Homework
 Work on Lab Project
paper and presentation due this week
presentation may be done next week
 Work Reading Assignment for Wednesday
 Work Mastering Physics Assignments
 Study for Exam
 Review Session?
Gravitational Force
 always attractive (never repulsive)
 between all pieces of things with mass
 on average acts between centers of objects
 F = GMm/r2

G = 6.67 x 10-11 Nm2/kg2
 force is the same
size on both objects
Where does mg come from?
 If the distance between the centers of the objects
is about the radius of the earth, the force is about
equal to mg
 F = m (GM/r2)
 g = GMearth/Rearth2
 g = (6.67 x 10-11 Nm2/kg2 )(5.97 x 1024kg)
(6.38 x 106 m)2
 g = 9.8 m/s2
 directed toward the center of the earth
Between all objects
 Estimate the gravitational force between two
people standing at arms length?
Does weight
change?
 What is the weight of a 70 kg man
 at the surface of the earth?
 at the top of a tall (100 m) building?
 in an airplane (10000 m)?
 orbiting the earth (350000 m)?
On the moon
 What is the weight of a 70 kg man on the moon?
 m = 7.35 x 1022 kg
 R = 1.74 x 106 m
In-class exercise
A satellite orbits the earth at a height of 2 earth radii. How
does its weight on earth compare with its weight in space?
 1) The two weights are the same.
 2) The weight on earth is 2 times its weight in space.
 3) The weight on earth is 1/2 its weight in space.
 4) The weight on earth is 3 times its weight in space.
 5) The weight on earth is 1/3 its weight in space.
 6) The weight on earth is 4 times its weight in space.
 7) The weight on earth is 1/4 its weight in space.
 8) The weight on earth is 9 times its weight in space.
 9) The weight on earth is 1/9 its weight in space.

Gravitational Potential Energy
(all cases: not necessarily near the earth’s surface)
 -U =  F  dr
 -U =  (-GMm/r2) dr
 ri = 
choosing zero for U
For h <<Rearth
reduces to:
 rf = r
this
U
 -U =(GMm/r) - (GMm/)
= mgh - C
 -U = GMm/r
where C is a very large
constant for U = 0 at .
 -(Ug - U0) = GMm/r
 Ug = -GMm/r
always negative
Example
 A 150 kg satellite is in circular orbit of radius 7.3 Mm
about the earth.
 Determine the potential energy.
 Determine the orbital speed.
 Determine the kinetic energy.
 What is the escape speed from
this altitude?
Exercise
 Why are
rocket
launch sites
located
nearer to the
equator
(rather than
the poles)?
Angular Momentum
in the Bohr Model of the Atom
In the Bohr model:
The electron orbits like a
planet.
The electron can only have
certain values of angular
momentum.
L = n (h/2)
where n is an integer
Angular Momentum
in Quantum Mechanics
 L = l (l  1)
(h/2)
gives length of angular
momentum vector
 Lz = ml (h/2)
gives orientation of the
angular momentum
vector
The Bohr quantum
number
Lz

L
Quantum Numbers determine
the shape of the state
1s
2s
2p
l=0
for s-state
l=1
for p-state
l=2
for d-state
L = mv x r
Only s-states (L = 0) can
have electrons at the origin.