Stuff you asked about:
I thought I understood the concepts in the pre-lecture until they went over the three
examples. I felt that it moved too fast especially when the video
was showing manipulations of equations.
I needed so much help with this. Please explain all of the checkpoint and lecture
questions. Also, give more examples!!!
I think work and energy is my favorite topic.
I think i know the answers, but don't know why and how to explain why it is right.
Well, the day I've been dreading has come. We have finished everything I've
previously known about physics and the rest of the semester is new. Time to start
learning.
We should discuss calc 2 because it is much more difficult than this.
This isnt that confusing to me
Many of the concepts of work are very confusing. I hope to go over this in detail
tomorrow
1. This stuff is super confusing. Discuss all of it. 2. I think everyone will be glad to know
the second I read about centrifugal force in my MCB lab manual, I dropped the class.
DON'T THEY KNOW PHYSICS?!?!
That was a lot to cover in one prelecture. How is dot product different from vector
sum?
“It seems like work was defined
differently to me in high school than
it is here. Then again, I didn't pay
much attention in high school”
You are old enough & smart
enough to see where the
formulas come from now.
“I really just don't understand work. Please try
to cover this in a very understandable way. The
pre-lecture just didn't do it for me! :)”
You aren't supposed to know
everything after the prelecture
Physics 211
Lecture 7
Today’s Concepts:
Work & Kinetic Energy
Work-Kinetic Energy Theorem
r2
W   F  dl
r1
“Integrals are a little scary, but the concepts themselves
don't seem to difficult.!”
The integral IS the concept !!
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   F  dl
NET
TOT
r1
1 2
K  mv
2
“Doesn't work-kinetic energy theorem have
anything to do with potential energy?."
Clicker Question
W  K
Does the work-kinetic energy theorem have
anything to do with potential energy?
A) YES
B) NO
The Dot Product
“Direction and magnitude of the total work done is confusing..”
“the vector dot thing. what is the point of it? Will we have to
use this in problems.”
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
W 
r2
 F  dl
r1
Work done by gravity near the Earth’s surface
“May we please discuss the concepts
of gravitational work?”
mg
Work done by gravity near the Earth’s surface
WTOT  W1  W2  ...  WN
 mg  dl1  mg  dl2  ...  mg  dlN
dlN
dl1
mg
dl2
dy1
dl1
dx1
mg
Work done by gravity near the Earth’s surface
WTOT  W1  W2  ...  WN
 mg  dl1  mg  dl2  ...  mg  dlN
 mgdy1  mgdy2 ...  mgdyN
  mg y
dlN
y
dl1
mg
dl2
Wg  mg ( y final  yinitial )
dr
rdq
dr
Fg
r2
GM e m  GM e m  GM m  1  1 
W   F (r )  dr  
dr


e
2

r
r
r
r

2
1 
r
r
1
r1
r2
1
r2
Close to the Earth’s surface:
r1 ~ r2 ~ Re:
1 1
Wg  GM e m   
 r2 r1 
 r1
r2 
 GM e m 


 r1r2 r2 r1 
GM e m

 r1  r2 
2
Re
mg
-y
So: Wg = -mgy
Work-Kinetic Energy Theorem
If there are several forces acting then W is the work
done by the net (total) force:
WNET  K
 W1  W2  ...
You can just add up the
work done by each force
WNET  WTOT
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
Less that 40% 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   F  dl
NET
TOT
r1
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
TOT
A) The car moves upward, in the positive direction, therefore the force
that caused it to move by a positive distance did positive work.
B) change in kinetic energy is zero, total work done is zero.
C) the work is being done by gravity, which is in the negative direction..
“Question 1 in the prelecture is wrong. It asks for the work done and
not the change in kinetic energy. Since the Apple is raised, there is
work from the change in gravitational potential energy.”
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:
Less that 40% got this right…
A) Positive
B) Negative
C) Zero
“How friction is related to work, and which direction work
goes in various cases”
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) since the static frictional force is acting in the same
direction as the motion, i believe the work would be positive.
B) Static means the box isn't moving, so the displacement is 0.
C) Friction always does negative work.
Work done by a Spring
“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.