Plk Vicwood K.T. Chong Sixth Form College

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. 1

Isochronous oscillation - period (or frequency) of an s.h.m. is independent of

the amplitude of oscillation. 1 2

(b) (i) At equilibrium, mg sin q = ke0 ½

When the block is displaced x from the equilibrium position

mg sin q - k(x + e0) = ½

mg sin q - kx - ke0 =

= and w2 = ½ + ½

Therefore the motion is s.h.m. with period T = which is

independent of q. ½ 2½

(ii) A is the amplitude of oscillation (i.e. greatest displacement) which ½

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 ½

which depends on the intrinsic properties (elasticity and inertia such as k

and m) of the system. 1 2½

(iii)

Velocity leads displacement by ½p (quarter cycle). ½ + ½

Acceleration is in opposite phase to displacement. ½ 3

provides the restoring force. ½ ½

(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. 2 2

(iii) Measure the period T of the simple pendulum using a stop watch for

different values of L. 1

A graph of T2 against L should be plotted which is a straight line passing

through the origin. ½

Using the formula T = , we have T2 = ½

Using the slope of the graph = . Hence g = . 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. 1 3½

2. (a) The telescope is in normal adjustment if the final image is at infinity, so that the 1

eye is in a fully relaxed state and the observer can view for long periods of time 1

without undue strain. (or so that the final image is at the position where the 2

observer expects to see it.)

(b) (i)

2½

Objective lens is used to collect large amount of light from distant object ½

and to form a real intermediate image at its focal plane acting as an ½

object for the eyepiece.

Eyepiece acts as a magnifying glass for magnifying the intermediate real ½

image formed by the objective and produce a virtual image. 4

(ii) Magnifying power M is defined as M = b/a where

b = angle subtended at the eye by the final image at infinity

(i.e. visual angle of object with aided eye) 1

a = angle subtended at the eye by the object without the telescope

(i.e. visual angle of the object with unaided eye)

Magnifying power can be increased by:-

- using objective lens of longer focal length f0 ½

- use eyepiece of shorter focal length fe ½

Limitations on magnifying power:-

- f0 cannot be too long as long tube length (f0 + fe) will cause

inconvenience. 1

- fe cannot be too short as too curved lens causes spherical/

chromatic aberration. 1 4

(iii) One major disadvantage is that the final image observed is inverted. ½

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. ½

or (Arrange two totally reflecting prisms (45° - 90° - 45°) between the 2

objective and eyepiece.)

(c)

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 1

destructive interference from the reflected light rays and from the

interfaces can occur. ½

Since complete interference is not possible simultaneously for every

wavelength of white light, an average wavelength for l, 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 4

3. (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. ½

By Lenz’s law, an induced current should flow in clockwise direction

(ADCBA) since this produces a flux entering the paper ½

so as to maintain the original flux. 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 1

constant).

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

Thus external mechanical work has to be done by an external agent ½

against this opposing force and converted into electrical energy and

dissipated as heat in the loop eventually. ½ + ½ 3½

Lenz’s law thus in fact follows 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 1

(ii) ALL different types of energy change into internal energy ultimately. 1

They turn from high-grade useful form to a low-grade useless form i.e.

energy is degraded as time goes on. ½

This is the reason why there is a need for new sources of high-grade

energy (which is known as an energy ‘crisis’). ½ 2

(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. 1½

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. 1½ 3

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. 2 2

(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. 1½

Typical conversion efficiency is 30 - 40%. ½ 2

4. (a) (i)

The commutator (split ring) is used to reverse the current in the coil ½

whenever it passes the vertical position (neutral plane) so as that the

torque is always maintained in the same direction. ½ 3

(ii) Wind several equally spaced coils on a laminated soft iron core and use ½

permanent magnets with curved pole pieces. ½ + ½

Several coils are used to provide a greater driving torque. The use of ½

the curved pole pieces together with the soft iron core produces a radial

field and thus the driving torque becomes more steady. ½

The soft iron core is laminated so as to reduce the power loss due to

eddy current heating. ½ 3

(iii) Electromagnets can give a stronger magnetic field, and they allow the ½

motor to work from an a.c. supply as well as from a d.c. supply. ½ 1

(b) (i) When armature (coil) of a motor rotates in the field, it cuts the magnetic

flux, an e.m.f. is thus induced. 1

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. ½ + 1

When a motor is started or suddenly jammed, the armature coil is at rest

(w = 0) and back e.m.f. Eb (Eb = NwAB) is zero. ½ + ½

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 w = 0), but as the ½

motor speeds up the back e.m.f. Eb increases (as Eb µ w). 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 t (t µ I) 1

produced just overcomes the small frictional torque at the motor’s axle. 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

Therefore the current I drawn from the supply increases while the back ½

e.m.f. decreases correspondingly as the motor slows down (as Eb µ w) to ½ + ½

its final steady value and the driving torque t (t µ I) increases until it

can just overcome the torque due to the load and friction. 4½

5. (a) (i) Thermionic emission is the emission of electrons from a heated metal

surface at very high temperature. ½ 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. ½

- 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.

- There exists a threshold frequency for photoelectric emission. 2 2½

(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 n0 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. 2 2

(ii) (I) hn is the energy of an incident photon of frequency n and h is the

Planck constant. ½

f is the work function of the metal which is the minimum amount of

energy to ‘free’ an electron from metal surface. ½ 1

(II) - Einstein proposed that when a photon collides with an electron, the

incident photon can either be scattered with no reduction in energy (if

hn < f) or it gives up the whole of its energy to only one electron on

the metal surface (if hn ³ f). 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. ½

- If the frequency n of the incident photon is less than the threshold

frequency n0, i.e. hn < f where f = hn0, none of the photons can

supply enough energy to free an electron from the metal surface. ½

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. 1

- 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 f) and the rest appears as the k.e. of the emitted

electron. 1

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 = hn - f and Kmax increases with n. ½ 3

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

wavelength l = where E = energy difference between energy