1967-05-26 — Page 14

日八十月四年来丁层复

第二張四第

WAH KIU YAT PO

英中會考物理科答累、

HONG KONG ENGLISH SCHOOL CERTIFICATE

EXAMINATION 1967.

Suggested Answers to. Physios.

Section A.

་

masa

a) The density of a substance is defined as

per unit volume. The specific gravity of a sub- stance is defined as the ratio of the weight of any volume of it to the weight of an equal vol➡) uma of water, or

(b)

9.0, of substance

•

weight of any volume o suostuNSO

weight of an équal volume of water

density of the substance

density of water

From the definition above, we see that density

is always expressed in appropriate units,e, g« gm/o.c. ex lb/cu.ft., but specific gravity is simply a number or ratio, If C.0.3. system is used, the numerical value of density of a sub- stance is the same as that of the specific gra- vity. This is due to the fact that density of water is 1 gm/c.o.

Archemedea' Principle: When a body is wholly or partially immersed in a fluid it experiences an upthrust equal to the weight of the fluid displaced.

(e) weight of the chain 75

length of the chain - 20 cn

density of the cheine 7. am/c.o. depth of water in the Eureka

Can - 10 cm

reading of the scale when the

10

chain is not emmersed 250

(1)Assume that the fine thread has no weight and volume, and the depth of the water

the outlet of the Eureka Can, JUBT up to When the bottom of the chain just touches the bottom of the can. there 18 no reaction on the bottom of the can. Since the chain is uniform, there 186 exactly half of the chain immersed in the water. From

density

volume of the chain

mass volume

weight of the chain density of the chain 75/7.5 D.C.

-

- 10

0.0.

volume of the chain immersed in

water = 10/2

D 5

C.C.

c.c.

uptbrust due to the water - 50.4, 14/0.01,

5

g

reading of the spring balances 75-5

70gm

Since 5 c.c. of the water. has been displaced and lost through the outlet, the reading of the soale 18 250 --5

89 or 245 g.

When all the chain reste on the bottom or the can. A

In this case, we can assume that there fa

no tension in the thread.

reading of the spring balance – CỦ

From volume of the chain - 10

There are 10 0.0. of water displaced by the chain flowing out from the Eureka Can

reading of the scale

250 + 75 - 10

335

60-300. -30 0.0

Volume of water 300.0..

voluna of oil

360

ô

E

with a steady velocity. The load and errors, are recorded in a table and the experiment repeated for a series of increasing loads.

For each pair of readings of effort and load/ obtained, the mechanical advantage should be calculated from the formïla K,A,- Load/Effort) and entered in the table.

Load (gm, wt. }-

Effort

M.A.-Load/Effort

The following in the graph of Mechanical Advantage against the Load.

Load in gm,wt.

The useless load consists of the weight of the lower pulley block and the string and friction in the strings and bearings. The useless load becomes a smelter, proportion of the total load as the total load increas88. Consequently, the mechanical advantage in- creades with load, but cannot exceèd 6 in this pulley system.

d) Let t F be the temperature difference of the

waterfall between at the top and at the bottom.

potential energy of the waterfall mh ft.lb.wt. where m is the mass of the water, h the height of the waterfall. R= 194.5 ft

Mechanical equivalent of heat 778 ft.lbe/B.Th.U.

80 ... 778 mt - mb à 100.

h x 80

194-5 180

•

778 x 100

778 X 100

.0.2°F.

Answers The temperature

of the waterfall at the bottom 18 0.2 wanner than the t

EDP.

the

(a)(1) If to forges acting at a point are represen-

ted Both in magnitude and direction by the adjacent sides of a parallelogram, their Tesultant will be represented both in mag- nitude and direction by the diagonal of the parallelogram drawn from the point

Quantities having an idea of direction as well as magnitude are vector quantities. This differs from scalar quantities which have magnitudes only. We a

tities by ordinary because the directi

sred. Usually ** scale to repr subtract the them into 10 axea by tr (111) Velocity

quan

ities

otor quan-

tion,

Qonsid rawn to

a or olve

LAST

日六廿月五年七六九一层公年六十五國民中

育数僑華

英中會考數學卷三答案

MATHEMATICS

SUGGESTED SOLUTIONS & ANSWERS TO PAPER II L MATHEMATICs Syllabus A GEOMETRY)

SECTION A

> Credit will only be given" for the conectTM answer) siis for questions 1 to 8, put the answer in the space provided on the question paper. "This Any working may be done on the last few

pages of the answer book but will not be marked? NOTE. The working shown here are only for reference." Is If two chords of a circle are squal, then is they'

subtend equal angles at the centre, and its they are equidistant from the centre.

they

ak

vax They can intersect at 14.25, but it is not necessary,

> They cannot bisect each other, unless diameters. A shown, if chordo AB. CD bisect each other, then AC DU is a ilgram

In #gram ACDD, ABCD

ACBD is either a

AB and CD are

rect. as square A

diameters

-

<*> All diameters of a circle, are squat, but)

equat

shords

A

[BY

May

not be diamėlers.

