Download PHYS16 - Lecture 28

PHYS16 – Lecture 28
Kepler’s Laws and Fluids
November 12, 2010
Kepler’s Laws
Orbits are elliptical
• Eccentricity = 0, then
circular
• Eccentricity = 1 then
linear
• Most planets have an
eccentricity close to 0
Equal areas in equal times
• The area of the triangle
swept out by the object is
equal for equal amounts
of time
• The further the object is
from the sun the lower
the speed.
dA
 constant
dt
Example Question: Earth Speed
• Where is the speed of the earth the greatest?
B
A
C
D
Period-squared is proportional to a3
GM
v 
r
GM
2 2
 r 
r
4 2 GM
 3
2
T
r
T2
 constant
3
a
2
Example Question: Venus’ Period
• Venus has a semi-major axis that is 0.723
times the Earth’s semi major axis. How long
does it take Venus to orbit the Sun?
A)
B)
C)
D)
204 days
224 days
264 days
294 days
Example Question: Seasons
• If the earth spends two less days in the winter
half of the orbit than the summer half of the
orbit (for N. hemisphere), what is its speed in
winter vs. summer?
A)
B)
C)
D)
Faster
Same
Slower
Not enough information
Supposed to be sweeping out equal areas in equal times.
But if times aren’t equal, then either the areas aren’t equal or
the Earth’s speed is faster in winter…
Main Points
• Gravitational Force and Potential
• Satellites
– Orbital energy
– Escape velocity
– Geostationary orbits
• Kepler’s Laws
– Orbits are elliptical
– Orbits sweep out equal area in equal time
– Orbital period-squared is proportional at a3
Fluids
This Week
•
•
•
•
Pressure and Pascal’s Principle
Buoyant Force and Archimedes’ Principle
Equation of Continuity
Bernoulli’s Equation
Fluids
• Fluid = a liquid or a gas, a substance that flows
• What happens when you apply a force to a
fluid?
– Gas compresses
(change density)
– Liquids are
incompressible
http://www.swe.org/iac/images/liquid-gas2.jpg
Pressure
• Pressure (p) – Force per unit area
– Direction of pressure is normal to a surface
– Unit is Pa=N/m2
• Air Pressure = 1E5 Pa = 1 atm = 760 mmHg
F
P
A
http://www.school-for-champions.com/science/pressure.htm
Example: Force due to Air Pressure
• What is the force on the lid of a pop can due
to air pressure ? (radius = r = 0.020 m)
F  PA  P(r )  (1E5 Pa)( )(0.02 m)
F  130 N
2
So why doesn’t the pop can get crushed?
2
Pascal’s Principle
• Pressure change in a confined fluid is the same at all
points in the fluid
• Mechanical advantage in hydraulic lift = Abig/Asmall
m = 1 kg
http://www.vectorsite.net/tpecp_08.html
Example: Cracking an Egg
• If I apply equal force to all sides of an egg, will
it crack?
No!
http://randywakeman.com/TragicEgg.jpg
Main Points
• Pressure = Force/Area
• Pressure change in a confined fluid is the
same at all points