Focus on conservation of mechanical energy

1. Lesson 5A
Conservation of Energy
Nelson References Pages:Nelson References Pages:
236 - 240236 - 240

2.  What does conservation of energy mean to us?
 Usually we think of using less energy.Usually we think of using less energy.
 Or, we may think of theOr, we may think of the Law of Conservation of
Energy, which states:which states: Energy can not be created or
destroyed but it can change its form..
 In physics, and other science courses,In physics, and other science courses,
conservation of energy means that the amountconservation of energy means that the amount
of energy we have (initially) does not changeof energy we have (initially) does not change
with time.with time.
 In situations where the amount of initial energyIn situations where the amount of initial energy
equals the amount of final energy we can sayequals the amount of final energy we can say
that “energy is conserved”.that “energy is conserved”.

3. What is aWhat is a System?
 In understanding conservation of energy, weIn understanding conservation of energy, we
often use the idea of aoften use the idea of a system, and there are 3and there are 3
types of systems:types of systems:
1. Open systems: Allows both matter and energyAllows both matter and energy
to leave or enter.to leave or enter.
2. Closed systems: Allows only energy to enter orAllows only energy to enter or
leave.leave.
3. Isolated systems: Neither matter nor energyNeither matter nor energy
can leave or be added.can leave or be added. Only in an isolated
system can energy be conserved.

4. Example
 A cart starts fromA cart starts from rest
at position “A”.at position “A”.
Determine the speed ofDetermine the speed of
the cart at position “B”the cart at position “B”
assuming that there isassuming that there is
no friction acting on theno friction acting on the
cart.cart.
Solution
 At position “A” the cartAt position “A” the cart
has only Ehas only Egg which canwhich can
be calculated using Ebe calculated using Egg
= mg= mgΔΔhh
S t a r t
1 5 .0 m
7 .5 m
D O M
A
C
B
2 .5 mG r o u n d
U p
DOM

5.  At position “B” we know that the cart hasAt position “B” we know that the cart has
lost half of its initial value of Elost half of its initial value of Egg; so where; so where
did this energy go?did this energy go?
 TheThe lost Eg was converted to Ek. The. The
amount of Eamount of Ekk at “B” would be equal to oneat “B” would be equal to one
half the initial amount Ehalf the initial amount Egg . To solve this. To solve this
problem we had to use conservation ofproblem we had to use conservation of
energy and “see” that a specific amount ofenergy and “see” that a specific amount of
EEgg changed form (intochanged form (into Ek).).

6. Mechanical Energy (ET)
 Is defined as being the energy of a mechanicalIs defined as being the energy of a mechanical
system. And a mechanical system is defined as asystem. And a mechanical system is defined as a
set of objects which interact with each other andset of objects which interact with each other and
their surroundings while obeying Newton’s Laws oftheir surroundings while obeying Newton’s Laws of
Motion.Motion. – do not have to copy this.
 We will defineWe will define ET as follows:as follows:
ET = Eg + Ek
((In grade 12 we will add EIn grade 12 we will add Eee which is elastic potential energywhich is elastic potential energy))
 TheThe Law of Conservation of Mechanical Energy
requires thatrequires that ET-Initial =ET-Final . For this to be true, frictionFor this to be true, friction
must not be acting on the moving objects andmust not be acting on the moving objects and
energy must not be added or taken away from theenergy must not be added or taken away from the
objects by other means.objects by other means.

7. Example
 Go back to the roller coaster cart and determineGo back to the roller coaster cart and determine
the speed of the cart at the lowest position.the speed of the cart at the lowest position.
Solution
 We analyze the problem by applying the law ofWe analyze the problem by applying the law of
conservation of mechanical energy.conservation of mechanical energy.
 There is aThere is a loss of Eg equal toof Eg equal to mg(15.0-2.5) thisthis
energy must have been transformed into Eenergy must have been transformed into Ekk. So,. So,
we can now solve the following equation:we can now solve the following equation:
 mg(12.5) =mg(12.5) = ½½ mvmv22
 122.6 =122.6 = ½½vv22
{the masses cancel}{the masses cancel}
 V = (122.6 x 2)V = (122.6 x 2) ½½
 V = 15.7 m/sV = 15.7 m/s
The speed at point “C” is equal to 15.7 m/s.The speed at point “C” is equal to 15.7 m/s.

8. Chalkboard Example
 Using energyUsing energy
methods, solve themethods, solve the
following problem:following problem:
 A rock is droppedA rock is dropped
from a height of 10.0from a height of 10.0
m above the ground.m above the ground.
Determine the speedDetermine the speed
of the rock just beforeof the rock just before
it hits the ground.it hits the ground.
G r o u n d
U p
R o c k
In it ia l P o s it io n
R o c k - J u s t B e f o r e
H it t in g t h e G r o u n d

9. Practice Problems
Nelson Textbook
 Page 241 # 1-3Page 241 # 1-3
 Page 263 # 27, 30, 34, 49, 50Page 263 # 27, 30, 34, 49, 50
Additional Questions from the McGraw-Hill Textbook:
A wrecking ball (A wrecking ball ( 315 kg ) hangs from a) hangs from a 10.0 m longlong
cable attached to a crane. The crane swings thecable attached to a crane. The crane swings the
wrecking ball causing a maximum angle ofwrecking ball causing a maximum angle of 300
toto
the vertical.the vertical. Determine both theboth the Ek and the speedand the speed
of the ball when it falls back down to the verticalof the ball when it falls back down to the vertical
position.position. [Ans. 4.14 kJ, 5.13 m/s ]

10. Videos:
Khan Academy on Cons. Of Energy
http://www.khanacademy.org/science/physics/work-and-energy/work-and-energy-tutoria