Gróf Andrea Karinthy Frigyes Gimnázium,...
Transcript of Gróf Andrea Karinthy Frigyes Gimnázium,...
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Gróf Andrea
Karinthy Frigyes Gimnázium, Budapest
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Description of motions
PHYSICS
•Choice of referenceframe emphasized.•But inertial frames usedexclusively.•Students corrected byteacher if they talk aboutcentrifugal force.
GEOGRAPHY
•Idea of reference frame not addressed.•"Natural" reference frame is non-inertial.•Explanations refer tocentrifugaland Coriolis forces.
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1. Survey on the understanding of
the physics behind geography
2. A possible introduction to inertial
forces:
merry-go-round example treated
quantitatively
3. Applications in physics and
geography
!
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1. Survey on the physics (mechanics) behind
geography
MCQ questions on timekeeping, the shape of the Earth,
motions of air and the seas, tides, etc.
215 students (16 and 17-year olds)
Background: 1 year of physical geography
and 1 year of physics
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A.Fcentrifugal << Fcentripetal for fast rotations 11%
B. Fcentrifugal only exists for astronomical sizes 10%
C. Observer does/does not rotate along 17%
D.Fcentrifugal always present, therefore not felt 49%
(no answer 13%)
Questions involving inertial forces
Q
A
Geography: oblate Earth explained in terms of the
centrifugal force.
Physics problems on rotating objects: such forces not
considered.
What is the difference?
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N
?Q
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S
??
Q
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A.South clockwise, north counterclockwise 56%
B. North clockwise, south counterclockwise 21%
C. Same sense 8%
D.Anything may happen 10%
(no answer 5%)
A
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https://www.youtube.com/watch?v=4llVfoDuVlw
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s
m14.3
3
5.122
T
rv
2
2
2
s
m58.6 r
r
va
N13268.520 maF
A
B
2. Describing motions on a playground
roundabout
The motion of A as seen by B:
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s
m64.35.014.3
N177.084.802.0merrynet
maFF
2
22
s
m84.8
5.1
64.3)(
r
uva
Tangential motion as described by the inertial observer B
For rotating observer A:
,s
m17.0
5.1
5.0
2
22
r
ua
0.177NN003.017.002.0net
maF
What other force is there?
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FcfFcoriolis
Fmerry= 0.177N
N003.0net
F N132.0cfF
N 042.0
132.0177.0003.0
N177.0merry
F
(inwards)
(inwards)
(outwards)
needed:
(outwards)
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r
uvmmaFF
2
merrynet
)(
r
mu
r
mvu
r
mv22
2
r
mvu
r
mvF
r
mu 22
merry
2
0.003 N = 0.177 N – 0.132 N – 0.042 N.
umur
vm
r
mvu 22
2
N042.05.1
5.014.302.02
maFnet
For B
For A
Algebraically:
Fcf
Fcoriolis
Fmerry= 0.177N
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For B
a = 0
A
B
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ω
The same motion as seen by A:
Radial speed constant
Tangential speed
increasest
rv
t t
trs
trta 2
)(2
1
vt
ra
22
t
t
t
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Latitude of Budapest: φ = 47.5º
(a) Magnitude and direction of
the centrifugal acceleration
in Budapest.
(b) Magnitude and direction of the
acceleration of free fall in Budapest?
mgFgrav
Ω
Fcf
(local) verticalWhich way is "down"?
Sports events?
(a) Gravitational, centrifugal acceleration and free
fall acceleration at the Equator?
(b) Athlete can jump to 8 metres at the poles. How
far can he jump on the Equator?
3. Applications: Inertial forces
on the rotating Earth
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Coriolis force at the Equator
Air moving at u = 20 m/s towards the west.
Magnitude of acceleration towards the centre of the Earth?
(a) according to an inertial observer?
(b) according to an Earth-based observer?
(c) What is the magnitude and direction of the Coriolis
acceleration?
