Transcript Conservation of Mechanical Energy

Energy Transformations
Physics 11 – Chapter 7
Another try at
humour…
Conservative and non-conservative
forces:
Conservative forces:
oWork is independent of the path taken, it depends only
on the final and initial positions
oWe can always/only associate a potential energy with
conservative forces.
o This energy can be converted back into other
forms of energy.
Examples: gravity, spring forces
Conservative and non-conservative
forces:
Non-conservative forces:
oWork does depend on path.
oA force is non-conservative if it causes a change in mechanical energy
(mechanical energy is the sum of kinetic and potential energy).
oThis energy cannot be converted back into other forms of energy
(irreversible).
oAn applied force can transfer energy into or out of the system.
Example: Frictional force
Sliding a book on a table
Review: Energy
conversions/transformations:
 Energy can be changed from one form to another.
 Changes in the form of energy are called energy
conversions or transformations
Kinetic-Potential Energy Conversion
Roller coasters work because of the energy that is
built into the system. Initially, the cars are pulled
mechanically up the tallest hill, giving them a great
deal of potential energy. From that point, the
conversion between potential and kinetic energy
powers the cars throughout the entire ride.
Kinetic-Potential Energy Conversions
 As a basketball
player throws the
ball into the air,
various energy
conversions take
place.
Ball slows down
Ball speeds up
The Law of Conservation of Energy
 Energy can be neither created nor
destroyed by ordinary means.
 It can only be converted from one form
to another.
 If energy seems to disappear, then
scientists look for it – leading to many
important discoveries.
Law of Conservation of Energy
 In 1905, Albert Einstein said that
mass and energy can be converted
into each other.
 He showed that if matter is
destroyed, energy is created, and if
energy is destroyed mass is created.
 E = MC2
 http://www.pbs.org/wgbh/nova/einstein/le
gacy.html
Law of conservation of
mechanical energy:
Only with conservative forces.
Only with an isolated system (no energy added or removed):
The total mechanical energy of a system remains constant!
The final and initial energy of a system remain
the same: Ei = Ef
Law of conservation of mechanical
energy:
Ek + EP +Es = Ek’ + Ep’ +Es’
 Prime (‘) used to represent conditions after
process has completed
 All units = Joules
 Don’t have to use all 3, depends on
situation
Example #1:
What kinds of energy?
Kinetic and gravitational potential
(A)
Ek + Ep = Ek’ + Ep’
½mv12 + mgh1 = ½mv22 + mgh2
**because all terms have m, we can divide each by “m”and it will “disappear!!!”
½v12 + gh1 = ½v22 + gh2
what we know: v1=2.0m/s, h1=40.m, h2=25m, v2=?
½(2.0)2 + 9.81(40.0) = ½v22 + 9.81(25)
(2) + (392) = ½v22 + (245)
2+ 392 -245 = ½v22
149/0.5 = v22
√298 = v
17.3 m/s = v2
(B)
Ek + Ep = Ek’ + Ep’
½mv12 + mgh1 = ½mv22 + mgh2
**because all terms have m, we can divide each by “m” and it will “disappear!!!”
½v12 + gh1 = ½v22 + gh2
what we know: v1=2.0m/s, h1=40.m, v2=10.0 m/s, h2=?
½(2.0)2 + 9.81(40.0) = ½(10)2 + 9.81h2
(2) + (392) = (50) + 9.81h2
2+ 392 -50 = 9.81h2
344/9.81 = h2
35.1m = h2
Try it :
 Pg 287 #1-8