Transcript Advanced Physics

Advanced Physics
Chapter 5
Circular Motion: Gravitation
Chapter 5: Circular Motion:
Gravitation
5-1 Kinematics of Uniform Circular Motion
5-2 Dynamics of Uniform Circular Motion
5-3 Highway Curves, Banked and Unbanked
5-4 Nonuniform Circular Motion
5-6 Newton’s Law of Universal Gravitation
5-7 Gravity near the Earth's Surface
5-8 Satellites and “Weightlessness”
5-10 Types of Forces in Nature
5-1 Kinematics of Uniform
Circular Motion
Uniform Circular Motion
object that moves in
a circle with constant
speed
magnitude of velocity
is constant but
direction is changing
5-1 Kinematics of Uniform
Circular Motion
Centripetal (radial)
acceleration (ar or ac)
 center-seeking
acceleration
 acceleration directed
toward the center of the
circle
 velocity and acceleration
vectors are perpendicular
to each other
5-1 Kinematics of Uniform
Circular Motion
Velocity
v = d/t
d = 2r
so v = 2r/T
where T = period of
revolution (sec)
and f = frequency
(sec-1)
T = 1/f
5-1 Kinematics of Uniform
Circular Motion
Centripetal acceleration
aR = v2/r
aR = 42r/T2
5-2 Dynamics of Uniform
Circular Motion
According to Newton’s
Second Law: Fnet = ma
FR = maR =
mv2/r
net centripetal force
(FR) must be
directed toward
center (why?)
centripetal force vs.
centrifugal force
5-3 Highway Curves,
Banked and Unbanked
 When a car goes around
a curve in the road what
keeps it on the road?
 When is the friction
between the tires and the
road greater, when they
are rolling or sliding?
 So to keep a car on the
road on a curve we
must……
5-3 Highway Curves,
Banked and Unbanked
 Banking a curve reduces
skidding why?
 Fn is at an angle toward
the center of the curve
 so a portion of the Fn
goes into FR so the tires
need to supply less
frictional force to make
up for the remaining FR
needed
5-3 Highway Curves,
Banked and Unbanked
Banking angle of road
Fnsin = mv2/r
since Fncos = mg
then Fn = mg/cos
mg(sin /cos) =
mv2/r
g(tan ) = v2/r
tan = v2/rg
 so banking angle of road
doesn’t depend on m, just
v,r and g
5-4 Nonuniform Circular
Motion
For an object in UCM; the only
acceleration is due to radial (centripetal)
acceleration
aR is caused by what? Equation?
But if the object in circular motion is
speeding up or slowing down there is
another type of acceleration, tangential
acceleration
5-4 Nonuniform Circular
Motion
Tangential acceleration (atan)
Acceleration caused by the change in
the magnitude of the velocity of an
object moving in a circular path
atan = v/t
5-4 Nonuniform Circular
Motion
Total vector acceleration (a)
Acceleration caused by the change in
the magnitude and direction of the
velocity of an object moving in a
circular path
It is the sum of both the tangential
and radial acceleration of an object
a = atan + aR
5-4 Nonuniform Circular
Motion
Total vector acceleration (a)
a = atan + aR
The magnitude of a at any moment is:
a =
2
(a tan
+
2
1/2
a R)
5-6 Newton’s Law of
Universal Gravitation
Newton’s Law of
Universal Gravitation
every particle in the
Universe attracts
every other particle
with a force that is
proportional to their
masses and inversely
proportional to the
distance between
them
5-6 Newton’s Law of
Universal Gravitation
Newton’s Law of
Universal Gravitation
the force of gravity
acts along a line
joining the two
particles.
F = Gm1m2/d2
G = 6.67 x10
Nm2/kg2
–11
5-6 Newton’s Law of
Universal Gravitation
Find the force of
gravity between two
electrons that are
2.3x10-2 nm apart
Answer:
1.05 x 10-49 N
5-7 Gravity near the
Earth's Surface
Since the force of
gravity is equal to the
weight of an object…
Gmome/r2 = mog
so….
g = Gme/r2
so..gravity (g) doesn’t
depend on the mass
of the object, just G,
me and r!
5-8 Satellites and
“Weightlessness”
Why do satellites
orbit the Earth?
How can a person
orbiting the Earth
experience
“weightlessness”?
Many nasty effects of
weightlessness on the
body
5-8 Satellites and
“Weightlessness”
What is the
relationship between
Fn, Fa, and Fg in the
following situations?
stationary
accelerating up
accelerating down
in free-fall
5-10 Types of Forces in
Nature
Four different fundamental
forces:
 gravitational force
force between any two objects
 electromagnet force
force between any two charged
objects
 strong nuclear force
force that holds the nucleus
together
 weak nuclear force
force involved in certain types of
nuclear decay
5-10 Types of Forces in
Nature
What is
GUT?