Download Lecture 6: Announcements

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Lecture 6: Announcements
Worksheets :
TAs are doing a great job preparing worksheets for section each week.
Those worksheets (and solutions) are posted on our website every Tuesday
night under the ‘Lectures and worksheet’ link.
Class website:
www.ucolick.org/~mfduran/AY2
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Today’s lecture
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•
•
•
•
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Escape velocity
Newton’s version of Kepler’s third law
Tides
Conservation of Energy
Angular momentum
Light, Energy and Matter
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Acceleration in a circle
•
Notice that the orbital velocity depends on the separation between the
masses
v=
�
GM
r
•
Does not depend on the mass of the ‘satellite’ (m)
•
If m orbits a more massive object (M gets bigger)
then it orbits faster
•
If m orbits M farther away then its orbital speed decreases
m
r
M
4
Acceleration in a circle
•
Notice that the orbital velocity depends on the separation between the
�
masses
vorbital =
•
GM
r
If we want an object to escape the gravitational attraction of a more
massive body, we need the object to achieve the escape velocity
vescape =
vescape =
�
√
2GM
r
2vorbital
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Question #1
•
Suppose the Earth suddenly collapsed to 50%
its current size. What would happen to the satellites
orbiting the Earth?
a) They would fall to the ground
b) They would fall to half their current height
c) They would float to twice their current height
d) They would float away
e) Nothing
m
r
M
you can discuss this one with your classmates!
6
Question #1
•
Suppose the Earth suddenly collapsed to 50%
its current size. What would happen to the satellites
orbiting the Earth?
a) They would fall to the ground
b) They would fall to half their current height
c) They would float to twice their current height
d) They would float away
e) Nothing
Fgravity
m
r
M
GmM
=
r2
G = 6.67 × 10−11 m3 kg −1 s−2
you can discuss this one with your classmates!
7
Question #1
•
Suppose the Earth suddenly collapsed to 50%
its current size. What would happen to the satellites
orbiting the Earth?
a) They would fall to the ground
b) They would fall to half their current height
c) They would float to twice their current height
d) They would float away
e) Nothing
Fgravity
GmM
=
r2
G = 6.67 × 10−11 m3 kg −1 s−2
does not depend on the size of the objects!
m
r
M
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Question #2
•
How does the gravitational force between two objects change if the
distance between them triples?
a) the force increases by a factor of three
b) the force increases by a fator of nine
c) the force remains the same
d) the force decreases by a factor of three
e) the force decreases by a factor of nine
m
r
M
you can discuss this one with your classmates!
9
Question #2
•
How does the gravitational force between two objects change if the
distance between them triples?
a) the force increases by a factor of three
b) the force increases by a fator of nine
c) the force remains the same
d) the force decreases by a factor of three
e) the force decreases by a factor of nine
Fgravity
m
r
M
GmM
=
r2
you can discuss this one with your classmates!
10
Question #2
•
How does the gravitational force between two objects change if the
distance between them triples?
m
a) the force increases by a factor of three
b) the force increases by a fator of nine
c) the force remains the same
d) the force decreases by a factor of three
e) the force decreases by a factor of nine
r
M
GmM
Foriginal =
r2
GmM
GmM
Fnew =
=
2
(3r)
9r2
Fnew
1 GmM
1
=
= Foriginal
2
9 r
9
Fnew
1
= Foriginal
9
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Newton’s version of Kepler’s 3rd law
•
Kepler did not know about gravity, he only described the movement of
the planets without knowing the meaning of the ‘constant’.
a3
= constant
2
p
•
Orbital speed is just distance over time
distance: perimeter of a circle
time: orbital period (how long it takes to go around one lap)
vorbital
distance
2πr
=
=
time
P
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Newton’s version of Kepler’s 3rd law
•
Kepler did not know about gravity, he only described the movement of
the planets without knowing the meaning of the ‘constant’.
a3
= constant
2
p
•
Orbital speed is just distance over time
distance: perimeter of a circle
time: orbital period (how long it takes to go around one lap)
vorbital
•
distance
2πr
=
=
time
P
Orbital speed for circular motion (from last time)
2πr
=
P
�
vorbital =
GM
4π 2 r2
GM
r3
GM
→
=
→ 2 =
2
r
P
r
P
4π 2
�
GM
r
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•
Newton’s version of Kepler’s 3rd law
Kepler’s version:
a3
= constant
2
p
3
a
GM
• Newton’s version:
=
2
p
4π 2
→
Constant for any planet
orbiting a star of mass M
•
a: average distance planet-star
p: orbital period for planet
G: gravitational constant
M: mass of the star
•
This is how we can calculate the mass of any star if we know the orbital
parameters of a planet that orbits it!
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Tides: differential force
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Tides are caused by the difference in the force at two locations
•
Force that the moon exerts on a droplet of water:
2
1
dearth−moon
d2−moon
d1−moon
Fdrop
GMmoon mdrop
=
d2
Fdrop
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Tides: differential force
•
Tides are caused by the difference in the force at two locations
•
Force that the moon exerts on a droplet of water:
2
1
dearth−moon
d2−moon
d1−moon
Fdrop
GMmoon mdrop
=
d2
Fdrop
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Tides: differential force
•
Tides are caused by the difference in the force at two locations
•
Force that the moon exerts on a droplet of water:
1
F0
2
F1
F2
dearth−moon
d2−moon
d1−moon
Fdrop
GMmoon mdrop
=
d2
Fdrop
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Tides: differential force
GMmoon mdrop
F1 =
d21
<
GMmoon mdrop
F0 =
d20
If we take the difference between F0 and F1,F2
1
F0
F1
2
F0 − F2 < 0 points to the right
F0 − F1 > 0 points to the left
As the Earth rotates we experience two high
tides and two low tides each day
F2
dearth−moon
d2−moon
d1−moon
<
GMmoon mdrop
F2 =
d22
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Tides
•
The Sun also causes a differential
force from one side to the Earth to
the other
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Spring tide: Sun and Moon reinforce
each other (highest tides)
•
Neap tide: Sun and Moon fighting
each other (lowest tides)
Spring tide
total change = a few feet
Neap tide
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Tides
•
Friction drags water along with the Earth’s rotation, making it go ahead of the
Earth-Moon line
•
Moon’s gravity pulls the water towards the Earth-Moon line, slowing Earth’s
rotation.
