CONSERVATION OF ENERGY CALCULATIONS

IMPORTANT FACTS TO REMEMBER ABOUT CONSERVATION OF ENERGY

Conservation of energy means energy is not lost or gained

Important equations:Etotal = KE + GPE

KE = ½ mv2

GPE = magravh

KEi + GPEi = Kef + GPEf

½mvi2 + mghi = ½mvf

2 + mghf

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 mv2 so when v=0 then KE=0)

STRATEGIES FOR SOLVING PROBLEMS USING CONSERVATION OF ENERGY

Look for information given at highest point or at zero height: At highest point, all energy is potential:½mvi

2 + mghi = Total energy = mghi

At zero height, all energy is kinetic:½mvi

2 + mghi = Total energy = ½mvi2

Will be 0!!

Will be 0!!

Use total energy to find other variables!

Let’s begin!

H=15metersKE=GPE=TE=v=

H=8metersKE=GPE=TE=v=

H=6metersKE=GPE=TE=v=

H=0metersKE=GPE=TE=v=

H=4metersKE=GPE=TE=v=

H=0metersKE=GPE=TE=v=

H=15metersKE=GPE=TE=v= Since this is the highest point, all of the

energy is potential, so:TE = KE+ GPE=

=0 + mgh=(5kg)(10m/s2)(15m) =

750J

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

H=15metersKE= 0GPE= 750 JTE= 750 Jv=0 m/s

H=8metersKE=GPE=TE=v=

H=6metersKE=GPE=TE=v=

H=0metersKE=GPE=TE=v=

H=4metersKE=GPE=TE=v=

H=0metersKE=GPE=TE=v=

CONTINUE EXAMPLES

SUMMARY

At highest pt, Etotal = all PE V = 0

At lowest pt, Etotal = all KE V is the highest at this pt

Etotal = KE + GPE To determine v, use KE = ½ mv2

To determine h, use GPE = mgh