Transcript Gravity - barransclass

Board Work
1. A satellite revolves
around its planet in a
perfectly circular orbit at a
constant speed.
a. At each of the four
positions, draw a vector
representing the net force
on the satellite. Label all
the force vectors F.
b. At each position, draw a vector to represent the
satellite’s velocity. Label each vector v.
Board Work
c. Are all F vectors the same
magnitude?
d. Are all v vectors the same
magnitude?
e. What is the angle between
F and v at any position of
the satellite?
f. Is any component of F ever
parallel to v?
g. Is the KE of the satellite varying or constant?
Gravity
The laws of physics are universal
What’s the point?
• Gravity is one of the fundamental forces.
Objectives
• Determine the gravitational attraction
between objects.
• Interpret vector and field line depictions of
gravitational fields.
Historical Background
• Earthly and celestial objects thought
fundamentally different
– Earthly objects seek a lowly position
– Celestial objects move in perfect circles
Newton’s Insight
• The force pulling us to the ground is the
same force curving the moon’s path:
gravity!
Poll Question
Which is greater?
A.
B.
C.
D.
The pull of gravity from the earth on the moon.
The pull of gravity from the moon on the earth.
Both forces are equally strong.
Cannot tell without more information.
Newton’s Law of Universal
Gravitation
Force between two objects:
m1m2
F=G
d2
m1, m2: masses of the objects
d: distance between objects’ centers of mass
G: universal gravitational constant,
6.672  10–11 Nm2/kg2
Properties of Gravity
m1m2
F=G
d2
• direction is toward the other object
• magnitude decreases as (distance)2
increases
• never becomes zero
• infinite at zero separation (?!)
Poll Question
Two satellites orbit at the same distance from a
planet. One has twice the mass of the other. How
do their gravitational attractions to the planet
compare?
A.
B.
They have the same attraction.
The massive satellite is attracted with
twice the force of the light satellite.
C. The massive satellite is attracted with
half the force of the light satellite.
Poll Question
Two satellites orbit at the same distance from a
planet. One has twice the mass of the other. How
do their gravitational accelerations toward the
planet compare?
A.
B.
They have the same acceleration.
The massive satellite accelerates
twice as much as the light satellite.
C. The massive satellite accelerates half
as much as the light satellite.
Poll Question
When two objects are separated by a distance D,
the gravitational force between them is F. If they
move closer, to 1/2 the distance (D/2), the force
becomes
F
F
D
A.
B.
C.
D.
F/2.
2F.
D/2
4F.
Cannot tell without more information.
Gravitational Potential Energy
Work to bring two objects from separation 
to separation d:
m1m2
PE = –G
d
• Negative because you must push against
gravity to hold them
• The farther the d, the less negative the PE
Escape Speed
• A fast enough object can “escape” a
gravitational field.
• Can occur if KE + PEgrav > 0.
• Although gravity forever pulls it back, it
never turns around!
Gravitational Field
• Gives the force acting on an object of
mass m
GM
F = m · field
field = g = 2
d
• M = mass of object creating the field
• d = distance from the object
• field is a vector!
Group Work
2. Draw gravitational field vectors for all
positions indicated. One is shown.
Poll Question
At which position is the
satellite speeding up?
A. Position A.
B. Position B.
C. Position C.
D. Position D.
E. None of these.
Quick Question
At which position is the
satellite slowing down?
A. Position A.
B. Position B.
C. Position C.
D. Position D.
E. None of these.
Poll Question
At which position is the
satellite changing its
direction but not its speed?
A.
B.
C.
D.
E.
Position A.
Position B.
Position C.
Position D.
None of these.
Board Work
3. Rank the positions in
descending order of:
a.
b.
c.
d.
e.
Gravitational force.
Acceleration.
Speed.
Kinetic energy.
Gravitational potential
energy.
f. Total energy.
g. Angular momentum.
Gravity between Real Objects
..
The actual force acting on an object is the
sum of all forces on all its particles from all
the particles of the other object!
A Lucky Break
The gravitational field around a sphere is the same
as would be around a point particle of the same
mass at the center of the sphere.
Gravity on Earth
•
•
•
•
G = 6.670  10–11 Nm2/kg2
Earth’s mass = 5.976  1024 kg = M
Earth’s radius = 6378174 m = d
so the field g is
g = (6.670  10–11 Nm2/kg2 )
= 9.8 N/kg
look familiar?
(5.976  1024 kg )
(6378174 m )2
Reading for Next Time
• Electric forces
• Big Ideas:
– Electric charge
– Coulomb’s force law
– Electric fields
• representation by field vectors
• representation by field lines
– Electric potential