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1
(a) A ball is thrown from point S, as shown on Fig. 1.1.
""
S
.
""
""
. ""
F
Fig. 1.1
The initial velocity of the ball is 25 m S-l at an angle to the horizontal of 45°. The mass
of the ball is 6.0 x 10-2 kg. The ball lands at point F. The points Sand F are at the same
horizontal level.
(i)
Calculate the vertical component of the ball's initial velocity.
vertical component
(ii)
= ....... !3.:.1........................
m S-l [1]
Show that the maximum height reached by the ball is 16 m, assuming no dissipative
forces.
2
o :;: . \1-1 +~(-q.~,)S
S~
11- t :L
- - = 1 5-~ ~ \bM
2(~
(iii)
[1]
'0
The kinetic energy of the ball at S is K. Calculate the kinetic energy and the potential
energy of the ball in terms of K at a height of
1.
16 m,
"
~ .}; "' 12 £'l}9.
I-
\:
If'
_
l\.t\ -\-\>·b\. :: '(-tj -H.\::'j
K
,•
2.
1- 0
~l<-£1
y, ~:: ~ K.
t
,
c.:y
f:.:\
W
'I
A~, Q riI
~1'{ -'S
I·V}
b-t)'o 'o1)t\'2.0~Ol~ \J.,
".£ ::~ m/2.~ '\
~ 2)
_
~·td-
-?)<:.
-= ~1Y\ 1soz[!.\:1\C:
F'
kinetic energy
= ···i ···································· .. ··········
potential energy
= .... ! ..~...........................................
8.0m.
~·E ~d)"", - K - ~Kv :::. ~ K (I)S~IA. ;~"f)() Q'r~&~~) ~
'
.
-K,
k Inetlc energy = .................................................... .
potential energy
= .........................................
:.4. K.
[5]
2
(a) Describe how band theory is used to explain the difference between the conduction
properties of insulators and intrinsic semiconductors.
·
l~~~)~~.~ ..~~ ..~.J~f.~...e. .~ .. ~~y. . J~~.r~\~<4:t: ..
9:
.<1) ......... ~~~~....... .
...\O.~~ ...9.c.iV\ ~ .. ~ ....~~·~~ ...~~ ..r.~~~~.....geM\too.~~ .. r:~ .....ho.'I.~.... . . ~, .......... ..
..~!l\t~ .... ~~.. ... ...~~ ...... l.~';1...:..........................................................................
.
!~V. .~ ... j~l~ ~71 , ...e\adfl?O~ ....;~ .-:r~.. ~~~n. ~ ~!:'.d............. .
• .. ~.~......1t:
... ...\D~t .. :......?!.~: .~g.~ .':';~.~~ .....q.~. ~)~ ..s.~.~ ~
......f.~ ..
..~........... .
..~~~....~t~~ . ...}~ ...&~ ....~~~ . %~ .. ~ ..~....fo.t-: ... . 0. .
.Th'!S. ..a~
.;()6:!... c. .....
:e r: ...l0. ~!-,l; ..~t
... ~ .. i:~ ... ~kr.:),~~ .....~~ ..0-~.h~.......
.. ~~~~~~~~~:1:~:~·· ~~.;;~i: ·····~····~·· ; [3l ~
(b) Explain the use of doping to change the con uction properties f semico ductor . h...t"t""
.
• . ~~~jml~Nj1.~~ ... ~.~.. ~.~ ...Th.. j~~~~S:.. ....~ O.~o.~ ~f.$. ............. ~~~~~~
...~.0. ~~ ~>. ......~~,~ . .~.....~~~'»if. ...
. .... ~~... ~~~~... .c.~.~1~
. . . . ..
.J~ ..~ ..~~~~...~r..~ .....~~~....~...~9.~ .. _..l~;:\\t... ~..~f ............ .
..f!:~.~. \). ~. ~.$. .. 1.S....it.\Q~ . :........................................................................................ .
• ... ~~~.... ~.. l~(\. ~ .... .. .. ¥.~w.:
....~.~.~(......... ~~~~... ~~~.... ..
.. C~ff~ .~$... ... ~.
