Grf Andrea Karinthy Frigyes Gimnzium, Budapest Description of - - PowerPoint PPT Presentation

Gróf Andrea Karinthy Frigyes Gimnázium, Budapest

Description of motions PHYSICS

• Choice of reference

frame emphasized.

• But inertial frames used

exclusively.

• Students corrected by

teacher if they talk about centrifugal force.

GEOGRAPHY

• Idea of reference frame

not addressed.

• "Natural" reference frame is

non-inertial.

• Explanations refer to

centrifugal and Coriolis forces.

• 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

 ! 

• 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

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?

N

?

Q

S

? ?

Q

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

https://www.youtube.com/watch?v=4llVfoDuVlw

s m 14 . 3 3 5 . 1 2 2        T r v

2 2 2

s m 58 . 6    r r v a  N 132 68 . 5 20     ma F

A B

• 2. Describing motions on a playground

roundabout

The motion of A as seen by B:

s m 64 . 3 5 . 14 . 3    N 177 . 84 . 8 02 .

merry net

     ma F F

2 2 2

s m 84 . 8 5 . 1 64 . 3 ) (     r u v a

Tangential motion as described by the inertial observer B For rotating observer A:

, s m 17 . 5 . 1 5 .

2 2 2

   r u a 0.177N N 003 . 17 . 02 .

net

     ma F

What other force is there?

Fcf Fcoriolis

Fmerry= 0.177N

N 003 .

net

  F

N 132 .

cf 

F

N 042 . 132 . 177 . 003 .     

N 177 .

merry

  F

(inwards) (inwards) (outwards) needed: (outwards)

r u v m ma F F

2 merry net

) (     r mu r mvu r mv

2 2

2    r mvu r mv F r mu 2

2 merry 2

  

0.003 N = 0.177 N – 0.132 N – 0.042 N.

u m u r v m r mvu        2 2 2

N 042 . 5 . 1 5 . 14 . 3 02 . 2       ma Fnet

For B For A Algebraically:

Fcf Fcoriolis

Fmerry= 0.177N

For B

a = 0

A B



ω

The same motion as seen by A:

Radial speed constant Tangential speed increases

t r v   

t 

t       t r s       t r t a      

2

) ( 2 1 v t r a        2 2

t  t  t 

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?

mg Fgrav Ω Fcf

(local) vertical

Which 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
• n the rotating Earth

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 2 6 5 2

10 38 . 6 20 ) 10 38 . 6 )( 10 29 . 7 ( ) (        



R u R a

2

m/s 0369 . 

2 5 6 2 2

m/s 10 27 . 6 10 38 . 6 20



     R u a down) y (verticall m/s 10 92 . 2 20 ) 10 29 . 7 ( 2 2

2 3 5  

        u a C

P P A 2π·sinφ

Coriolis force elsewhere

Foucault pendulum, Paris: φ = 48.8° What is the local angular speed?

  sin  

v a C      sin 2

φ φ A P

Paris

http://enggar.net/page/12/?s/

     



3 . 11 rad 197 . 3600 10 49 . 5

5

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

• n a circle of radius 3 m?

rad 10 01 . 9 4 . 16 10 49 . 5

4 5  

     t 

mm 7 . 2 3 10 01 . 9

4

    



r t 

s / 10 49 . 5 8 . 48 sin 10 29 . 7 sin

5 5  

          

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 2 2

m/s 5 . 02 . 1 .    r v a  sin 2   v a C

2 5 5

m/s 10 1 5 . 47 sin ) 10 3 . 7 ( 1 . 2

 

      

Is the Coriolis force important?

No No

Find (a) radius of spot 1° corresponds to ≈ 9° means r ≈ 1.1·107 m (b) acceleration of gas (c) Coriolis acceleration

m 10 2 . 1 360 10 4 . 1 360 2

6 8

      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 m 10 9



  a

2 4 C

s m 10 3 . 1



  a

Ye Ye s

www.celestiamotherlode.net/catalog/jupiter.php

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°

        



35 sin 10 3 . 7 6 . 3 200 2 sin 2

5

 v a C g 0005 . s m 0047 .

2 



No No

Golfer in Scotland (N55°) can hit the ball to 300 m at 45° angle. What is the deviation of the ball

• wing to the Coriolis force?

g v t  sin 2 

   g v g v v     cos sin 2 sin 2 cos

2

m 300 8 . 9 8 . 9 2 1 2 1 2

2 2

      v v , s m 54 8 . 9 300    v

s t 7 . 8 8 . 9 45 sin 54 2    

       cos sin 2

C

v a

2 5

s m 0046 . 45 cos 54 55 sin 10 3 . 7 2         



cm 17 7 . 8 0046 . 2 1 2 1

2 2 C

     t a d

No No

Artillery missile, N50°, v0 = 700 m/s towards the East, at 45° angle. Deviation owing to the Coriolis force?

    g v g v v     cos sin 2 sin 2 cos Range

2

km 50 8 . 9 2 1 2 1 700 2

2

   

               

2 2 C

sin 2 ) cos sin 2 ( 2 1 2 1 g v v t a d   

        cos sin sin 4

2 3 2

v g m 280 45 cos 45 sin 700 8 . 9 50 sin 10 3 . 7 4

2 3 2 5

         



Ye Ye s

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°?

v r v     sin 2

2 local

2 sin 2      r v s mm 61 . 15 5 . 47 sin 10 3 . 7 2 sin 2

5

         



r v  km) 7.0 km, (39 km 3 . 9 5 . 47 sin 10 3 . 7 2 1 sin 2

5

       



 v r

An interesting kind of motion

Buoy in the Baltic Sea, SE of Stockholm, N57°

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 .

g r 

2



2

s m 10 05 . s m 1 2          

s 1 25 .    m 160 25 . 10

2 2

    g r

http://www.astronautix.com/craft/span1984.htm

Both forces to consider

References Anders O. Persson The Coriolis Effect: Four centuries of conflict between common sense and mathematics, History

• f Meteorology 2 (2005)

THE END

Thank you for your attention