3/6/15 Announcements
•  Today: Centripetal force and gravity
•  Wednesday: Finish Gravity
•  Reading for Wednesday: Chapter 10, focus
on figs. 10.3, 10.17, & 10.31
•  I am working on the midterms! They should
be ready by the end of this week, or next
Monday at the latest. Scores will be posted
on iLearn, and you’ll be able to come pick up
your tests in my office.
Centripetal Force
Centripetal Force
•  Centripetal means “towards the center.”
Whenever an object
moves along a
circular path, there
must be a force on
that object in the
direction of the
center of the circle.
•  In such a case, the force is said to be centripetal
Example: The spin cycle!
•  Any force directed toward a fixed center is
called a centripetal force.
–  Centripetal means “center-seeking” or “toward
the center.”
F = mv2/r
r = radius of circle
v = tangential velocity
Example
Chapter 9: Gravity
You are riding at the very edge of a merrygo-round with a radius of 2 m. Your friend
runs alongside, pushing the merry-go-round
so that it’s tangential speed is 3 m/s.
a.  What force is keeping you from sliding
off?
b.  If you have a mass of 75 kg, what is the
strength of that force?
1 3/6/15 Newton’s Law of Gravity
•  Everything with mass pulls on
everything else with mass
•  Gravity is always attractive
•  The closer the object, the stronger
the pull
Newton’s Law of Gravity
F = GMm/r2
•  M = mass of 1st object
•  m = mass of 2nd object
•  r = distance between objects
•  G = gravitational constant
M
r
m
= 6.67 × 10-11 N m2/kg2
Newton’s Law of Gravity
Inverse-Square Laws
•  Applies to gravitational strength, light,
and other phenomena
F = GMm/r2
•  Force grows or shrinks with distance
squared
– If you get 2x closer, force is 4x stronger
– If you get 3x farther away, force is 9x
weaker
•  Called Inverse-square relation
The Moon and Earth pull on
each other with equal strength
and in opposite directions
You and Earth pull on each
other with equal strength and
in opposite directions
Fg
Moon
Earth
Fg
Fg
Fg
Earth
2 3/6/15 At which point does the satellite feel
the strongest gravitational force from
Earth? (C is exactly half-way between
Earth and the Moon)
At which point does the satellite feel
the strongest total (or net)
gravitational force from both Earth
and the Moon?
Moon
C
Earth
D
Moon
E
B
A
Announcements
•  Today: Finish Gravity, Projectile Motion
•  Friday: Orbits, maybe start CH 11
•  Reading: Sections 12.1-12.3 and 13.1,
focus on density and pressure
C
Earth
B
A
Moon
C
•  On the surface of the Earth, we are about
6,380 km from the center of the Earth.
The astronauts on the ISS are about 6,720
km from the center of the Earth. Compare
the gravitational force on two people: one
on Earth’s surface, and one in the ISS.
E
If the satellite is at location C halfway
between the Moon and Earth, in what
direction will the net force on the
satellite point?
Earth
Example: The ISS
D
D
E
B
A
Application: Ocean Tides
•  Tides are primarily due to the moon’s
gravitational pull on our oceans.
•  Sun contributes too, but the Earth-Sun
distance doesn’t change very much.
3 3/6/15 Application: Black Holes
Chapter 10: Projectile Motion
•  Black holes are not cosmic vacuum
cleaners, they’re just very very compact!
• 
From “Foxtrot” by Bill Amend
Projectile Motion
•  A ball thrown
across the room
follows an arced
trajectory.
•  Both vertical and
horizontal motion
Projectile Motion vs. Free-Fall
At the instant a cannon fires a cannonball horizontally
over a level range, another cannonball held at the side
of the cannon is released and drops to the ground.
Which strikes the ground first?
Projectile Motion
Combines
uniform
horizontal
motion with
free-fall
vertical
motion.
Launching at an Angle
•  With no gravity,
projectile would
follow a straight
line.
•  Due to gravity,
projectile falls
beneath this line,
just as if released
from rest.
No
a
Gr
y
vi t
4 3/6/15 Range
•  Range depends on both horizontal speed
and angle (Maximum at 45º)
Projectile Motion & Curvature
•  For initial speeds that are faster and faster,
the range of the projectile is farther and
farther.
•  For very large speeds, the curvature of Earth
starts to be noticeable.
Distance Fallen
The distance fallen
is the same
whether falling
straight down or in
projectile motion.
