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Stuff you asked about:
Yeeeeeah, that "reassuring intro" was pretty necessary. I have no clue
what just happened.
Whoooaaa, so thats why Calc III was useful.
Often times, we are given the derivation of several formulas. Will it be
necessary to know or understand the derivation or can we just simply
apply the formulas?
We should have cookies in lecture one day
You were right at the beginning, this was very difficult. I think I understand
some of it, but there were so many different equations I know that they are
extremely easy to mix up.
Can we go over the dot things? And wow, this was all quite confusing. I
know you told us not to freak out, but I am freaking out.
Can you go over the definition of work again more slowly? I am still
unsure how to tell which direction work is acting in.
I'm confused. Very confused. Also, will we get some sort of equation
sheet on our exams/tests?
It's late. I'm sleepy. I rushed through this. I feel bad now that I'm lacking
physics knowledge :(
“I very much prefer the traditional
method. I feel extremely confused by
the integral way. Keep it simple, stupid,
right? Sure it's nice to know how they
come about, but forcing us to use it by
not telling us the other stuff is just over
complicating what could be much easier..”
You are old enough to know
where formulas come from.
“i don't know. its impossible to learn without a decent book.
The book is the exact same as these stupid videos.”
Hi ___,
The library will have a number of good textbooks that we have used in past
semesters that you can look at if the prelectures aren’t enough. I would
suggest the one by Tipler & Mosca since I have assigned some end of
chapter problems from this book as the optional HW problems in
smartPhysics.
We used this book, and several others, before we made the prelectures.
The reason we stopped requiring students to buy the book it is that we
found that so few students actually read the book that it wasn’t worth having
everyone spend the money.
Mats
I would really like it if you could give us some advice on where to find
more practice problems. I kind of get this stuff, but I'd really like to
practice more than the ten questions we get on smart physics. Can you
recommend anywhere else to go?
Optional HW problems
Look at practice exams….
First midterm is on Wednesday Feb 20th at 7pm (see Syllabus)
We will give a conflict exam at 5:15 pm the same day. You will be able to
sign up for this in your grade book.
If you have a double conflict please contact Prof. Bezryadin
([email protected])
Several People Asked about Vertical Loop:
You were tempted to say
something like this:
“Normal force is
centripetal acceleration
minus mg since they act
in opposite directions”
This is not correct.
You need to keep track
of cause and effect:
a = v2/R
v
FNET = ma
N - mg = mv2/R
N = mv2/R + mg
N
mg
Physics 211
Lecture 7
Today’s Concepts:
Work & Kinetic Energy
Work-Kinetic Energy Theorem
r2
W 
F

dl

r1
“Are we ever going to have to integrate anything, or are the
integrals just there to make sure we understand where the
math we will be doing is coming from?”
No tricky integrals on exams –
but you need to understand them
conceptually…
Work-Kinetic Energy Theorem
The work done by force F as it acts on an object that
moves between positions r1 and r2 is equal to the
change in the object’s kinetic energy:
W  K
TOT
r2
W 
TOT
F

dl

NET
r1
K 
1
mv
2
Integrating is just adding up a bunch of
parts to get a whole…more on this later.
2
The Dot Product
“I keep mixing up when the work is positive, negative or zero.”
“Can you go over the dot product and how it works with work.”
F
W>0
a
D
F
W<0
v
Speeding up, K increasing
v
Slowing down, K decreasing
a
D
Work-Kinetic Energy Theorem: 1-D Example
If the force is constant and the directions aren’t
changing then this is very simple to evaluate:
car
F
d
r2
W   F  dl  F  d
r1
In this case
= Fd
since cos(0)=1
This is probably what you remember from High School.
Clicker Question
A lighter car and a heavier van, each initially at rest, are
pushed with the same constant force F. After both
vehicles travel a distance d, which of the following
statements is true? (Ignore friction)
F
d
W= Fd
car
same
F
d
van
K= W
Same too
A) They will have the same velocity
B) They will have the same kinetic energy
C) They will have the same momentum
r2

