Homework  Work on Lab Project paper and presentation due this week presentation may be done next week  Work Reading Assignment for Wednesday  Work Mastering.

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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/r 2  G = 6.67 x Nm 2 /kg 2  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/r 2 )  g = GM earth /R earth 2  g = (6.67 x Nm 2 /kg 2 )(5.97 x kg) (6.38 x 10 6 m) 2  g = 9.8 m/s 2  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 ( m)?

On the moon  What is the weight of a 70 kg man on the moon?  m = 7.35 x kg  R = 1.74 x 10 6 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  d r  -  U =  (-GMm/r 2 ) dr  r i =  choosing zero for U  r f = r  -  U =(GMm/r) - (GMm/  )  -  U = GMm/r  -(U g - U 0 ) = GMm/r  U g = -GMm/r always negative For h <<R earth this reduces to: U = mgh - C where C is a very large constant for U = 0 at .

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 =  (h/2  ) gives length of angular momentum vector  L z = m l (h/2  ) gives orientation of the angular momentum vector The Bohr quantum number L LzLz 

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