~f\ .. J~f... x'\~~ ....... ......~~.... L .~ .... ..t.W'.d.......\~.'.........~ ....... [2]
~ ~~t\l\~\c... ~r'\~(\o\\.(,~r 't ~ ('l~ \()-rGff 4V\o.t\/ 4'n.t..-"f\~ J)~~
~f4\\c..~ a..~r
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3
An a.c. power supply is connected to a resistor R, as shown in Fig. 3.1 :
;-'--
I
c.r.o.
R
'--~
I
Fig. 3.1
A cathode ray oscilloscope (c.r.o.) is used to show the potential difference (p.d.) across R.
The screen of the c.r.o. displays the variation with time of the p.d. across R, as shown in
Fig. 3.2.
Fig. 3.2
On the vertical scale, 1.0cm represents 5.0V. On the horizontal scale, 1.0cm represents
10ms.
(a) Use Fig. 3.2 to determine
(i)
the frequency of the a.c. supply,
4
X \Ofl\6
4
x"
0-1. ~ :
0 - 045
frequency
2.5
= ............................................
Hz [2]
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4
A small metal sphere S is supported by an insulating string that is fixeq at point P, as shown
in Fig. 4.1 .
P
Sphere S has a weight of 0.49 x 10-3 N and charge - 3.6 nCo Another metal sphere R with
a charge of +7.2 nC is placed 0.060 m from S. The diameter of the spheres is negligible
compared to the distance between them.
A line joining Rand S is horizontal. The string makes an angle () with the vertical.
(a)
(i)
On Fig. 4.1, draw electric field lines to represent the electric field in the region
[3]
between Rand S.
(ii)
Calculate the magnitude of the electric field strength at the mid-point between R
and S.
~ -I
l(
N1k: ih-t.
0
~ (0.
t
30
( fwo
ta~fll~l\1
--
c
f,{)~X ICfS
. .
~lililll~
OlAt TO ~
at'\d ~ ~~
~\~"t\ iV\
~Me_~(r~)
[2]
electriC field strength = ..... ... .......... ..................... N C
(iii)
Show that the electric force acting on S is 6.S
x
10- 5 N.
[2]
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5
Plutonium-239 decays by a-emission to form the isotope uranium-X. The half-life ·of
plutonium-239 is 2.4 x 104 years. The half-life of uranium-X is 7.1 x 108 years.
(a) (i)
Explain the term isotope .
.~~~.~ ..~ ......~ ...~ ..~.................. ~.~ .. ~~~.~!: .. ~ .l.~~~.~~ ...~~.t ...........
Jt ~-f.~n............k
(ii)
..... . ..~~1.... ................................................................. [1]
Define half-life.
..
..
.. . . ..~......~.~. ~~.. . . . . . . . .
", ..~L7:1.i. .......~ ...#-t~ ~~.~ ~.~ ~~
.. J.' ..... ~ ..!'~~~ .........I:f1.~~.. ~.~..
(iii)
.. .' .. .1.... ~~~ ... .. :......................[1]
Complete the nuclear equation for the nuclear reaction below.
239
,-L
, :-:r;
Pu --7
2~~
92
U
...
+
9
.~
[2]
a
(b) A pure sample of plutonium-239 has N nuclei at time t = O. On Fig. 5.1. sketch graphs to
show the variation with t of the number of nuclei of
(i)
plutonium-239 (label this graph P).
(ii)
uran ium-X (label this graph U).
Your graphs should cover the range from t = 0 to t = 5.0 x 104 years.
1.0
2.0
3.0
4 .0
5.0
t / 104 years
Fig. 5.1
[3]
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(c) In the nuclear reaction in (a), 5.26 MeV of energy is released . The energy of the emitted
a-particle is 5.15 MeV.
Suggest and explain why these two values are different.
..1k....~.y.~.~~Y- . . .~·!~.~~.. .e.~ ...r-r . 0.'!r4..~~....~~.~... ?f'?4.~~ .. {.~\~~1j
.~.~ . . .e~ . . ..~~. ~~~.~~. :t.~~............. .\+ .........~.~. . ?~~...~ .... .1h ...te6~~..i. ~..
...
...~... ~ . ... ....~ ...f.rn~ ... :I~ t.hL.ti9.JP..j.... ~~tS:) ..... .1~... ~.~. ~ .
