Forces and potential energy

Suppose that we want to compute the gravitational potential energy of a bullet which travels very, very, VERY far away from the surface of the Earth. If the bullet moves many hundreds of kilometers upwards, then the gravitational force on it is no longer simply F = - m * g . Instead, we have to use the more general form for the force of gravity:



   GPE(B)  -  GPE(A)  =        ???

Here's a somewhat more sophisticated map showing potential energy -- electric potential energy in this case -- as a function of position on a table.


  Q:  What is the change in potential energy
      per meter at location A, if one
      moves to the right on this map?  If one moves
      downwards on this map?

  Q:  What is the change in potential energy
      per meter at location B, if one moves
      to the right on this map?  If one moves
      downwards on this map?


  Q:  What is the size, and direction, of the
      force on a particle at point A?
      Express this force in unit-vector notation.


  Q:  At what locations is the total force on 
      a particle zero?  At which of these places
      is there a stable equilibrium?

Suppose that in some region of space, the potential energy U (measured in Joules) is a function of position (x, y) (measured in meters) like this:

What are the units of q?
What is the force on a particle in the x-direction?
What is the force on a particle in the y-direction?
Suppose the numerical value of the coefficient is q = 0.25 . Express the force on a particle at (3 m, 6 m) as a vector, in component notation. Don't forget the units!