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Dynamics
Dynamics
Rotational K.E.
Tides
g as a function of latitude
Part IV – “If I have
ever made any valuable
discoveries, it has been
owing more to patient
attention, than to any other
talent.”
Revision:
READ the Textbook!
Do the past papers – ideally
under exam like conditions
http://www.hep.manchester.ac.uk/u/parkes/Chris_Parkes/Teaching.html
October 2012
Chris Parkes
Gravitational Force
Myth of Newton & apple.
He realised gravity is universal
same for planets and apples
•Any two masses m1,m2 attract each other
with a gravitational force:
F
F
m1m2
F G 2
r
r
m2
m1
Newton’s law of Gravity
Inverse square law 1/r2, r distance between masses
The gravitational constant G = 6.67 x 10-11 Nm2/kg2
•Explains motion of planets, moons and tides
24kg,
m
=5.97x10


mE m
GmE
E
Gravity on
m
F G
 
RE=6378km
2
2

earth’s surface
RE
RE 
Mass, radius of earth

GmE
1
 9.81ms
Or F  mg Hence, g 
2
RE
N.B. general solution is an ellipse not a circle - planets travel in ellipses around sun
Satellites
•Centripetal Force provided by Gravity
Mm mv2
F G 2 
R
R
M
2
M
v G
v

G
R
R
m
R
M
Distance in one revolution s = 2R, in time period T, v=s/T
R
T  2R / v  2R
GM
T2R3 , Kepler’s 3rd Law
•Special case of satellites – Geostationary orbit
•Stay above same point on earth T=24 hours
3
24  60  60  2
R  42,000km
R2
GM E
Comparable masses in orbit
Masses m1,m2;
Radii r1,r2
4p 2 r 3
T =
G(m1 + m2 )
2
•
•
•
•
•
K.E. = 12 mw 2 r 2
Example Pluto (dwarf planet) and Charon (a moon)
mPluto = 1.31 x 1022 kg
orbit 6.39 days
r (mean) =19,600 km
Find mCharon/mPluto (11%)
Photo Hubble Space Telescope
Tides
• Tides caused by
difference in force
exerted by moon on
mass at near side and
far side of Earth
aTidal
[Zooniverse]
2GM Moon REarth
=±
3
rEarth-Moon
• Tides on both sides
of Earth – given point
two tides per day
In middle of ocean variation in water level approx. 50 cm
Neap tide / Spring tide
• Sun attraction also
has tidal effect
– See Q4 week 12
question sheet
• When moon and sun
align – stronger –
spring tide
• When out of phase –
weaker – neap tide
• Occur twice per lunar
month
Apparent weight with latitude
• Earth rotates on its axis – not an inertial frame
• At Equator require
net force on body to
keep in circular
motion – hence
apparent weight
changes
N = mg - mw rcos f
2
2
Where ϕ is angle from equator plane