3.  Conservation of energy means energy is not lost or gained  Important equations: E total = KE + GPE KE = ½ mv 2 GPE = ma grav h KE i + GPE i = Ke f + GPE f ½mv i 2 + mgh i = ½mv f 2 + mgh f

4.  At the highest point, KE = 0 and all energy is potential.  At the zero height GPE = 0 and all energy is kinetic.  When object changes direction, the velocity is zero (because KE= ½ mv 2 so when v=0 then KE=0)

5.  Look for information given at highest point or at zero height:  At highest point, all energy is potential: ½mv i 2 + mgh i = Total energy = mgh i  At zero height, all energy is kinetic: ½mv i 2 + mgh i = Total energy = ½mv i 2 Will be 0!!

6.  Use total energy to find other variables!  Let’s begin!

7. H=15meters KE= GPE= TE= v= H=8meters KE= GPE= TE= v= H=6meters KE= GPE= TE= v= H=0meters KE= GPE= TE= v= H=4meters KE= GPE= TE= v= H=0meters KE= GPE= TE= v=

8. H=15meters KE= GPE= TE= v=  Since this is the highest point, all of the energy is potential, so: TE = KE+ GPE= =0 + mgh= (5kg)(10m/s 2 )(15m) = 750J

9.  H=15meters  KE= 0  GPE= 750J  TE= 750J  v=0 m/s

10. H=15meters KE= 0 GPE= 750 J TE= 750 J v=0 m/s H=8meters KE= GPE= TE= v= H=6meters KE= GPE= TE= v= H=0meters KE= GPE= TE= v= H=4meters KE= GPE= TE= v= H=0meters KE= GPE= TE= v=

12.  At highest pt, E total = all PE  V = 0  At lowest pt, E total = all KE  V is the highest at this pt  E total = KE + GPE  To determine v, use KE = ½ mv 2  To determine h, use GPE = mgh