HomeworkHomework

Work on Lab Projectpaper and presentation due this weekpresentation may be done next week

Work Reading Assignment for Wednesday Work Mastering Physics Assignments Study for Exam Review Session?

Gravitational ForceGravitational 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

Where does mg come from?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/Rearth

2

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 objectsBetween all objects

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

Does weight change?

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 moonOn 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 exerciseIn-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)

Gravitational Potential Energy (all cases: not necessarily near the earth’s 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 <<Rearth this

reduces to: U = mgh - Cwhere C is a very large constant for U = 0 at .

ExampleExample

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?

ExerciseExercise

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

Angular Momentum in the Bohr Model of the

Atom

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 MechanicsAngular 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

)1( ll

LLz

Quantum Numbers determine the shape of the state

Quantum Numbers determine the shape of the state

1s2s

2pl = 0 for s-state

l = 1 for p-state

l = 2 for d-state

LL = mvv x rr

Only s-states (L = 0) can have electrons at the origin.