Download Conserves mechanical energy

Physics 218
Lecture 14
Dr. David Toback
Physics 218, Lecture XIV
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Checklist for Today
•Things due awhile ago:
– Read Chapters 7, 8 & 9
•Things that were due Yesterday:
– Problems from Chap 7 on WebCT
•Things that are due Tomorrow in
Recitation
– Chapter 8
– Reading for Lab
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The Schedule
This week: (3/3)
• Chapter 7 due in WebCT
• 5th and 6th lectures (of six) on Chapters 7, 8 & 9
• Chapter 8 in recitation
Next week: (3/10) Spring Break!!!
Following Week: (3/17)
• Chapter 8 due in WebCT
• Reading for Chapters 10 & 11
• Lecture on Chapters 10 & 11
• Chapter 9 and Exam 2 Review in recitation
Following Week: (3/24)
• Chapter 9 due in WebCT
• Exam 2 on Tuesday
• Recitation on Chapters 10 & 11
• Reading for Chapters 12 & 13 for Thursday
• Lecture 12 & 13 on Thursday
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Chapters 7, 8 & 9 Cont
Before:
– Work and Energy
– The Work-Energy relationship
– Potential Energy
– Conservation of Mechanical Energy
This time and next time:
– Conservation of Energy
– Lots of problems
Physics 218, Lecture XIV
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Physics 218, Lecture XIV
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Different Style Than the Textbook
I like teaching this material
using a different style than
the textbook
1. Teach you the concepts
2. Give you the important
equations
3. Then we’ll do lots of problems
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Mechanical Energy
• We define the total
mechanical energy in a
system to be the kinetic
energy plus the potential
energy
• Define E≡K+U
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Conservation of Mechanical Energy
• For some types of problems, Mechanical
Energy is conserved (more on this next
week)
• E.g. Mechanical energy before you drop a
brick is equal to the mechanical energy
after you drop the brick
K2+U2 = K1+U1
Conservation of Mechanical Energy
E2=E1
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Problem Solving
• What are the types of examples we’ll
encounter?
– Gravity
– Things falling
– Springs
• Converting their potential energy into
kinetic energy and back again
E = K + U = ½mv2 + mgy
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Falling onto a Spring
We want to measure the
spring constant of a
certain spring. We drop a
ball of known mass m
from a known height Z
above the uncompressed
spring. Observe it
compresses a distance C.
Before After
Z
Z
C
What is the spring
constant?
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Quick Problem
A refrigerator with mass
M and speed V0 is sliding
on a dirty floor with
coefficient of friction μ.
Is mechanical energy
conserved?
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Non-Conservative Forces
• We’ve talked about three different types
of forces:
1.Gravity: Conserves mechanical
energy
2.Normal Force: Conserves
mechanical energy (doesn’t do
work)
3.Friction: Doesn’t conserve
mechanical energy
• Since Friction causes us to lose mechanical
energy (doesn’t conserve mechanical
Physics 218, Lecture XIV
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energy) it is a Non-Conservative
Law of Conservation of Energy
• Mechanical Energy NOT always
conserved
• If you’ve ever watched a roller
coaster, you see that the friction
turns the energy into heating the
rails, sparks, noise, wind etc.
• Energy = Kinetic Energy + Potential
Energy + Heat + Others…
– Total Energy is what is
conserved!
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Conservative Forces
If there are only conservative forces in the
problem, then there is conservation of mechanical
energy
• Conservative: Can go back and forth along any
path and the potential energy and kinetic energy
keep turning into one another
– Good examples: Gravity and Springs
• Non-Conservative: As you move along a path, the
potential energy or kinetic energy is turned into
heat, light, sound etc… Mechanical energy is lost.
– Good example: Friction (like on Roller
Coasters)
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Law of Conservation of Energy
• Even if there is friction, Energy is
conserved
• Friction does work
– Can turn the energy into heat
– Changes the kinetic energy
• Total Energy = Kinetic Energy + Potential
Energy + Heat + Others…
– This is what is conserved
• Can use “lost” mechanical energy to
estimate things about friction
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Roller Coaster with Friction
A roller coaster of mass m starts at rest
at height y1 and falls down the path with
friction, then back up until it hits height
y2 (y1 > y2).
Assuming we don’t know anything about the
friction or the path, how much work is
done by friction on this path?
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Energy Summary
If there is net work done on an object, it
changes the kinetic energy of the object
(Gravity forces a ball falling from height h
to speed up Î Work done.)
Wnet = ΔK
If there is a change in the potential energy,
some one had to do some work: (Ball falling
from height h speeds up→ work done → loss
of potential energy. I raise a ball up, I do
work which turns into potential energy for
the ball)
ΔUTotal = WPerson =-WGravity
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Energy Summary
If work is done by a non-conservative force
it does negative work (slows something
down), and we get heat, light, sound etc.
EHeat+Light+Sound.. = -WNC
If work is done by a non-conservative
force, take this into account in the total
energy. (Friction causes mechanical
energy to be lost)
K1+U1 = K2+U2+EHeat…
K1+U1 = K2+U2-WNC
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Friction and Springs
A block of mass
m is traveling on
a rough surface.
It reaches a
spring (spring
constant k) with
speed Vo and
compresses it a
total distance D.
Determine μ Physics 218, Lecture XIV
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Bungee Jump
You are standing on a
platform high in the air
with a bungee cord
(spring constant k)
strapped to your leg.
You have mass m and
jump off the platform.
l
l
1.How far does the cord
stretch, l in the picture?
2.What is the equilibrium
point around which you
will bounce?
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Coming up…
• Lectures:
– Last lectures on Chaps 7, 8 and 9
• Chapter 7 was due in WebCT on
Monday
• For Recitation
– Chap 8 problems due
– Lab reading
• Reading for Lecture next week
– Chaps 10 & 11: Momentum
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