Transcript 5.3 Conservation ME

November √36th 2009
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Objectives
SWBAT identify situations when they should use the
conservation of mechanical energy
SWBAT Solve problems using mechanical energy
SWBAT recognize the different forms that energy takes
Catalyst
If you start with a $5 bill and you split it into 4 $1 bills
and 4 quarters was your money conserved? Why?
You have 10min to finish the problems from the HW
Agenda
HW Review
 Work-KE
 Potential For Energy?
 Practice!
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HW Answers
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1.
2.
3.
4.
Pg 176
7.8m
21m
5.1m
300N
Conservation of
Mechanical Energy
5-3
Problem
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A 70.0kg stuntman is attached to a bungee cord with an unstretched length of 15m. He
jumps off a bridge spanning a river from a height of 50.0m. When he finally stops, the cord
has a stretched length of 44.0m. Disregard the weight of the bungee cord. Assuming the
spirng constant of the bungee cord is 71.8 N/m, what is the total potantial energy relative to
the water when the man stops falling?
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Problem
2
When a 2kg mass is attached to a verticali spring, the spring is stretched 10cm
such that the mass is 50cm above the table.
a.
b.
c.
What is the gravitational potential energy associated with this mass relative to the table?
What is the spring’s elasticf potential energy is the spring constant is 400 N/m?
What is the total energy of this system?
Pendulum Demo
Take a looksee….
 Where is the PE of the pendulum the
highest?
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 Why
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the top of course, Mr. McKnight!
Exactly! So, where is the KE of the
pendulum the highest?
 Why
the bottom of course, Mr. McKnight! It is
moving the fastest at the bottom!!
What kinds of Energy do we know
about?
Kinetic Energy
 Gravitational Potential Energy
 Elastic Potential Energy
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There are also nuclear, chemical,
internal and electrical energy
These are all
classified as
Mechanical
Energy. The
energies
involved in
motion
These are
classified as
non-mechanical
Energy
Tell me something I don’t know
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Mechanical Energy is conserved…
 Your
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initial ME equals your final ME
Conservation of mechanical Energy:
MEi=MEf
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*****This is ONLY when we neglect friction
(which we often do)
Misconception Alert!!!
While ME is conserved,
TOTAL Energy is also
conserved (all the different
kinds of Energy…we just
won’t analyze it here)
Let’s see if it works…
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I’m going to drop this 1kg object to the floor from
a height of 1.5m…
 What
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At the top when KE = 0
 What
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is the maximum PE?
is the maximum KE? (hint ME is conserved)
At the bottom when PE = 0
 Let’s
prove it…with our handy dandy kinematic
equations!
So…sum it up
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We can use the distance the egg has fallen and
a kinematic equation to find the speed at any
time (KE)
Or…We can use the height of the egg to find
the PEg at any time.
The great part…
KE+ΣPE = 14.7J EVERY TIME in this case
Data Table…
Height above ground (m)
Displacement (m)
ie. How far
the object
has
dropped
1.5
0
0
0
14.715
14.715
1.2
0.3
2.426108
2.943
11.772
14.715
0.9
0.6
3.431035
5.886
8.829
14.715
0.6
0.9
4.202142
8.829
5.886
14.715
0.3
1.2
4.852216
11.772
2.943
14.715
0
1.5
5.424942
14.715
0
14.715
Vf
KE
PE
ME = KE + PE
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Problem…
Starting from rest, a child zooms down a frictionless slide from an initial
height of 3.00m. What is her speed at the bottom of the slide? Assume she
has a mass of 25kg.
7.67m/s
Last thing
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Energy is conserved even
if acceleration varies.
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So if the slide in the last
problem had varying angles
on the way down, we
wouldn’t be able to calculate
the acceleration easily,
meaning no Kinematic
formulas 
BUT, b/c we know the ME
we can skip acceleration and
find the final speed without
all the extra work!
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Group Whiteboard it!!!!!
A small 10.0g ball is held to a slingshot that is stretched 6cm. The
spring constant is 2.0x102 N/m.
a.
b.
c.
d.
What is the elastic potential energy of the slingshot before it is
released?
What is the KE of the ball just after the slingshot is released?
What is the ball’s speed at that instant?
How high does the ball rise if it is shot directly upward?
Questions…
Pg185; 1, 2, 4, 5
 Pg186; 1, 2, 3,
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