•
Earth’s gravity tries to speed up the moon in its orbit, increasing it’s orbital
distance.
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Tides
The asymmetry eventually causes
“tidal locking”
This is what causes the poorly-named
‘dark side of the moon’: the same face
of the Moon always faces the Earth
One rotation per orbit (29.5 days)
Lunar ‘day’ = 1 month
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Break Time
(5 mins)
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Energy
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•
Kinds of Energy
Kinetic Energy (movement)
mv 2
K.E. =
2
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Kinds of Energy
•
Kinetic Energy (movement)
•
Potential Energy (stored energy)
mv 2
K.E. =
2
GM m
P.E. = −
r
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Kinds of Energy
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Kinetic Energy (movement)
•
Potential Energy (stored energy)
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Other kinds:
-Thermal: the kinetic energy of particles in an object
-Chemical potential: Energy stored in chemical bonds
-Radiative: Light! (Next lecture)
mv 2
K.E. =
2
GM m
P.E. = −
r
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Kinds of Energy
•
Kinetic Energy (movement)
•
Potential Energy (stored energy)
•
mv 2
K.E. =
2
GM m
P.E. = −
r
Energy unit: Joule
m2 kg
Joule =
s2
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Conservation of Energy
•
In an isolated system, total energy is always conserved
This means that the total energy = constant value
•
•
It can change for or be exchanged between objects, but total doesn’t change!
Example: Swinging pendulum
At top of swing: no kinetic energy (it stops)
and largest potential energy
At bottom: smallest potential energy and
highest kinetic energy since v is highest at
bottom of swing
h
h: change in distance
from center of earth
Total energy = K. E. + P.E.= constant
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Conservation of Energy and Orbits
•
•
Kepler’s second law: Planets sweep equal areas in equal times
•
At aphelion (largest distance)
P.E. is largest
K.E. is smallest
At perihelion (smallest distance)
P.E. is smallest: closest to the Sun
K.E. is largest: fastest speed
Total energy = K. E. + P.E.= constant
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Quizzyou#6
can discuss this one with your classmates!
1. A swing in a playground is a bad pendulum because it will not swing for very
long once you release it. It stops after a few trips back and forth
1.1.Is energy conserved?
a) yes
b) no
1.2.The ‘closed system’ in this situation must include
a) the swing & the earth
b) the swing & the earth & air
c) the swing & the earth & air & support structure
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Quizzyou#6
can discuss this one with your classmates!
1. A swing in a playground is a bad pendulum because it will not swing for very
long once you release it. It stops after a few trips back and forth
1.1.Is energy conserved?
a) yes
b) no
1.2.The ‘closed system’ in this situation must include
a) the swing & the earth
b) the swing & the earth & air
c) the swing & the earth & air & support structure
2. When I drive my car at 30 miles per hour, it has more kinetic energy than it
does at 10 miles per hour.
a) Yes, it has three times as much kinetic energy
b) Yes, it has nine times as much kinetic energy
c) No, it has the same kinetic energy
a) No, it has three times less kinetic energy
a) No, it has nine times less kinetic energy
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Quizz #6
1. A swing in a playground is a bad pendulum because it will not swing for very
long once you release it. It stops after a few trips back and forth
1.1.Is energy conserved?
a) yes
b) no
1.2.The ‘closed system’ in this situation must include
a) the swing & the earth
b) the swing & the earth & air
c) the swing & the earth & air & support structure
2. When I drive my car at 30 miles per hour, it has more kinetic energy than it
does at 10 miles per hour.
a) Yes, it has three times as much kinetic energy
b) Yes, it has nine times as much kinetic energy
c) No, it has the same kinetic energy
a) No, it has three times less kinetic energy
a) No, it has nine times less kinetic energy
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Angular Momentum
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L: Angular momentum (the ‘oomph’ in rotation)
m : mass of the object
v : rotational speed
r : radius
•
The angular momentum of a
closed system is conserved
•
Examples:
-You, spinning on ‘ideal’ ice
(frictionless)
-A protostellar cloud:
A could of rotating and
collapsing gas
-A planet (and star) in orbit
rotating around each other.
L = mvr
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Angular Momentum
•
L: Angular momentum (the ‘oomph’ in rotation)
m : mass of the object
v : rotational speed
r : radius
•
The angular momentum of a
closed system is conserved
•
Examples:
-You, spinning on ‘ideal’ ice
(frictionless)
-A protostellar cloud:
A could of rotating and
collapsing gas
-A planet (and star) in orbit
rotating around each other.
L = mvr
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Angular Momentum
•
L: Angular momentum (the ‘oomph’ in rotation)
m : mass of the object
v : rotational speed
r : radius
•
The angular momentum of a
closed system is conserved
•
Examples:
-You, spinning on ‘ideal’ ice
(frictionless)
-A protostellar cloud:
A could of rotating and
collapsing gas
-A planet (and star) in orbit
rotating around each other.
L = mvr