BRITISH PHYSICS OLYMPIAD 2016-17
BPhO Round 1
Section 1
18th November 2016
你这套题有404 分了
做了多久有计时吗
This question paper must not be taken out of the exam room.
Instructions →
没太明⽩怎么计分的
Time: 1 hour 20 minutes on this section.
保 sectionI 可以每题写但是最
都多
Questions: students may attempt any parts of Section 1. Students are not expected to
complete all parts.
Working: working, calculations and explanations, properly laid out, must be shown for full
credit. The final answer alone is not sufficient. Writing must be clear.
40 分
,
不
多给分
但⼀共分的题
Marks: a maximum of 40 marks can be awarded for Section 1. There is a total of 70 marks
allocated to the problems of Question 1 which makes up the whole of Section 1.
所以你
可以挑着写或者
Solutions: answers and calculations are to be written on loose paper or in examination
booklets. Graph paper and formula sheets should also be made available. Students should 跳过不会
ensure that their name and their school are clearly written on each and every answer sheet. 的题
Setting the paper: There are two options for setting BPhO Round 1:
• Section 1 and Section 2 may be sat in one session of 2 hours 40 minutes.
• Section 1 and Section 2 may be sat in two sessions on separate occasions, with
1 hour 20 minutes allocated for each section. If the paper is taken in two sessions on
separate occasions, Section 1 must be collected in after the first session and
Section 2 handed out at the beginning of the second session.
Important Constants
m s-1
Speed of light