........ ~ ..,... ~.L'... ~... ~~.~ .... }.~ ..... ~ .... ~.~~..~j .... ~~~J~~....~o/.: ....... ~ ..... [2]
~ Vrd~~ (U-J~S oCtet l4.e) OlS we , 0 ~ "..- ~l~\'\. •
LtDe
+0
"*,,,,-1 U-')35 emo Ylo.'S Kif\e"m e~ wC{uU-- C{ccord l<1~
[()~ w vo.~ ~ M~-hJM) U-:t ~ ~ ~I\C~ H..t. g\1o~ \d be.
kMvO
tI\()\I\I\~ t'A o~~~v~ C:rIN?e.~V\
+1) p:- <}'~9
~u>+ ",gk( dt ~ .
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6
Viscosity is a measure of the resistance to flow of a liquid. Apparatus that can be used to
measure the viscosity is shown in Fig. 6.1.
liquid
reservoir
tube T
:============0
liquid in
~
""overflOw
beaker to collect liquid
Fig. 6.1
Liquid flows through the horizontal tube T. By maintaining a constant liquid level in the
reservoir, liquid flows through T at a constant rate.
The rate of flow of the liquid is measured for different tubes T with the same length but of
different radii r. The same liquid level is used in each experiment.
The volume of liquid collected per second is Q. The variation with rof 0 is shown in Fig. 6.2.
5.0
OJ
10-6 m3 s- 1
4.0
3.0
2.0
1.0
o
0.9
1.0
1.1
1.2
1.3
Fig. 6.2
1.4
1.5
1.7
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(iii)
Using your answer in (ii), determine the magnitude of k.
((=)cr1\..-
l~
:: l~}t
()
t-1\.,
U
\J~Il'q ( - 1.t-~5 -5· lJ ()\,
\..J
')
'.
~f\
1\;-
I
-3, t ~.Lj- (S\f\U.. {\.,.~ ~f\
- .Prtll)
e- -'1)(\0 ~~
I
-~-magnitude of k = ................................................. [2]
4- L- '<~~ S')
5·qt :9 \<'-= ~·l)(\O ~
-- S"~ tto =- ,~~ +
l31< ~
'<J r
(c) Theory suggests that k is given by the expression
_ nt1P
k ~ 81]L
where t1P is the pressure difference between the two ends of the tube T of length Land
1] is the viscosity of the liquid. For this experiment, t1P = 500 Pa and L = 0.20 m.
(i)
Calculate the magnitude of the viscosity
1].
----- -4-, J-J'. ,0
magnitude of
(ii)
1]
-~
= .................................................
[2]
Determine the SI base units for viscosity.
\
::.
--
[A1[L1(\(]
. _
K3
~
-
m. . . . . . . . . . . . . . . . . . .
~ M-I~'"
SI base units - .... .. .
\
[3]
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(d) The radius of tube T is reduced from R to
ratio
~.
Use your answer in (b) to determine the
pressure difference for ~
pressure difference for radius R
to maintain the same volume of liquid collected per second.
~'lL K
...._
-~--
a1, l
t}.,
'1
,1.8
-
=,.
tA~rt /)t\.t
t
.
= 16
ratio = .........
\.~.................................... [2]
(e) The graph of Fig. 6.2 was obtainee for water. Suggest what change to Fig. 6.2 would
occur if the experiment were repeated with cooking oil.
. Q:.....~ ....................~ . ~..... ~.... ~.~.~.... ~~.r.., .j-~~t.\~... 1;~:c. '. ~.\ . . ... ::.~ .
.~:I.~ . .~.~~.~.~. . . . . . . ~:.~.~. .~ . ~~~. ~. . . ~......~.~. . ~. . , ~ . . .
. 8(.~~~. ~~1 .~ ... ~.. ~(.1\
r .... j~ ....... ...~.t:...................................................... .
.................. ......... .. .............................. ........ ....... ................. ....... ............................ ........ [1]
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7
When a wire is stretched between two points A and B and is made to vibrate, stationary
waves can be set up on the wire. A possible shape (mode of vibration) for the stationary
waves is shown in Fig. 7.1.
...
...
""
,
A' ,
" ....
"
... ... "
- .... "
,,
B'
Fig. 7.1
The frequency of vibration of the wire in this mode of vibration is thought to depend on the
tension in the wire , the length of the wire and the mass per unit length of the wire.