AD ( e moitian of „ABC.

ABC is QUR

any triangle

جمس

<ar Let hy of the attitude on BG

& ABD =¿ (8P){ bq)

* ACD =

Then

ADF.LY.

ABDALD;

<b> AD bisects - BAC it amet ņ isosceler «<> It AD bisects <BAC, (ie the internal angle

for), then

ABAC BD BC

AD is given as a median,

So this only when ABC is isoscele

AD B

bisecti

AD

As shown, A

an, by definition

AD

A Afgessary be the 4 bisector

GABC

of ech

are collinear pt.

B. fits between A and

ABL BC

ABC is a st. line,

ķi is any point between A and C essary be the mid- pont of AC

The whole equals the

AB ↑ BC = AC

sum of its parts.

ZABC #180", ad on stiva the proportion

1B BC = BCY AL

not generally hus

When a solid is placed into the measuring oylinder, the volume of the solid immersed In water is 36 - 30.0.0.96 0.0, volume of the solid immersed

in bil - 71′′ - 36 - 30 0.6.

(** total volume of the solid

5

11

epecific gravity of the solid – 0.9 (1) Rane of the solid – density x volume

-0.9 11 -9.9

(11) Let d gm/o.c. be the density of all, thep

from Arohimedes Principle:

Weight or water displaced weight of off displaced weight of the solid

.6 x 15 x d - 9.9

54- 3.9.

10,78 gm/0.0.

Ansvari(1) The mass of the solid is 9.7

m.

(11) The density of the oil is 0.78 gm

2. (*)(1) & root found is the work done when a forse

of one pound moves one feat in its ow direction

((11) The ratio of the useful work done by the

machine to the total work put into the ma- chine is called the efficiency of the machine.

Work output

100 per bent.. Efficiency-

(b) We know that heat is a form of energy. We une

derstand that energy ia the capacity of doing work, and work is the product of force and dis- tance. Hence, heat can be converted into mechan- ical energy. This was experimented by Joule. The modern value of this mechanical equivalent is.. 778 ft. 108 wt. per B. Ph.D. Tháa means that the work done required to produce ons 3.9h.U. of heat is 778 ft.lbs, wt. (0)(1).

A single rope. pulley eyetem having

A velocity ratio of

(11) The pulleys are set up as in (1), sosie pans

being provided for the addition of weights to represent load and effort. These pana can be treated as part of the machine itself. ∙Ar initial load of, say 50 gm,wt. is put to the load pan, and weights are then added to the erfort pan until the load just rides slowly

LIBRA

et the centre of gravity be looated from A along the rod. From the above déagram(2) taka moments about:A.

10 12 20 30X - 60 - 240

10 re

30X

Answer: The position of the

of the loaded rodas 10 ft. along the rođ.-

Pram

(ii)Since the rod 18 uniform, we can assume two

weights to represent the weight of the rod, Taare 18 & weight of 10

1b# -8-

· 10

ANS

Given ABC D

then ABCD is either a rectangh

a square.! necessary

acting at the mid point of BD, Also there is

ing weight of 2x10/12 lb 1 lbs. vertically at the mid point of AB Sum of the Clockwise moments about Bi

20x10Cos16° • 8——x5Cos30°

[«As If AC OBD,

square.

! But Not

resib,

20000# 30°. 125 0030

125

(2004 J CO30

209.1

(111) The tension in the cord GE.

ft-lb.

Let the tension in the cord CE be T Ib.wt. the anticlockwise moments about D is

Tx 4C0830° 1- xCos30°

From (11) the sum of the clockwise momants. about B 19 (2002)Cos30

ft.lb.

Since the rod is in equilibrium, the clock vise moments is equal to the anticlockwise moments about B.

200 - -)Cos30° «(4T + —— }Cos30°

T60 Lbs, wt.

Answer: The tension in oord CE is 60 lb.WI ivi The vertical components at B is the sum of the vertical components of all forces, Let Nht be the vertical component at

N2010-6000860

Get R 1b,wt, be the horizontal component

TABY

#* TCos30°

60 x 3/

~3013

52

ib.wt to the left,

Anaver. The vertical component at Bi

Bero. The horizontal component at B is approximately 52 1b.wt. to the left.

To be continuad!

If rect, ABCD with ACLBP, than « CAB =

ABCD must be a square.

If ABCD is u rect, the ph A. B. CO are con

supp > This is also time for ABCO cyclio sopp

однам

Yet, ABCD may not be a squai

<dy AC BD are diagonals of rect ABCD

ве

The diagonals bisect each other. ( Although this is also a property for square, yet the figure

A squat. Y If ABCD is a rect. then by definition

-D-90° (Again, as medi

ABCD here is not necessary.

not sufficient to show that ABCD is a squams

VOTE Candidates should pay

the above

cix In questions

questions

ANS

closed attention

and of the requirements

Put a "v" in the box opposite each of the followm state wants which must be truce

Hence the correct answers are non-unigur

Retually, each question contains of answers.

the In question 3, each of the statements

uds is equivalent to the giver statement have Concert answer again.

AZNAREWASA