1.  E is always constant, but KE and PE can change  If PE and KE change, they must change in such a way as to keep E constant Example Consider the 1D free-fall of an object of mass m from a height of y 0 =h y m y 0 =h, t 0 =0, v 0 =0 y 0 The initial energy of the system defines the total energy system

2. System – the collection of objects being study to the exclusion of all other objects in the surroundings, in this example, we consider the object of mass m only Some time later, KE and PE have changed, but E has not Energy y 0 h E PE=mgy KE What is KE, PE, and v when y=h/2?

3. For y=0 (just before the object hits the ground)? Note: we have neglected air resistance and what happens when the object hits the ground.

4. Example A hockey puck slides across the ice. Its speed slows from 45.00 m/s to 44.67 m/s after traveling a distance of 16.0 m. Determine the coefficient of kinetic friction between the ice and the puck. Solution: Given: v 0 =45.00 m/s, v f =44.67 m/s, x=16.0 m=s Method: Use work-energy theorem FNFN fkfk mg s

5. Conservative and Non-conservative Forces Conservative Force: a force for which the work it does on an object does not depend on the path. Gravity is an example.

6. h y m A BC A mgs s s B C Š Non-conservative Force - a force for which the work done depends on the path - friction - air resistance

7. If both conservative and non-conservative forces act on an object, the work-energy theorem is modified For the case of gravity