Forces and potential energy

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 centimeter 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 centimeter at location B, if one moves
      to the right on this map?  If one moves
      downwards on this map?

The graphical way of taking a partial derivative is to make a slice on a map, like this:

  Q:  What is the size, and direction, of the
      y-component of the force on a particle at 
      (y = 20 cm)?


  Q:  At what locations is the y-component of the 
      force zero?  At which of these places
      is the y-position stable?

Try your hand at a more realistic example, using a topographic map near the RIT campus.

Imagine that the landscape is covered with a perfectly frictionless blanket of snow. You pull a sled of mass M = 20 kg across the snow ....

1. How much work would it take to pull the sled from point A to the top of the hill at the River View Cemetery?
2. How much work would it take to pull the sled from point A to point B?
3. How much work would it take to pull the sled from point A to point C?
4. If you started at the top of the hill and slid down to point C, how fast would you be going?
5. What is the average gravitational force pulling the sled along the surface from the top of the hill to point A?
6. What is the average gravitational force pulling the sled along the surface from the top of the hill to point B?
7. Why are the answers to the two previous questions different?
8. If you released your sled from rest at point A, which direction would it slide?
9. What is the gradient of the gravitational potential energy of the sled at point A? Express your answer as a vector.

Copyright © Michael Richmond. This work is licensed under a Creative Commons License.