Download PPT

Physics 218
Lecture 12
Dr. David Toback
Physics 218, Lecture XII
1
Checklist for Today
•Things due for Last Thursday:
– Read Chapters 7, 8 & 9
•Things that were due Yesterday:
– Chap 5&6 turned in on WebCT
•Things due for Wednesday’s Recitation:
– Problems from Chap 7
•Things due for this coming Monday:
– Problems from Chap 7 on WebCT
Physics 218, Lecture XII
2
The Schedule
This week: (2/25)
• HW on Chaps 5&6 on WebCT
• 3rd and 4th lectures (of six) on Chapters 7, 8 & 9
• Chapter 7 in recitation
Next week: (3/3)
• Chapter 7 due in WebCT
• 5th and 6th lectures (of six) on Chapters 7, 8 & 9
• Chapter 8 in recitation
• Following Wee
Following 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
• Reading for Chapters 12 & 13 for Thursday
• Lecture 12 & 13 on Thursday
Physics 218, Lecture XII
3
Chapters 7, 8 & 9 Cont
Last time:
– More on Work
This time
– Work and Energy
– The Work-Energy relationship
– Potential Energy
– Conservation of Mechanical Energy
– Conservation of Energy
Physics 218, Lecture XII
4
Physics 218, Lecture XII
5
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
Physics 218, Lecture XII
6
Kinetic Energy and Work-Energy
• Energy is another big concept in physics
• If I do work, I’ve expended energy
– It takes energy to do work (I get
tired)
• If net work is done on a stationary box
it speeds up. It now has energy
• We say this box has “kinetic” energy!
Think of it as Mechanical Energy or the
Energy of Motion
Kinetic Energy =
Physics 218, Lecture XII
2
½mV
7
Work-Energy Relationship
•If net work has been done on an
object, then it has a change in its
kinetic energy (usually this means
that the speed changes)
•Equivalent statement: If there is a
change in kinetic energy then there
has been net work on an object
Can use the change in energy to
calculate the work
Physics 218, Lecture XII
8
Summary of equations
Kinetic Energy =
2
½mV
W= DKE
Can use change in speed
to calculate the work, or
the work to calculate the
speed
Physics 218, Lecture XII
9
Multiple ways to
calculate the work
done
Multiple ways to
calculate the velocity
Physics 218, Lecture XII
10
Multiple ways to calculate work
1.If the force and direction is
constant
– F.d
2.If the force isn’t constant, or the
angles change
– Integrate
3.If we don’t know much about the
forces
– Use the change in kinetic energy
Physics 218, Lecture XII
11
Multiple ways to calculate velocity
If we know the forces:
• If the force is constant
F=ma →V=V0+at, or V2-V02 = 2ad
• If the force isn’t constant
–Integrate the work, and look at
the change in kinetic energy
W= DKE = KEf-KEi
= ½mVf2 -½mVi2
Physics 218, Lecture XII
12
Quick Problem
I can do work on an object
and it doesn’t change the
kinetic energy.
How? Example?
Physics 218, Lecture XII
13
Problem Solving
How do you solve Work
and Energy problems?
BEFORE and AFTER
Diagrams
Physics 218, Lecture XII
14
Problem Solving
Before and After diagrams
1.What’s going on before
work is done
2.What’s going on after
work is done
Look at the energy before and
the energy after
Physics 218, Lecture XII
15
Before…
Physics 218, Lecture XII
16
After…
Physics 218, Lecture XII
17
Compressing a Spring
A horizontal spring has spring
constant k
1. How much work must you do to
compress it from its
uncompressed length (x=0) to a
distance x=-D with no
acceleration?
You then place a block of mass m
against the compressed spring.
Then you let go.
2. How much work will be done by
the spring?
3. Assuming no friction, what will
be the speed of the block when
it separates at x=0?
Physics 218, Lecture XII
18
Potential Energy
•Things with potential: COULD do
work
– “This woman has great potential as
an engineer!”
•Here we kinda mean the same thing
•E.g. Gravitation potential energy:
– If you lift up a brick it has the
potential to do damage
Physics 218, Lecture XII
19
Example: Gravity & Potential Energy
You lift up a brick (at rest) from the
ground and then hold it at a height Z
• How much work has been done on the
brick?
• How much work did you do?
• If you let it go, how much work will be
done by gravity by the time it hits the
ground?
We say it has potential energy:
U=mgZ
– Gravitational potential energy
Physics 218, Lecture XII
20
Mechanical Energy
• We define the total
mechanical energy in a
system to be the kinetic
energy plus the potential
energy
• Define E≡K+U
Physics 218, Lecture XII
21
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
Physics 218, Lecture XII
22
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 =
2
½mv
Physics 218, Lecture XII
+ mgy
23
Problem Solving
For Conservation of Energy problems:
BEFORE and AFTER
diagrams
Physics 218, Lecture XII
24
Quick Problem
We drop a ball from a
height D above the ground
Using Conservation of
Energy, what is the speed
just before it hits the
ground?
Physics 218, Lecture XII
25
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
Physics 218, Lecture XII
26
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?
2
U(x) = ½kx
Physics 218, Lecture XII
27
Problem Solving
For Conservation of Energy
problems:
BEFORE and AFTER
diagrams
Physics 218, Lecture XII
28
Conservation of
Energy
Problems
Before…
Physics 218, Lecture XII
29
After
Physics 218, Lecture XII
30
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?
Physics 218, Lecture XII
31
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
Physics 218, Lecture XII
32
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 Non-Conservative force!
Physics 218, Lecture XII
33
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!
Physics 218, Lecture XII
34
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)
Physics 218, Lecture XII
35
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
Physics 218, Lecture XII
36
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?
Physics 218, Lecture XII
37
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
Physics 218, Lecture XII
38
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
Physics 218, Lecture XII
39
Next time…
•More problems on
Chapters 7, 8 & 9
•Recitation tomorrow
on Chapter 7
problems
Physics 218, Lecture XII
40
Physics 218, Lecture XII
41
Next Week
• Reading for Next Time:
– Finish Chapters 7, 8 and 9 if
you haven’t already
– Non-conservative forces &
Energy
• Chapter 5&6 Due Monday on WebCT
• Start working on Chapter 7 for
recitation next week
Physics 218, Lecture XII
42
Energy
• Conservation of
Mechanical Energy
problems
• Conservative Forces
• Conservation of Energy
Physics 218, Lecture XII
43
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?
Physics 218, Lecture XII
44
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)
Physics 218, Lecture XII
45
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
Physics 218, Lecture XII
46
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
Physics 218, Lecture XII
47
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?
Physics 218, Lecture XII
l
48