Transcript AP Physics C IF

AP Physics C I.F
Oscillations and Gravitation
Kepler’s Three Laws for
Planetary Motion
1. All planets move in an
elliptical orbit (barely) with the
sun at one of the foci.
2. A line that connects the
planets with the sun sweeps out
equal areas in equal time
periods. This means the planet
moves more slowly farther away
from the sun and more rapidly
closer to the sun.
Conservation of angular
momentum revisted
Newton’s Universal Law of
Gravity
The falling apple
3. The square of the period of a
planet is directly proportional to
the cube of its orbital radius.
(This isn’t a boxer but you will be
asked to derive it)
Gravitational attraction due to
an extended body
Note! A uniform shell does not
exert a gravitational force on a
particle inside it. As we descend
into the earth (or any planet)
only the mass underneath us
exerts a net gravitational force.
The mass falling from pole to pole
The speed of a satellite
Gravitational Potential Energy
Escape velocity
Ex. With what minimum speed must an object of
mass m be launched in order to escape the Earth’s
gravitational field?
Ex. A satellite of mass m is in a circular orbit of radius
R around the Earth (radius rE, mass M). a) What is the
total mechanical energy of the satellite? b) How much
work is required to move the satellite into a new orbit,
with radius 2R?
Oscillations
A block on a spring
Note: the net force is zero and
the speed is maximum when the
block is at its equilibrium
position
A quick review on energy and
SHM
Ex. A block of mass m = 2.0 kg is attached to an ideal
spring of force constant k = 500 N/m. The amplitude
of the resulting oscillations is 8.0 cm. Determine the
total energy of the oscillator and the speed of the
block when it is 4.0 cm from equilibrium.
Ex. A block of mass m = 3.0 kg is attached to an ideal
spring of force constant k = 500 N/m. The block is at rest
at its equilibrium position. An impulsive force acts on
the block, giving it an initial speed of 2.0 m/s. Find the
amplitude of the resulting oscillations.
Concept Check. A block is attached to a spring and
set into oscillatory motion, and its frequency is
measured. If this block were removed and replaced
by a a second block with ¼ the mass of the first
block, how would the frequency of the oscillations
compare to that of the first block?
Concept Check. A student performs an experiment
with a spring-block simple harmonic motion oscillator.
In the first trial, the amplitude of the oscillations is 3.0
cm, while in the second trial, the amplitude of the
oscillations is 6.0 cm. Compare the values of the
period, frequency and maximum speed of the block
for the two trials.
The spring-block oscillator for
vertical motion
Ex. A block of mass m = 1.5 kg is attached to the end
of a vertical spring of force constant k = 300 N/m.
After the block comes to rest, it is pulled down a
distance of 2.0 cm and released. a) What is the
frequency of the resulting oscillations? b) What are
the minimum and maximum distances the spring
stretches during the oscillations of the block?
Ex. A simple harmonic oscillator has an amplitude of
3.0 cm and a frequency of 4.0 Hz. At time t = 0, its
position is x = 0. Where is it located at time
t = 0.30 s?
Time out for a calculus lesson
Instantaneous velocity and
accleration
Differential equation for SHM.
Any object that has motion
described in this form undergoes
SHM. Or, the acceleration of any
object that undergoes SHM
motion is described by this
equation. As every third grader
knows, this differential equation
is the hallmark of SHM.
Period of a spring revisited
Describing the motion of a
simple pendulum
Ex. A meter stick swings about a pivot point a distance L
from its center of mass. What is its period?