1. Potential Energy

2. Height  Work is a process.  When a box is lifted, work is done on the box.  At the end, the box is resting – no kinetic energy.  Where did the work go? y1y1 F =  mg h y2y2

3. Path Dependence  What happens to work as a rollercoaster goes down hill then up again?  What if the roller coaster took a less steep path?

4. Reversible Process  If an object is acted on by a force has its path reversed the work done is the opposite sign.  This represents a reversible process. y1y1 F =  mg h y2y2

5. Closed Path  If the work done by a force doesn’t depend on the path it is a conservative force.  Conservative forces do no work on a closed path. From 1 to 2, the path A or B doesn’t matter From 1 to 2 and back to 1, the path A then the reverse path B gives no work

6. Nonconservative Force  Not all forces are conservative.  In particular, friction and drag are not conservative. Negative work is done by friction to get here Negative work is also done returning the box F =  F N d dd F =  F N

7. Net Work  The work-energy principle is  K = W net.  The work can be divided into parts due to conservative and non-conservative forces. Kinetic energy  K = W con + W nonKinetic energy  K = W con + W non FfFf d FgFg

8. Kinetic and Potential Energy  Potential energy is the negative of the work done by conservative forces. Potential energy  U =  W conPotential energy  U =  W con  The kinetic energy is related to the potential energy. Kinetic energy  K =  U + W nonKinetic energy  K =  U + W non  The energy of velocity and position make up the mechanical energy. Mechanical energy E mech = K + UMechanical energy E mech = K + U

9. Conservation of Energy  Certain problems assume only conservative forces. No friction, no air resistanceNo friction, no air resistance The change in energy,  E =  K +  U = 0The change in energy,  E =  K +  U = 0  If the change is zero then the total is constant. Total energy, E = K + U = constantTotal energy, E = K + U = constant  Energy is not created or destroyed – it is conserved.

10. Solving Problems  There are some general techniques to solve energy conservation problems. Make sure there are only conservative forces and kinetic energy in the problemMake sure there are only conservative forces and kinetic energy in the problem Identify all the potential and kinetic energy at the beginningIdentify all the potential and kinetic energy at the beginning Identify all the potential and kinetic energy at the endIdentify all the potential and kinetic energy at the end Set the initial and final energy equal to one anotherSet the initial and final energy equal to one another next