Earth’s Curvature
•  Curvature of the Earth is about 5 meters
over a distance of 8000 meters (which is
about 5 yards over 5 miles).
Missing the Ground
Orbits and Centripetal Force
•  Suppose you throw a ball at a speed of
8000 m/s (about 18,000 mph).
•  After one second, ball travels 8000 meters
and falls 5 meters. In that distance, Earth
curves by same amount (5 meters).
•  Gravity provides the centripetal force
required for planets & satellites to move in
orbit
5 3/6/15 Which of the following is true?
A. Satellites orbit at least 150 km above the
surface of Earth because there is almost no
gravity there.
B. Satellites orbit at least 150 km above the
surface of Earth because there is almost no
air resistance there.
Elliptical Orbits
•  For speeds higher than 8 km/s, the orbit is
elliptical instead of circular.
Application: Black Holes
•  Black holes are not cosmic vacuum
cleaners, they’re just very very compact!
• 
Getting into Orbit
•  Rocket needs to lift above the
atmosphere and then fire
thrusters to acquire the
required orbital speed of
about 8 kilometers per
second.
•  Returning to Earth, air
resistance slows the
spacecraft during reentry
Escape Velocity
If speed exceeds
11.2 km/s then
object escapes
Earth because
gravity weakens
(as object gets
further away) and
never slows the
object enough to
return it back
towards Earth.
Imagine a planet in its orbit around the
Sun. Rank the four positions shown (A-D)
in order of the gravitational force from
greatest to least.
A.  A, B, C, D
B.  A, B=C, D
C.  D, C=B, A
D.  D, C, B, A
E.  D=C=B=A
6 3/6/15 Imagine a planet in its orbit around the
Sun. Rank the four positions shown (A-D)
in order of the planet’s acceleration from
greatest to least.
A.  A, B, C, D
B.  A, B=C, D
C.  D, C=B, A
D.  D, C, B, A
E.  D=C=B=A
Chapter 11: The Atomic Nature of
Matter
Announcements:
•  Today: Atoms and structure of matter
•  Monday: More on density and pressure
•  Reading: Finish Chapter 13, focus on
buoyancy and flotation
•  Midterm scores & grade update will get
posted this afternoon! Average score was
right in the middle of the C range.
What is the structure of matter?
Electron
Cloud
Atom
Atomic Structure
All matter is made of atoms
•  Characteristics of Atoms:
–  Very tiny
–  Very numerous
–  Always in motion
•  Substances made of only 1 type of atom
are called elements
Nucleus
An atom is composed of
•  Nucleus
–  Contains most of the atomic mass
–  made up of protons (+ electric charge) and neutrons (no
electric charge)
–  Very, very small (<10-14 m)
•  Electrons
–  even smaller than nucleus
–  2000 times less massive than nucleus
–  negative electric charge (same amount as proton)
–  may be thought of as “orbiting” nucleus
Number of electrons in a neutral atom is equal to
number of protons in nucleus
7 3/6/15 Atomic Terminology
Elements & The Periodic Table
•  Atomic Number = # of protons in nucleus
•  Atomic Mass Number = # of protons + neutrons
•  Molecules: consist of two or more atoms (H2O, CO2)
Relative Sizes of Atoms
Atomic Terminology
•  Isotope: same # of protons but different # of
neutrons. (4He, 3He)
Examples:
Dark matter & Antimatter
•  Antimatter
–  atoms with opposite electrical charge (or some other
property).
–  Antiprotons, positrons
–  Antimatter and regular matter destroy each other &
release energy
•  Dark matter
–  Detected via the gravitational force that it exerts on
stars & galaxies, but invisible
–  Dark matter makes up almost ¼ of all the matter in
the universe
8 3/6/15 Chapters 12-14: Phases of
Matter
Density
Sequence of increasing molecule motion
(and kinetic energy)
Solid
Liquid
Gas
Example: Density
•  Compute density of a gold brick.
•  Dimensions: (20.5 cm)x(10 cm)x(5 cm)
•  Mass: 19.8 kg
•  The densities of most liquids and solids
vary slightly with changes in temperature
and pressure
•  Densities of gases vary greatly with
changes in temperature and pressure
Mass Density vs. Weight Density
•  Mass density = mass/volume (kg/m3)
•  Weight density = weight/volume (N/m3)
•  What is the weight density of the gold brick
from the previous example?
9