With all other variables kept constant, the relation between the frequency f of this mode of
vibration of the wire and the mass per unit length ,u of the wire is
where k and n are constants.
You are provided with an oscillator that can vibrate the wire over a large range of unknown
frequencies. You may also use any of the other equipment usually found in a Physics
laboratory.
Design an experiment using different wires to determine the value of n.
You should draw a labelled diagram to show the arrangement of your apparatus. In your
account you should pay particular attention to
(a)
(b)
(c)
(d)
(e)
the equipment you would use,
the procedure to be followed ,
the control of variables,
how the frequency of vibration of the wire would be measured,
any precautions that would be taken to improve the accuracy of the experiment.
[12]
Diagram
(
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~)
..... ...... 1W:...~... ~.~... ~....
Q. ~!.~!~~.C ............................................................................. .
........................................... ~ . .~.:~ . . . .~ . A.'·1~1t. . .~~~........~. .~~~. . . (;~.
~
...... .......................................5
~ ~ ~.~~.
•••
.....
d
'.(
~ ""'0 \ tl te/.)
f) ~,.-:;-;~
hPr........................ .. ................ .
............................................
~~!~~~ ...~ ~ ... ~'0.~.~.~ ...~(. 0....w..~~.........................................
•• . . .
....~.. F.~~... ~~..... ~.~.~ ..J j?.... ::~Q.~
..........~~~~~......'l~............. t
. ±<i!~
....~..... :~ ... ... f~.0t.-..... ~.*~
....... .
...............................................................................
.... ::-:-.. ~ ... ~~.\ ........, ' ........... L ....... 1. ...~J~t\.
....... .l~,(~~ . ~ .... N..S.......... .
. . .=. . . . . . . . . . . . . . .W:t..~?..........~ .L ........ t .. .....
f).. .... ~ ... ~J~.\!1 ....
~.\.~e. ........ ..
"
..r........ .
C}
.:o.:;~. ..... .'.'!t .....(~.~ ~.~l,!".. ~.. ...... ~~ ..... C."'~~ ..~ ..
..::..........,."... .(\1 ..... J .~. 9.0.~\k... .\~ .....:£~t.1. 0.':":1>:\ .... ~.....(':').rlt. ~ ....'.lI.\:1:~. . ~ .
...........h~~.:!.~ ...... J(! . ~..1.:.1.........................................................................................
..... ~ .......~.f...... i .)\ ....~.o "'.........~~ ......~~~~....... . ~~.~t..........................
) .J:b...1II\~...............
~~~ ... ..........~... w,~..... A~.. JI"d ...... ..t:-........ .
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. . ~ . . 0....~Y; \ .......\J.~~.~.... ~~0 .. .1~ ....~..r-.. .~. :~.0.~ .......~.~..:~ ............ .
.... ~.4~v:\~...9~.trJ.~.. \n~~·~'fu~ ..... \~~~~~.v... ~} ..~~~... ~~ ..~....~~.... .
...... ~.~1j®. . .~.~~ ......fut...~l~
~:.I.t ...~ .....ft...C .... s.~]..c.~~ .. :.... T.t:M~..iN.: .. .
....
. . ~~~.~.~J. . . j . ~~........... ~te. ....(~~..~ ......l)~
....
·c'?:1 .... ~~~~·OO ...... ..
.....:1~· ···~~·~v.-&~··8··-xu·····~\@.~·&~·····~·~·~··· ..... :...................................
..1Q....~f!'.d. ...'(\c .................................................................... ................................................ .
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. . .~. . . . . . ~\~ . . . . . \~.J. . .~.~~~~.~ . . ~. .~ . . f!.M ..... ".b~~~....~..... ~...~ ..~............. .
""~(,'v\. \~ f\. .
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.
....~) ......~.c~.~~~~~... ~ .....~~r ~.r~ ....-}.{.... ~~~~.....~~..~:. ..
..............................................~.....w.~/. .. ct. .... (~~ , .~~ . ~ ....~ .............~~~.......... .
............................................... . .. .'.............
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~~.~~.....
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.................. :... ..........................
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.. ..
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,\\~(,~V\ .
... .... ............... ..........................................................................................................................
,
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~~~
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