Homework

1
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?

2
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 samesize on both objects

3
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

4
Between all objects

• Estimate the gravitational force between two
  people standing at arms length?

5
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)?

6
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

7
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.

8
Gravitational Potential Energy (all cases not
necessarily near the earths surface)

• -?U ? F ? dr
• -?U ? (-GMm/r2) dr
• ri ? choosing zero for U
• rf r
• -?U (GMm/r) - (GMm/?)
• -?U GMm/r
• -(Ug - U0) GMm/r
• Ug -GMm/r always negative

For h ltltRearth this reduces to
U mgh - C where C is a very large constant
for U 0 at ?.
9
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?

10
Exercise

• Why are rocket launch sites located nearer to the
  equator (rather than the poles)?

11
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
12
Angular Momentum in Quantum Mechanics

• L ? (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
?
13
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.