Transcript Lecture 12

Physics 218
Lecture 12
Dr. David Toback
Physics 218, Lecture XII
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This week…
• This week we will finish up
Chapters 6 & 7
–Last set of topics for Exam 2
• Exam 2: Thurs, October
th
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• Covers chapters 1-7
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The Schedule
This week: (10/9)
• Finish up Chapters 6&7 in lecture
• Chapter 6 in recitation
Next week: (10/16)
• Chapter 6 HW due
• Chapter 8 in lecture (reading questions due)
• Chapter 7 in recitation
Following week: (10/23)
• HW 7 due
• Chapter 9 in lecture on Tuesday (reading questions due)
• Chapter 8 in Recitation
• Exam 2 on Thursday October 26th
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Energy
• Conservation of
Mechanical Energy
problems
• Conservative Forces
• Conservation of Energy
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Potential Energy
A brick held 6 feet in the air has potential energy
• Subtlety: Gravitational potential energy is
relative to somewhere!
Example: What is the potential energy of a book 6 feet
above a 4 foot high table? 10 feet above the floor?
• DU = U2-U1 = Wext = mg (h2-h1)
• Write U = mgh
• U=mgh + Const
Only change in potential energy is really
meaningful
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Other Potential Energies: Springs
Last week we calculated
that it took ½kx2 of
work to compress a
spring by a distance x
How much potential
energy does it now how
have?
U(x) =
2
½kx
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Problem Solving
For Conservation of Energy
problems:
BEFORE and AFTER
diagrams
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Conservation of
Energy
Problems
Before…
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After
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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.
What is the spring
constant?
Before
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Z
After
Z
C
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Roller Coaster
You are in a roller coaster car of mass M that
starts at the top, height Z, with an initial
speed V0=0. Assume no friction.
a) What is the speed at the bottom?
b) How high will it go again?
c) Would it go as high if there were friction?
Z
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Non-Conservative Forces
• In this problem there are three different
types of forces acting:
1. Gravity: Conserves mechanical energy
2. Normal Force: Conserves mechanical
energy
3. Friction: Doesn’t conserve mechanical
energy
• Since Friction causes us to lose
mechanical energy (doesn’t conserve
mechanical energy) it is a NonConservative force!
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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 on an object, it changes the
kinetic energy of the object (Gravity forces a ball
falling from height h to speed up  Work done.)
Wnet = DK
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)
DUTotal = 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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Next time…
•More problems on
Chapters 6 & 7
•Recitation on Chapter
6 problems
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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). An odometer
tells us that the total scalar distance traveled is d.
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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What if the Roller Coaster had Friction?
•If there were no friction, the
roller coaster would go back
up to height Z and come to a
stop (then come back down
again)
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Roller Coaster
You are in a roller coaster car of mass M that starts
at the top, height Z, with an initial speed V0=0.
Assume no friction.
a) What is the energy at the top?
b) What is the speed at the bottom?
c) How much work is done by gravity in going from
the top to the bottom?
Z
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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 by
an amount D.
Determine m
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Bungee Jump
A jumper of mass m
sits on a platform
attached to a bungee
cord with spring
constant k. The cord
has length l (it
doesn’t stretch until
it has reached this
length).
How far does the cord
stretch Dy?
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