Potential Energy and Conservation of Energy

To prepare for today's topic, let's consider several trails down the same mountain:

• Three trails down the same mountain

Here's a brief review of the idea behind potential energy:

• Notes on potential energy

One of the most common examples of potential energy is Gravitational Potential Energy (GPE). And the most fun you can have (legally) with gravitational potential energy is ... using it in rollercoasters!

• The physics of a big roller coaster

Let's make a little rollercoaster and see if all this theory actually works ...

• Testing a very small roller coaster
  • Example solutions to the very small coaster, using data from class
  • Answers in a single PDF document
  • Answers in a series of GIF images: Page 1 and 2 and 3 and 4 and 5

Some problems can be attacked either via forces or via energy ....

• A spring and a block and a ramp
• Ditto, with friction

If you finish early, consider this rather slippery problem.

• You sit on top of a perfect hemisphere of ice, balanced perfectly on the very top. A gust of wind blows you forward, and you slide without friction downwards along the curved surface. At what angle from the top of the hemisphere will you fly off the ice and fall through the air?

  Hint: draw a big picture, and assign symbolic values like m, R, etc., to any quantities that you think might be relevant. Consider both conservation of energy and the motion of an object in a circular path ...

• practice problems

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