2. Conservation of Energy
System

3. Energy of Gravitational Interaction -- Gravitational Potential Energy
If the system contains Earth and an object (or objects), then the system has gravitational potential energy.
Gravitational potential energy depends on distance: greater distance, greater potential energy; less distance, less potential energy.
if y << Radius of Earth
Earth

4. Closed and Open Systems
closed system
open system

5. Conservation of Mechanical Energy
System is Earth and the rock; assume no energy inputs or outputs.
System
Earth
As the rock falls, the system loses gravitational potential energy, and the system gains kinetic energy.

6. Conservation of Mechanical Energy
System
Earth
System is Earth and the rock; assume no energy inputs or outputs.
As the ball falls, the total energy is constant.

7. Tips on solving conservation of energy problems
Sketch a picture of the situation showing the system at two different states: 1 and 2.
Record any knowns such as y1, y2, v1, and v2.
Sketch bar graphs showing kinetic and potential energy. Note: they should add so that they equal the total energy.
Solve for the unknown.

8. Example
The Kingda Ka roller coaster goes to the top of a 139-m tall hill. It drops to a height of 12 m above the ground. What is its speed at the bottom, if its speed at the top is 1.0 m/s?

9. Poll
Does your answer to the previous question depend on whether the roller coaster is full of people? (In other words, does your answer depend on mass?)
yes no

10. Poll
Does the speed of the roller coaster at the bottom of the hill depend on whether it is frictionless or not?
yes no

11. Example
Suppose that the mass of the Kingda Ka rollercoaster, full of people, is 1800 kg. If its speed at the bottom is 45 m/s, how much mechanical energy is lost due to friction as it travels down the hill?

12. Poll
Does your answer to the previous question depend on whether the roller coaster is full of people? (In other words, does your answer depend on mass?)
yes no