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Exam II
Physics 101: Lecture 9
Work and Kinetic Energy
 Today’s
lecture will be on Textbook
Sections 6.1 - 6.4
Hour Exam 1, Monday 7:00 pm!
Conflict Monday 5:15 signup in grade book
Review Session: Sunday 8 pm (Lincoln Hall Theatre)
Physics 101: Lecture 9, Pg 1
Energy is Conserved
 Energy
is “Conserved” meaning it
can not be created nor destroyed
Can change form
Can be transferred
 Total
Energy does not change with
time.
This
is a BIG deal!
Physics 101: Lecture 9, Pg 2
10
Energy
 Forms
Kinetic Energy
Potential Energy
Heat
Mass (E=mc2)
 Units
Motion (Today)
Stored (Monday)
later
p102
Joules = kg m2 / s2
Physics 101: Lecture 9, Pg 3
12
Work: Energy Transfer due to Force
 Force
to lift trunk at constant speed
Case a Ta – mg = 0 T = mg
Case b 2Tb - mg =0 or T = ½ mg
 But
in case b, trunk only moves ½
distance you pull rope.
F
* distance is same in both!
Ta
Tb Tb
W = F dcos(q)
mg
mg
Physics 101: Lecture 9, Pg 4
15
Work by Constant Force
A) W>0
B) W=0
C) W<0
 Only
component of force parallel to
direction of motion does work!
F
W = F Dr cos q
F
1)
q
2)
Dr
WF > 0: 90< q < 180 : cos(q) > 0
Dr
F
F
WF = 0: q =90 : cos(q) =0
Dr
F
3)
4)
WF < 0: 90< q < 270 : cos(q) < 0
Dr
Dr
Dr
q
Note Change in r!
q
F
F
WF > 0: 0< q < 90 : cos(q) > 0
Physics 101: Lecture 9, Pg 5
18
Work by Constant Force
 Example: You pull a 30 N chest 5 meters
across the floor at a constant speed by applying
a force of 50 N at an angle of 30 degrees. How
much work is done by the 50 N force?
W = F Dx cos q
= (50 N) (5 m) cos (30)
N
T
f
mg
= 217 Joules
50 N
30
Physics 101: Lecture 9, Pg 7
21
Where did the energy go?
 Example: You pull a 30 N chest 5 meters
across the floor at a constant speed, by applying
a force of 50 N at an angle of 30 degrees.
 How much work did gravity do?
Dr
W = F Dr cos q
90
= 30 x 5 cos(90)
mg
=0
N
 How much work did friction do?
f
X-Direction: SF = ma
T cos(30) – f = 0
f = T cos(30)
W = F Dr cos q
= 50 cos(30) x 5 cos(180)
= -217 Joules
T
mg
f
Dr
180
Physics 101: Lecture 9, Pg 8
25
Preflight 1
FN
You are towing a car up a hill with constant velocity.
The work done on the car by the normal force is:
1. positive
2. negative
correct
3. zero
W
V
T
“The work done on the car by the normal force
is 0 because it is perpendicular”
32%
5%
63%
0%
20%
40%
60%
80%
Physics 101: Lecture 9, Pg 9
28
0%
Preflight 2
FN
You are towing a car up a hill with constant velocity.
The work done on the car by the gravitational force is: T
1. positive
correct
2. negative
3. zero
W
V
The work done on the car by the gravitational
force is negative because it hinders motion up the
hill
7%
68%
25%
20%
40%
60%
80%
Physics 101: Lecture 9, Pg 10 30
Preflight 3
FN
You are towing a car up a hill with constant velocity.
The work done on the car by the tension force is:
correct
1. positive
2. negative
3. zero
V
T
W
89%
6%
the work done on the car by the tow rope is positive
because the car is moving up
6%
0%
20%
40%
60%
80%
100%
Physics 101: Lecture 9, Pg 11 32
Kinetic Energy: Motion
 Apply
constant force along x-direction to
a point particle m.
W = Fx Dx
= m ax Dx
= ½ m (vf2 – v02)

1 2 2
recall : ax Dx = (vx - vx 0 )
2
Work changes ½ m v2
 Define
W=DK
Kinetic Energy K = ½ m v2
For Point Particles
Physics 101: Lecture 9, Pg 12 35
Preflight 4
FN
You are towing a car up a hill with constant velocity.
The total work done on the car by all forces is:
1. positive
2. negative
3. zero
correct
V
T
W
70%
The total work done is positive because the car is
moving up the hill. (Not quite!)
4%
26%
0%
20%
Total work done on the car is zero because the
forces cancel each other out.
40%
60%
80%
Physics 101: Lecture 9, Pg 13 37
Example: Block w/ friction

A block is sliding on a surface with an initial speed of 5
m/s. If the coefficent of kinetic friction between the block
and table is 0.4, how far does the block travel before
y
stopping?
Y direction: SF=ma
N-mg = 0
N = mg
Work
WN = 0
Wmg = 0
Wf = f Dx cos(180)
= -mmg Dx
5 m/s
N
f
x
mg
W=DK
-mmg Dx = ½ m (vf2 – v02)
-mg Dx = ½ (0 – v02)
mg Dx = ½ v02
Dx = ½ v02 / mg
= 3.1 meters
Physics 101: Lecture 9, Pg 14 44
Falling Ball Example
 Ball
falls a distance 5 meters, What
is final speed?
Only force/work done by gravity
SW = DKE
Wg = ½ m(vf2 – vi2)
Fg h cos(0) = ½m vf2
mg
mgh = ½m vf2
Vf = sqrt( 2 g h ) = 10 m/s
Physics 101: Lecture 9, Pg 15 47
Work by Variable Force
W
= Fx Dx
Force
Work is area under F vs x plot
Work
Distance
Spring F = k x
» Area = ½ k x2 =Wspring
Force
Work
Distance
Physics 101: Lecture 9, Pg 16 49
Summary
 Energy
is Conserved
 Work = transfer of energy using force
Can be positive, negative or zero
W = F d cos(q)
 Kinetic
Energy (Motion)
K = ½ m v2
 Work
= Change in Kinetic Energy
S W = DK
Physics 101: Lecture 9, Pg 17 50