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1. Conservation of MechanicalConservation of Mechanical
EnergyEnergy
6.56.5

2. Mechanical EnergyMechanical Energy
KE and PE = total mechanical energyKE and PE = total mechanical energy
E = KE + PEE = KE + PE
Actually there are other forms of energy to include,Actually there are other forms of energy to include,
but we haven’t met them yet in the bookbut we haven’t met them yet in the book

3. Work Energy Theorem (again)Work Energy Theorem (again)
WWncnc = (KE= (KEff – KE– KE00) + (PE) + (PEff – PE– PE00))
RearrangeRearrange
WWncnc = (KE= (KEff + PE+ PEff) – (KE) – (KE00 + PE+ PE00))
WWncnc = E= Eff – E– E00
Nonconservative forces change the totalNonconservative forces change the total
mechanical energy of the systemmechanical energy of the system

4. WWncnc = 0= 0
WWncnc = E= Eff – E– E00
If WIf Wncnc = 0 like if friction or air resistance is= 0 like if friction or air resistance is
negligiblenegligible
0 = E0 = Eff – E– E00
EEff = E= E00
If all forces are conservative, then the totalIf all forces are conservative, then the total
mechanical energy does not changemechanical energy does not change

5. Conservation of Mechanical EnergyConservation of Mechanical Energy
If there is no work done byIf there is no work done by
nonconservative forcesnonconservative forces
Total mechanical energy is constantTotal mechanical energy is constant
KEKE00 + PE+ PE00 = KE= KEff + PE+ PEff

6. Example 1Example 1
A cyclist approaches the bottom of aA cyclist approaches the bottom of a
gradual hill at a speed of 11 m/s. The hillgradual hill at a speed of 11 m/s. The hill
is 5.0 m high, and the cyclist estimatesis 5.0 m high, and the cyclist estimates
that she is going fast enough to coast upthat she is going fast enough to coast up
and over it without pedaling. Ignoring airand over it without pedaling. Ignoring air
resistance and friction, find the speed atresistance and friction, find the speed at
which the cyclist crests the hill.which the cyclist crests the hill.
v = 4.8 m/sv = 4.8 m/s

7. Example 2Example 2
A slingshot fires a pebble from the top of aA slingshot fires a pebble from the top of a
building at a speed of 14.0 m/s. Thebuilding at a speed of 14.0 m/s. The
building is 31.0 m tall. Ignoring airbuilding is 31.0 m tall. Ignoring air
resistance, find the speed with which theresistance, find the speed with which the
pebble strikes the ground when the pebblepebble strikes the ground when the pebble
is fired (a) horizontally, (b) verticallyis fired (a) horizontally, (b) vertically
straight up, and (c) vertically straightstraight up, and (c) vertically straight
down.down.
v = 28.3 m/sv = 28.3 m/s

8. Conceptual ExampleConceptual Example
A rope is tied to a tree limb and used by aA rope is tied to a tree limb and used by a
swimmer to swing into the water below.swimmer to swing into the water below.
The person starts from rest with the ropeThe person starts from rest with the rope
held in the horizontal position, swingsheld in the horizontal position, swings
down and then lets go of the rope. Threedown and then lets go of the rope. Three
forces act on him; W, T, and airforces act on him; W, T, and air
resistance. Can conservation ofresistance. Can conservation of
mechanical energy be used to find themechanical energy be used to find the
speed when he lets go of the rope?speed when he lets go of the rope?

9. Conceptual ExampleConceptual Example
In order to use conservation of mechanicalIn order to use conservation of mechanical
energy, Wenergy, Wncnc = 0= 0
Nonconservative force in exampleNonconservative force in example
TensionTension  perpendicular to the motion so W = 0perpendicular to the motion so W = 0
Air ResistanceAir Resistance  opposite and parallel to motionopposite and parallel to motion
– Work does not equal 0Work does not equal 0
Cannot use conservation of MECannot use conservation of ME

10. Reasoning Strategy forReasoning Strategy for
Conservation of MEConservation of ME
Identify the external conservative andIdentify the external conservative and
nonconservative forces that act on thenonconservative forces that act on the
object. For this principle to apply, the totalobject. For this principle to apply, the total
work done by nonconservative forceswork done by nonconservative forces
must be zero.must be zero.
Choose the location where the PE is takenChoose the location where the PE is taken
to be zero.to be zero.
Set the final total ME equal to the initialSet the final total ME equal to the initial
total ME.total ME.

11. Practice WorkPractice Work
Don’t conserve energy to solve theseDon’t conserve energy to solve these
problems!problems!
174 CQ 12 – 14, P 34 – 36, 38, 40, 41174 CQ 12 – 14, P 34 – 36, 38, 40, 41
Total 9 problemsTotal 9 problems