as heat in the loop eventually.
Lenz’s law thus in fact follows the principle of conservation of energy.
½ + ½ 3½
Alternative answer
If the current flows in anti-clockwise direction, the magnetic force
on BA would favour the motion of the loop and hence accelerate
the loop to the right. Consequently the loop will gain k.e. as well
as generate electrical energy, i.e. energy would be created from
nothing and this violates the principle of conservation of energy.
(b) (i) High-grade form of energy such as electrical energy can do work more
efficiently (i.e. with greater efficiency).
½+½
(ii) ALL different types of energy change into internal energy ultimately.
They turn from high-grade useful form to a low-grade useless form i.e.
energy is degraded as time goes on.
This is the reason why there is a need for new sources of high-grade
energy (which is known as an energy ‘crisis’).
(iii) favourable factors: - less pollution.
- reduce the dependence on sources like coal, oil.
- energy is consumed locally, no need for distant
transmission.
- practically unlimited supply.
1
1
½
½
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@½
1½
2
98 AL Physics/Essay Marking Scheme/P.5
unfavourable factors: - require large area facing the sun for the
installation of solar cells.
- the cost for the equipment is high.
- only suitable for tropical/subtropical region
where sunlight is available throughout the year.
- supply is not steady due to seasonal changes.
(c) (i)
- Electrical energy can be transmitted and distributed efficiently through
long distance to remote areas using transformers and cables.
- Electrical energy can be easily and efficiently converted into other
forms of energy using suitable transducers.
- Electrical energy is clean when used, producing no polluting gases or
waste materials.
ANY
THREE
@½
3
2
2
1½
½
2
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(ii) ‘Chemical energy’ of coal in furnace changes to ‘Internal energy’ of
steam in boiler, then to ‘Kinetic energy’ of the rotating turbines and
finally ‘Electrical energy’ from the generator.
Typical conversion efficiency is 30 - 40%.
4.
1½
(a) (i)
Coil + magnets
Brushes + supply
Commutator
Direction of rotation
The commutator (split ring) is used to reverse the current in the coil
whenever it passes the vertical position (neutral plane) so as that the
torque is always maintained in the same direction.
½
½
½
½
½
½
(ii) Wind several equally spaced coils on a laminated soft iron core and use
permanent magnets with curved pole pieces.
½
½+½
Several coils are used to provide a greater driving torque. The use of
the curved pole pieces together with the soft iron core produces a radial
field and thus the driving torque becomes more steady.
The soft iron core is laminated so as to reduce the power loss due to
eddy current heating.
½
(iii) Electromagnets can give a stronger magnetic field, and they allow the
motor to work from an a.c. supply as well as from a d.c. supply.
(b) (i) When armature (coil) of a motor rotates in the field, it cuts the magnetic
flux, an e.m.f. is thus induced.
This e.m.f. opposes the applied voltage V and tends to reduce the current
in the coil, therefore called a back e.m.f. Eb = V - Ir.
When a motor is started or suddenly jammed, the armature coil is at rest
( = 0) and back e.m.f. Eb (Eb = NAB) is zero.
3
½
½
3
½
½
1
1
½+1
½+½
98 AL Physics/Essay Marking Scheme/P.6
The armature current (I = V/r) would be so large that the coil is liable to
be burnt as the coil resistance is usually very small.
½ + ½ 4½
(ii) Case (I):When the motor is just switched on, Eb is zero (as  = 0), but as the
motor speeds up the back e.m.f. Eb increases (as Eb  ).
½
½
Therefore the current I (I = (V - Eb)/r) surges to high value and then
falls gradually to a final steady value when the driving torque  (  I)
produced just overcomes the small frictional torque at the motor’s axle.
1
½
Case (II):If the motor is connected to a mechanical load, an additional driving
torque (usually much greater than the frictional torque) is required to
drive the load.
½
½
½+½
Therefore the current I drawn from the supply increases while the back
e.m.f. decreases correspondingly as the motor slows down (as Eb  ) to
its final steady value and the driving torque  (  I) increases until it
can just overcome the torque due to the load and friction.
5.
4½
(a) (i) Thermionic emission is the emission of electrons from a heated metal
surface at very high temperature.
½
(ii) Photoelectric emission is the emission of electrons from a metal surface
exposed to electromagnetic radiation such as visible light, ultra violet
light, X-rays etc.
- Thermionic emission can be achieved easily by heating a metal
directly or indirectly using electrical means.
- Photoemission of electrons from illuminated surface highly depends
on its state of polish and the cleaniness of the surface.
½
½
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2 2½
- There exists a threshold frequency for photoelectric emission.
(b) (i) - Photoemission occurs almost instantaneously when the metal surface
is exposed to radiation (i.e. nearly no time delay).
- For a given metal there is a certain minimum frequency 0 of radiation
(called threshold frequency or cut-off frequency) below which no
photoemission occurs regardless of the intensity of radiation.
- The maximum k.e. of photoelectrons increases with the frequency of
radiation, but is independent of the intensity of radiation.
(ii) (I) h is the energy of an incident photon of frequency  and h is the
Planck constant.
 is the work function of the metal which is the minimum amount of
energy to ‘free’ an electron from metal surface.
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2
2
½
½
1
98 AL Physics/Essay Marking Scheme/P.7
(II) - Einstein proposed that when a photon collides with an electron, the
incident photon can either be scattered with no reduction in energy (if
h < ) or it gives up the whole of its energy to only one electron on
the metal surface (if h  ).
½
The photon cannot deliver its energy to more than one electron.
½
Photoemission results from a one-to-one interaction between an
electron and an incident photon, so there is no time delay before
emission starts.
- If the frequency  of the incident photon is less than the threshold
frequency 0, i.e. h <  where  = h0, none of the photons can
supply enough energy to free an electron from the metal surface.
According to photon theory, increasing the light intensity merely
increases the number of photons (passing unit area) but does not
increase the energy of each individual photon.
- Einstein reasoned that part of the energy imparted by a photon is used
to remove the electron from metal surface by overcoming the
attractive force between the electron and the remaining positive ion
(i.e. the work function ) and the rest appears as the k.e. of the emitted
electron.
As many of the emitted electrons are involved in collisions on their
way out of the surface and therefore emerge with a range of k.e. from
zero up to a maximum. Hence Kmax = h -  and Kmax increases with .
(c) (i) When a hydrogen atom is excited from the ground state to a higher
energy level, it becomes unstable and eventually falls back to one of its
lower energy levels.
1
The excess energy E is emitted as electromagnetic radiation of
hc
wavelength  =
where E = energy difference between energy
E
levels.
The hydrogen spectrum is an emission line spectrum in the visible range
characterised by the energy levels of the hydrogen atom.
In an X-ray tube, energetic electrons bombard the metal target and may
eject an electron from the innermost shell (K-shell) of an atom.
The atom so excited is unstable and an electron from, say, the L-shell
may move into the vacancy.
The excess energy E is emitted as electromagnetic radiation of very
hc
short wavelength  =
as E is very large for transitions of electrons
E
between inner shells of metal atoms.
(ii) Some bombarding electrons lose energy as they decelerates when hitting
the metal target and emit the energy in the form of radiation.
Since most of the electrons usually have more than one encounter with
the metal atoms before losing all their energy, several X-ray photons
with different energy are emitted, which contribute to the continuous
spectrum.
The minimum wavelength of the continuous spectrum corresponds to
the bombarding electrons losing energy in a single encounter, which is
bounded by the maximum kinetic energy of the electrons.
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@ 1½
½
½
1
1
½
3
½
½
1
½
1 4½
1
1
½ 2½