3.00 × 10
Planck constant
ℎ
6.63 × 10
Js
Electronic charge

1.60 × 10
C
Mass of electron

9.11 × 10
kg
Gravitational constant

6.67 × 10
N m2 kg-2
Acceleration of free fall

9.81
Permittivity of a vacuum

8.85 × 10
F m-1
Avogadro constant

6.02 × 10
mol-1
2
m s-2
BPhO SPONSORS
Worshipful Company of Instrument Makers
3
!
<
Question 1.
⼦
“
⼗
!
←
-
a
图没问题
,
;
→
(a) Sketch the electric field lines due to two point charges, of magnitudes +
at A and B, separated by a distance !.
and +2 ,
fieldstrength合起来是
(i)
0
Determine the location of the neutral point, P, where the electric field is zero.
⼆
⼀
场线越
稀疏
越⼩
,
(ii)
场强
Why does the magnitude of the electric field vary along a field line?
E
=
o
fieldstreugthisonverselypropostional
the
,
vanies with
the radious
sguane of
(b) A charge of 0.5 x 106 C passes through a 12 V battery when the battery discharges. of field lines
Assuming that the p.d. across the terminals remains constant, calculate the time for
which it can supply 0.45 kW.
[2]
12
0 5 X 106×
UQ
E
6 x 106 J
the the
{
p=
=
.
⼆号
t
50
6×
:
33 × 104 s
.
1
:
≈ 3
69
h
←
(i)
two resistors in series which are, in turn, in series with three resistors in
parallel.
(ii)
five resistors that are not in series or parallel, or in a combination of series
and parallel arrangements.
⼀
?? ?
→
⼀
Calculate the resistance in (i) and (ii) if all the resistors have resistance ".
① 序
官 x 3 soRT =
l
,
品
⼾
宁
l
电桥双台
⼀
RT
[5]
:
⼆号
RTO
tR
+
R
RT
=
号R
√
balarced
i
isR .
iT
wheatstone
(d) Two spheres, of uniform density, one of mass  and radius # and the other of
mass  and radius # , attract each other gravitationally . What is their relative
speed at the instant of collision if they are released from rest when a great distance
apart?
[7]
Gm
conservation of momentum
注 mvz
⼀
:
.
√
(c) Draw a general resistive network diagram with:
☆
density
magnitude
.
=
=
E
[5]
品
:
mV
, tmzs
v
=
J
bridge
Grm
'
=
,
mz
⼀
mc + ri
也要考虑
⼀
G
三 bu
( mitmz
)
,
4
mz
( r, +^z
}
①
②
G
嘴
mvi
=
=
Im vi+ zim 吃
m 2Vz
、
.
VaVtrz
=
—
舞
2G ( m
(e) A bicycle tyre has a volume of 1.2 x 10-3 m3 when fully inflated. A bicycle pump has a
working volume of 9.0 x 10-5 m3. How many strokes, $, of the pump are needed to
inflate the completely flat tyre, containing no air, to a pressure of 3.0 x 105 Pa? The
atmospheric pressure is 1.0 x 105 Pa. Assume the air is pumped in slowly so that there
is no change in temperature.
[5]
pV
nRE
=
P,
3
×
V,
105 ×
VPz
n
=
1 2 x 203
so
n
9 x 105
nxCx 105 x
=
,
√
40
=
(f) A van, travelling at constant speed of 80 km hr-1 (km/hour), passes a car. The car
immediately begins to accelerate at a constant rate of 1.2 m s-2 and passes the van
0.50 km further down the road. What is the speed, %, of the car when it passes the
van?
UWar :80kmth g
1s
[4]
S
0 5 km
bow
⼀
0
m
=
τ
S
=
合⼆算
25
VE
-
2北 U
点
2
at
=
⽴x
-
500
⽐
"
x2
=
50
. 2
√
]
A calorimeter contains 0.800 kg of water at a temperature of 15.0 oC.
)
=
soV
(g)
m
:
.
1
ms
)
The heat
capacity of the calorimeter is 42.8 J C . 0.400 kg of molten lead is poured into the
calorimeter. The final equilibrium temperature is 25.0 oC. What was the initial
temperature of the lead?
mCo θ
E
o -1
⼀
=
The specific heat of molten lead is 158 J kg-1 oC-1, the specific heat of solid lead is 137 J
kg-1 oC-1 and the specific latent heat is 2.323 x 104 J kg-1. Lead freezes at 327 oC. The
specific heat of water is 4200 J kg-1 oC-1.
323 × 10 号
4
) 40 . 4 × 158
.x 2
= 15 ) + 0 8 × 4 Ox ( 25 - 15
[5]
⼀
42 8
.
×
(
25
-
340 ③≈
T
.
457 C
327
)
.
63 2 T +
=
⼀
5175
.
( 3 z)
2
,
0
T
-
)
× 0
.
4 × (3
)
执学的题都做的不错
(h) A small object of mass  rests on a scale-pan which is supported by a spring. The 很简单
period of vertical oscillations is 0.50 s. When the amplitude of the oscillations
√
⼼
exceeds the value, &, the mass leaves the scale-pan. Determine &.
-
ma
Gmnx
A
=
=
ng
a
=
9
.
8
)
ω
:
琴
:
器
WZA
9 8)
.
=
前
=
0
.
0621
m
,
5
√
=
4π
F
=
mg
[3]
Gauss
'
Law
s
