1. CONSERVATION OF ENERGY

2. Conservative Force
A conservative force converts potential energy to other forms of mechanical energy when it does work.
In other words, a conservative force does not change the mechanical energy of a system
Remember that mechanical energy is potential energy + kinetic energy

3. NonConservative Force
So, what would be a nonconservative force???
Friction is most common example (air resistance is a form of friction)
Work done by friction becomes microscopic internal energy in the object, raising its temperature
The internal energy cannot be recovered and turned back into kinetic energy

4. Law of Conservation of Energy
Energy cannot be created or destoyed, only changed from one form to another
Ei = Ef
KEi + PEi = KEf + PEf + HE
½ mv2 i + mghi = ½ mv2 f + mghf + HE

5. Example

6. Example
A 65 kg snowboarder starts at rest, travels down a hill into a gulley and back up the other side as shown. Find his speed at top of the 2nd hill.

7. Example
A 5.0 kg block of wood is pushed down a ramp with a velocity of 6.0 m/s. The ramp is 1.5 m tall and 3.5 m long. At the bottom of the ramp it is traveling at 7.5 m/s. How much thermal energy is generated due to friction? Determine the force of friction and the coefficient of friction.

8. Work-Energy Theorem Net work = change in kinetic energy.
This means that the net work on a system causes a change in speed of the system

9. Work-Energy Theorem
If you know how much energy you want a system or object to have, then you can calculate how much work you need to perform to get it there. Conversely, if you know how much energy a system has, you can calculate how much work that energy can perform.  This has literally MILLIONS of real-life examples:
The energy of wind movement performs work when it turns a Wind Turbine
The chemical energy in gasoline performs work on a piston, which in turn performs work on a vehicle to create kinetic energy.
Work is performed on air as it enters a Jet Engine to speed up the air, which results in higher kinetic energy of the air particles, which pushes the airplane
Stirring a pot of water performs work in the form of heat transfer, which results in a higher temperature in the water (higher temp = higher energy)
When you throw a water balloon at someone’s face, their face performs work on the balloon, which then increases in pressure (higher pressure = higher energy) until it pops.

10. Example
A 60 kg sprinter exerts a net force of 260 N over a distance of 35 m. What is his change in kinetic energy? If started at rest, what is speed at finish?

11. Example
A student pushes a 25 kg crate which is initially at rest with a force of 160 N over a distance of 15 m. If there is 75 N of friction, what is the final speed of the crate?

12. In Summary
If there is a change in height in a system, you should use conservation of energy to solve the problem

13. Physics C Extras
Derivation of Work Energy Theorem