Transcript Chapter 5: Gravity

Chapter 5
Gravity
Describing motion
• Speed: Rate at which object moves

speed = distance units of m

s

time

example: 10 m/s
• Velocity: Speed and direction
example: 10 m/s, due east
• Acceleration: Any change in speed or
direction
units: speed/time (m/s2)
• Constant velocity means a = 0
The Acceleration due to Gravity
• All falling objects
accelerate at the
same constant rate
• On Earth, g ≈ 10
m/s2: speed
increases 10 m/s
with each second of
falling.
The Acceleration of Gravity (g)
• Galileo showed that
g is the same for all
falling objects,
regardless of their
mass.
Apollo 15 demonstration
Forces
• A force changes an object’s velocity
• A spinning or orbiting object has angular
momentum: a force is required to change the
rate of spin
There are usually lots of forces acting on an object.
Forces are caused by other objects.
An object can’t exert a force on itself!!
Newton’s Laws of Motion
1. Bodies at rest tend to stay at rest…
2.  F = ma
3. Forces come in pairs: every action has an
equal and opposite reaction:
Force that A exerts on B = force that B exerts on A
Weight vs. Mass
• Weight is the force w = mg, directed toward the
center of the Earth
• The “normal force” is what a scale says
• Mass is a property of an object
Why are astronauts ‘weightless’
in space?
• There is gravity in
space
• “Weightlessness”
= scale reads 0
• due to a constant
state of free-fall
Conservation of Momentum
• The total momentum of
interacting objects
cannot change unless an
external force acts on
them
• Interacting objects
exchange momentum
through equal and
opposite forces
What keeps a planet rotating, and
orbiting the Sun?
Conservation of Angular
Momentum
angular momentum = mass x velocity x radius of orbit
• The angular momentum of an object cannot
change unless a force acts on it
• Earth’s rotation and orbit will continue
(almost) forever because it can’t “get rid of”
angular momentum
Conservation of angular momentum
Total Energy is conserved
• Kinetic (motion)
• Radiative (light)
• Stored or potential
Energy can easily change
type but cannot be
destroyed.
Professor Kress:
Ive read all of 5.1 and can't get the answer for number 2.
so far i checked
-The acceleration due to gravity near Earth’s surface is 9.8 m/s2.
-The speed of falling objects increases at a constant rate.
-Objects tend to slow down naturally unless propelled by a force.
These ones are hard!!
Homework problem #2
The acceleration due to gravity near Earth’s surface is 9.8 m/s2
Inertia is an object's tendency to resist changes in its motion.
The speed of falling objects increases at a constant rate.
Galileo's experiments yielded similar results to Aristotle's
theories about motion.
5. The speed of a falling object depends on its weight.
6. According to tradition, Galileo dropped objects of different
mass from the leaning tower of Pisa.
7. Objects tend to slow down naturally unless propelled by a
force.
1.
2.
3.
4.
Homework problem #3: A student sent me this….
QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.
Homework problem #3
QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.
Newton’s Universal Law of Gravitation:
1. Every mass attracts every other mass.
2. Attraction is directly proportional to the product of
their masses.
3. Attraction is inversely proportional to the square of
the distance between their centers.
F=
G M1 M 2
d2
M2
d
M1
Newton’s Version of Kepler’s Third Law
a3
p2
= M1 + M2
p = orbital period
a=average orbital distance (between centers)
(M1 + M2) = sum of object masses, relative to
Sun (Solar masses)
Now we see why orbital period does not depend on the mass
of the planet!
Kepler’s 2nd Law explained
More gravitational energy;
Less kinetic energy
• Total orbital energy
(gravitational +
kinetic) stays constant
if there is no external
force
• Orbits cannot change
without help from an
Less gravitational energy; outside object
More kinetic energy
• Conservation of
angular momentum!
Total orbital energy stays constant
Thought Question:
Which has a total force of 0?
1.
2.
3.
4.
A car rolling to a stop.
A rock freely falling through the air.
A skydiver moving at terminal velocity.
A bicycle going around a curve at constant
speed.
5. A moon orbiting Jupiter.
On the Moon:
A.
B.
C.
D.
My weight is the same, my mass is less.
My weight is less, my mass is the same.
My weight is more, my mass is the same.
My weight is more, my mass is less.
If you jump out of a plane
without a parachute:
A.
B.
C.
D.
E.
My weight is the same, my mass is zero.
My weight is zero, my mass is the same.
My weight is more, my mass is the same.
My weight is more, my mass is zero.
My mass and weight are both zero.
Why are astronauts weightless
in space?
a. Their mass has become zero.
b. The astronauts are so far from Earth, they
don’t feel Earth’s gravity
c. The Moon pulls on them in the opposite
direction as Earth, balancing out
d. They are actually in free-fall
Thought Question:
Is the force the Earth exerts on you larger, smaller, or
the same as the force you exert on it?
A. Earth exerts a larger force on you.
B. I exert a larger force on Earth.
C. Earth and I exert equal and opposite forces on
each other.