PHY 113 C Fall 2013 Lecture 7 1 PHY 113 C General Physics I 11 AM 1215 P M MWF Olin 101 Plan for Lecture 7 Chapter 7 The notion of work and energy Definition of work Examples of work ID: 228749
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Slide1
9/17/2013
PHY 113 C Fall 2013 -- Lecture 7
1
PHY 113 C General Physics I
11 AM – 12:15
P
M MWF Olin 101
Plan for
Lecture 7:
Chapter 7 -- The notion of work and energy
Definition of work
Examples of work
Kinetic energy; Work-kinetic energy theorem
Potential energy and work; conservative forcesSlide2
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7.3,7.15,7.31,7.34Slide3
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Webassign
questions for Assignment 6 -- #1
52. Consider a large truck carrying a heavy load, such as steel beams. … Assume that a 10,000-kg load sits on the flatbed of a 20,000-kg truck initially moving at v
i
=12 m/s. Assume that the load on the truck bed has a coefficient of static friction of
m
S
=0.5. When the truck is braked at constant force, it comes to rest in a distance
d
. What is the minimum stopping distance
d such that the load remains stationary relative to the truck bed throughout the breaking?
v
i
a
f
mSlide4
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4
Webassign
questions for Assignment 6 -- #1 -- continued
v
i
a
m
f
iclicker
exercise
--
Do we have enough information to calculate
a
?
Yes
NoSlide5
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Webassign
questions for Assignment 6 -- #1 -- continued
v
i
a
m
fSlide6
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6
A block of mass 3 kg is pushed up against a wall by a force
P
that makes an angle of
q
=50
o
with the horizontal.
m
s
=0.25. Determine the possible values for the magnitude of P that allow the block to remain stationary.
f
mg
N
f
Webassign
questions for Assignment 6 -- #4Slide7
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7
f
mg
N
fSlide8
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Webassign
questions for Assignment 6 -- #6
FSlide9
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Preparation for the introduction of work:
Digression
on the definition of vector “dot” product
qSlide10
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Digression: definition of vector “dot” product -- continued
qSlide11
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Digression: definition of vector “dot” product –
component form
q
Note that the result of a vector dot product is a
scalar
.Slide12
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Definition of work:
F
d
r
r
i
r
jSlide13
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13
Units of work:
work = force
·
displacement = (N
·
m) = (joule)
Only the component of force
in the direction
of the displacement contributes to work.
Work is a
scalar quantity.If the force is not constant, the integral form must be used.Work can be defined for a specific force or for a combination of forcesSlide14
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14
iclicker
question:
A
ball with a weight of 5 N follows the trajectory shown. What is the work done by gravity from the initial
r
i to final displacement r
f
?
(A)
0 J
(B)
7.5 J
(C) 12.5 J (D) 50 J
1
m
1
m
2.5
m
r
i
r
f
10
mSlide15
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15
mg
r
i
r
f
W=
-
mg(
r
f
-
r
i
)<0
mg
r
i
r
f
W=
-
mg(
r
f
-
r
i
)>0
Gravity does
negative
work:
Gravity does positive work:Slide16
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Work done by a variable force:Slide17
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Example:Slide18
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Example – spring force:
F
x
= -
kxSlide19
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x
F
Positive work
Negative workSlide20
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Detail:Slide21
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More examples:
Suppose a rope lifts a weight of 1000N by 0.5m at a constant upward velocity of
4.9m/s
. How much work is done by the rope?
(A) 500 J (B) 750 J (C) 4900 J (D) None of these
Suppose a rope lifts a weight of 1000N by 0.5m at a constant upward acceleration of
4.9m/s
2
. How much work is done by the rope
?
(A) 500 J (B) 750 J (C) 4900 J (D) None of these Slide22
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F
P
q
mg
n
f
k
x
i
x
f
Assume F
P
sin
q
<<mg
Work of gravity?
0
Work of F
P
?
F
P
cos
q
(
x
f
-x
i
)
Work of
f
k
?
-
m
k
n
(
x
f
-x
i
)=
-
m
k
(mg- F
P
sin
q)
(
x
f
-x
i
)
Another exampleSlide23
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iclicker
exercise:
Why should we define work?
Because professor like to torture students.
Because it
is always good to do work
Because it will help us understand motion.
Because it will help us solve the energy crisis.
Work-Kinetic energy theorem.Slide24
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Back to work:
F
d
r
r
i
r
jSlide25
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Why is work a useful concept?
Consider Newton’s second law:
F
total
= m
a
F
total
·
dr
= m a ·
dr
W
total
= ½ m v
f
2
-
½ m vi2
Kinetic energy (joules)Slide26
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Introduction of the notion of Kinetic energy
Some more details:
Consider Newton’s second law:
F
total
= m
a
F
total
· d
r= m a
· dr
W
total
= ½ m v
f
2
- ½ m v
i2
Kinetic energy (joules)Slide27
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Kinetic energy: K = ½ m v
2
units: (kg) (m/s)
2
= (kg m/s
2
) m
N m = joules
Work – kinetic energy relation:
W
total
= K
f
– KiSlide28
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Kinetic Energy-Work theorem
iclicker
exercise:
Does this remind you of something you’ve seen recently?
Yes
NoSlide29
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Kinetic Energy-Work theoremSlide30
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Kinetic Energy-Work theorem
Example: A ball of mass 10 kg, initially at rest falls a height of 5m. What is its final velocity?
i
f
h
0Slide31
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Example
A block, initially at rest at a height h, slides down a frictionless incline. What is its final velocity?
h
h=0.5m
0Slide32
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Example
A block of mass
m
slides on a horizontal surface with initial velocity v
i
, coming to rest in a distance d.
v
i
v
f
=0
d
Determine the work done during this process.
Analyze the work in terms of the kinetic friction force.Slide33
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Example -- continued
v
i
v
f
=0
d
fSlide34
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34
Example
A mass m initially at rest and attached to a spring compressed a distance
x=-|x
i
|, slides on a frictionless surface. What is the velocity of the mass when
x=0
?
k
0Slide35
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Special case of “conservative” forces
conservative non-dissipativeSlide36
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kSlide37
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37
iclicker
exercise:
Why would you want to write the work as the difference between two “potential” energies?
Normal people wouldn’t.
It shows a lack of imagination.
It shows that the work depends only on the initial and final displacements, not on the details of the path.Slide38
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Work-Kinetic Energy Theorem for conservative forces:Slide39
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Energy diagramsSlide40
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Example: Model potential energy function U(x) representing the attraction of two atoms