6
2652
1038.6
20)1038.6)(1029.7()(
R
uRa
2m/s 0369.0
25
6
22
m/s 1027.61038.6
20
R
ua
down)y (verticallm/s 1092.220)1029.7(22235
uaC
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PPA
2π·sinφ
Coriolis force elsewhereFoucault pendulum, Paris: φ = 48.8°
What is the local angular speed?
sin
vaC
sin2
φ
φ
A
P
Paris
http://enggar.net/page/12/?s/
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3.11rad197.036001049.55
t
In Paris: φ = 48.8°
One period of the Panthéon pendulum is 16.4 sec.
(a) How much does it turn in an hour?
(b) Displacement between two successive swings
on a circle of radius 3 m?
rad1001.94.161049.545
t
mm7.231001.94
rt
s/1049.58.48sin1029.7sin55
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r = 2 cm, v = 10 cm/s
(a) Find the acceleration towards
the centre.
(b) What is the contribution of the
Coriolis force to this?
2
22
m/s 5.002.0
1.0
r
va
sin2 vaC
255m/s1015.47sin)103.7(1.02
Is the Coriolis force important?
No
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Find (a) radius of spot
1° corresponds to
≈ 9° means r ≈ 1.1·107 m
(b) acceleration of gas
(c) Coriolis acceleration
m102.1360
104.1
360
2 68
R
Jupiter: T = 9.8 hours,
R = 71 900 km (equatorial)
Great Red Spot φ = 22° (S),
wind v ≈ 100 m/s
2
4
s
m109
a
2
4
Cs
m103.1
a Ye
s
www.celestiamotherlode.net/catalog/jupiter.php
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http://www.japantimes.co.jp/news/2014/06/18/national/shinkansen-tops-list-100-innovative-postwar-technologies/#.Va84VPkmHpE
Shinkansen train v = 200 km/h
Tokyo to Osaka, both N55°
35sin103.76.3
2002sin2
5va
C
g0005.0s
m0047.0
2
No
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Golfer in Scotland (N55°)
can hit the ball to 300 m at 45° angle.
What is the deviation of the ball
owing to the Coriolis force?
g
vt
sin20
g
v
g
vv
cossin2sin2cos
2
000
m3008.98.9
2
1
2
12 2
0
2
0
v
v
,s
m548.9300
0v st 7.8
8.9
45sin542
cossin2 0C va
2
5
s
m0046.045cos5455sin103.72
cm177.80046.02
1
2
1 22
C tad No
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Artillery missile, N50°,
v0 = 700 m/s towards the East, at 45° angle.
Deviation owing to the Coriolis force?
g
v
g
vv
cossin2sin2cosRange
2
00
0km50
8.9
2
1
2
17002
2
2
00
2
C
sin2)cossin2(
2
1
2
1
g
vvtad
cossin
sin4 23
02v
g
m28045cos45sin7008.9
50sin103.74 23
2
5
Ye
s
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Frictionless and horizontal ice rink, 30 m wide,
Puck given an initial velocity.
Coriolis force only: circular motion
Find:
(a) speed needed in Budapest (N47.5°)
Note:
(b) What is the radius if the speed is 1 m/s?
At 10° latitude? At 80°?
vr
v sin2
2
local2sin2
r
v
s
mm61.0155.47sin103.72sin2
5
rv
km) 7.0 km, (39 km3.95.47sin103.72
1
sin25
vr
An interesting kind of motion
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Buoy in the Baltic Sea,
SE of Stockholm, N57°
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Design a space station:
• Cylindrical shape
• Artificial gravity is provided
by centrifugal force owing to
spinning about the axis.
• Coriolis force on crew walking
at 1 m/s is no greater than
0.05mg .
gr 2
2s
m1005.0
s
m12
s
125.0
m16025.0
10
22
gr
http://www.astronautix.com/craft/span1984.htm
Both forces to consider
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References
Anders O. Persson The Coriolis Effect: Four centuries of conflict between common sense and mathematics, History of Meteorology 2 (2005)
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THE END
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