F  dl   K
Derivation – not so important
Concept – very important
r1
r2
 F  dl
r1
A force pushing over some distance
will change the kinetic energy.
 K
q
r2
W 
F
r1
 dl
Work done by gravity near the Earth’s surface
mg
Work done by gravity near the Earth’s surface
W TOT  W1  W 2  ...  W N
 m g  d l1  m g  d l 2  ...  m g  d l N
dlN
dl1
mg
dl2
dy1
dl1
dx1
mg
Work done by gravity near the Earth’s surface
W TOT  W1  W 2  ...  W N
 m g  d l1  m g  d l 2  ...  m g  d l N
dlN
  m gdy1  m gdy 2 ...  m gdy N
 mg y
y
dl1
mg
dl2
Wg  mg y
dr
rdq
dr
Fg
r2
W 
 F ( r )  dr
r1
r2
 
r1
GM em
r
2
dr 
GM em
r
r2
r1
 1
1
 GM em   
 r2 r1 
Close to the Earth’s surface:
r1 ~ r2 ~ Re:
 1
1
W g  GM em   
 r2 r1 
 r1
r2 
 GM em 


 r1 r2 r2 r1 

GM em
R
2
e
mg
 r1  r2 
-y
So: Wg = -mgy
Same !!
Work-Kinetic Energy Theorem
If there are several forces acting then W is the work
done by the net (total) force:
W NET   K
 W1  W 2  ...
You can just add up the
work done by each force
W N ET  W TO T
Checkpoint
Three objects having the same mass begin at the same
height, and all move down the same vertical distance H. One
falls straight down, one slides down a frictionless inclined
plane, and one swings on the end of a string. In which case
does the object have the biggest net work done on it by all
forces during its motion?
H
Free Fall
A) Free Fall
Frictionless incline
B) Incline
C) String
String
D) All the same
Clicker Question
Three objects having the same mass begin at the same
height, and all move down the same vertical distance H.
One falls straight down, one slides down a frictionless
inclined plane, and one swings on the end of a string.
What is the relationship between their speeds when they
reach the bottom?
H
Free Fall
Frictionless incline
A) vf > vi > vp
B) vf > vp > vi
String
C) vf = vp = vi
Checkpoint
A car drives up a hill with constant speed. Which statement
best describes the total work WTOT done on the car by all
forces as it moves up the hill?
A) WTOT > 0
B) WTOT = 0
C) WTOT < 0
Only 1/3 got this right…
Clicker Question
A car drives up a hill with constant speed. How does
the kinetic energy of the car change as it moves up
the hill?
A) It increases
B) It stays the same
C) It decreases
Clicker Question
A car drives up a hill with constant speed.
The acceleration of the car:
A) Points up the hill
B) Points down the hill
C) Is zero
Clicker Question
A car drives up a hill with constant speed.
The net force on the car:
A) Points up the hill
B) Points down the hill
C) Is zero
Reminder
We know two expressions that involve WTOT
W  K
TOT
r2
W 
TOT
F

dl

NET
r1
Checkpoint
W  K
r2
A car drives up a hill with constant speed.
Which statement best describes the total
work WTOT done on the car by all forces as
it moves up the hill?
W 
 F  dl
r1
A) WTOT > 0
B) WTOT = 0
C) WTOT < 0
TOT
“…some of the situations, like the car moving uphill with
constant velocity, are confusing as I have always thought of
changing the position of an object can change its total
energy (Potential energy) …”
“First you said the total work in lifting an apple up one shelf was
zero, then in the very next slide you said work depended the change
in height. How was work not done on the apple then?
Hand does positive work. Gravity does negative work.
The sum of these is zero since Wtot = Whand + Wgravity = K = 0
Checkpoint
A box sits on the horizontal bed of a moving truck. Static
friction between the box and the truck keeps the box from
sliding around as the truck drives.
S
a
The work done on the box by the static frictional force as the
truck moves a distance D is:
A) Positive
B) Negative
Less that half got this right…
C) Zero
From Last Lecture
A box sits on the horizontal bed of a moving truck. Static
friction between the box and the truck keeps the box from
sliding around as the truck drives.
S
a
If the truck moves with constant accelerating to the left as
shown, which of the following diagrams best describes the
static frictional force acting on the box:
A
B
C
Checkpoint
F
S
a
D
The work done on the box by the static frictional
force as the truck moves a distance D is:
A) Positive
B) Zero
C) Negative
A) The force and the displacement are in the same direction so
the work is positive.
B) Work is change in kinetic energy.
C) Since the movement is negative the work is also negative.
Work done by a Spring
“Show the integrals as
areas under a graph. This is
what helps me see the
conceptual part of it best.”
“Can you clarify the directions of positive or negativity for springs when
they are compressing and uncompressing?”
Use the formula to get the magnitude of the work
Use a picture to get the sign (look at directions)
In this example the spring does negative work since F and x are in
opposite direction. The axes don’t matter.