(i) Uncharged metallic spheres of radii 6", 3" and 2" are mounted on insulated stands.
The spheres of radii 2" and 6" are charged to a potential ' above earth potential.
All three spheres are then briefly joined by a copper wire. What, in terms of ' , is the
subsequent potential of the sphere of radius 3" ?
What fraction of the original total charge is held by the sphere of radius 3" ?
Q
.
potential 不是体积
V
是
V
已qr
=
[5]
(j) The maximum kinetic energy of photoelectrons ejected from a tungsten surface by
monochromatic light of wavelength 248 nm is 8.60 x 10-20 J.
What is the value of the work function, (, of tungsten?
uf
d
⽐
>
1
,
品
dug
W
ng
2
↓
.
1
xc
2
[3]
"
0 '
%
6 63
=
×
.
-
8 6 × 10
1024 xix
-
-
,
19
JV
7 16
.
F
:
UcR
=
o
-
.
4
a
xsmug
3
ngx o h xasso
×
0 -
: Vnice
s 2
e
.
ng
xcoshit l
\
\ngx aL
0
=
G
9
=
0,
.
⼀
904
,
2 ngxLxos to ' 3 mgxLyos
(l) A smooth ball of radius 10.0 cm, mass 0.600 kg, hangs by a weightless string from a
support. What is the speed of a horizontal wind necessary to keep the string inclined
at 39o to the vertical? Make the assumption that the wind speed drops to zero on
collision with the ball. The density of the air is 1.293 kg m-3. ⽤动量做
6
TxCos 390
g
[4]
F
MUB )
政
0
=
T
35
=
√
6
=
岁 mvz
4
=
.
.
9
⽅
c
E
McO 4
0
-
(k) A ladder of length ) and mass , with a uniform density, rests against a frictionless
vertical wall at an angle of 60o to the wall. The lower end rests on a flat surface with
a coefficient of static friction of *+ = 0.40. A student with a mass - = 2 attempts
to climb the ladder. What θ
fraction of the distance up the ladder will the student have
√
Thovef
reached when the ladder begins to slip?
. 04 %
肾
,
⼚
R
30
ng troug
3 + J3 + 6
[5]
amg
M
B
0
①
=
R
三个
frx
fλ
V=
F
g
7 ]
=
.
×
'
t2
.
F
了
s
,
b 3
{
:
4
,
.
e
↴
答
=
ng
3 ?)
39 "
=tan
F
=☆ 筑
(m) The activity of polonium, Po, fell to one eighth of its initial value in 420 days. Calculate
the half-life, ./ , of polonium.
京 A11
Aoe
-
:
9Po
^t
=
lm
brwsf f
⼀
字
e :
七定⼆
≈
-
λ=
λ
>
=α
→
+
?
Pb
+
0
f
=
:
CA 3
2
Give the numerical values of a, b, c, d, e, and f in the nuclear equation
”
.
=
lar
2
」
B
Aγ
[4]
3600 xx
x 420 x
分 73
X
哭 =×
-
20
s
=
8
③
C
d
4
=
G
的
=
≈
4
halflife
的 = 14
t
306
2 t 82 +
.
√
r
e
:
=
o
.
√
go
6 21 xu 7
s
≈
6
to
Of
=
z 1
o
84
α
⽣你会
,
gamma就是
INo =
p
这是电磁⽪的⼀种
oday
N4
^j
1 kg
多
kg
4
kg
Oa
Si
.
kg
(n) Four masses of 1 kg, 4 kg, 3 kg, and 4 kg are arranged∞
cyclically at the corners of a
square of side 2C and centre O. A thin circular metal ring has radius D, mass 8 kg, and
with the same centre O lies in the same plane as the square. Determine the position
of the centre of mass of the system from O.
∞
[3]
+3 x ( 站 ) + 4
}
站 ) + ×\
占 )+8 x ( 8 =
kg 4
的
之b
!
⼀
π
-
|B
b
+ 3
13 - 3
Lb
4
x
20 x
=
b
:
Y
(
)
,
ob
=
y
-
=
⼀ ob
2x
)
=b
sod
=P
)
√
(o) A trumpeter travelling in an open car sounds a note at 440 Hz. A stationary
pedestrian directly in the path of the car hears a note at frequency 466 Hz. What is
the speed of the car? The velocity of sound is 331 ms-1.
466
[3]
0
-
靠
=
V
=
466
=
19
, m
6
440
.
m
'
,
公式不对
s
号
√s
(p) A beam of protons is accelerated from rest through a potential difference of 2000 V
and enters a uniform magnetic field which is perpendicular to the direction of the
proton beam. If the flux density is 0.2000 T, calculate the radius of the path of the
it s
beam.
TH
for
How is the result modified for deuterons? 2! H
105
G 可与
v
[4]
靠
= vO
⼀
'
γ=
X
E
r
=
⽴叫 x
=
7 ×0-
bitxilmmms
higxoi
0
2×
1,
6
x 10
' 9
woxibx
:
=
0
.
032
☆
1
r
=
.
67
的
×
=
)
X 2
20
,
x
605
4 38 x
,
—
0
rm
.
⽉ X
1 6
.
x
6049
(q) A particle, mass m, slides down the smooth track, Figure 1(q), from a height E under
gravity. It is to complete a circular trajectory of radius " when reaching its lowest
point. Determine the smallest value of E.
[3]
号
.
00457
√
-
m
⼀
{
Ttmg
I ≥
m .
⼀
√
Img
m
=
m
O
0
0
≈
-g
3
≥
vn
Wheon
v
gt
=
=
7
=
9
mg
2
=
H
End of Section 1
2
2
Rt
m
H
Figure 1(q).
V
=
R
+
IR
5R
√
们
kg