physics 2210 fall semester 2014belz/phys2210/lecture09.pdf · physics 2210 fall semester 2014....
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Lecture 09: Work and Potential Energy II
Physics 2210Fall Semester 2014
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Today's Concepts:a) Energy and Frictionb) Potential Energy and Force
Mechanics Lecture 8, Slide 2
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Unit 9: Prelecture Feedback
Mechanics Lecture 8, Slide 3
● Block sliding down the ramp checkpoint.● Macroscopic work● Connection between force and potential
energy.● Please keep going through problems like
the homework
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Energy and Friction
● Last time: Mechanical Energy (K+U) is a constant of the motion for conservative forces.
● Today: Change in mechanical energy is equal to work done by nonconservative forces.
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Last Time:Generalize mechanical energy conservation to conservative systems including springs:
Spring P.E. K.E.
Gravitational P.E.
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Energy and Friction
● Last time: Mechanical Energy (K+U) is a constant of the motion for conservative forces.
● Today: Change in mechanical energy is equal to work done by nonconservative forces.
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Mechanics Lecture 9, Slide 7
Macroscopic Work done by Friction
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Macroscopic Work:
This is not a new idea – it’s the same “work” you are used to.
Applied to big (i.e. macroscopic) objectsrather than point particles (picky detail)
We call it “macroscopic” to distinguish it from “microscopic”.
Mechanics Lecture 9, Slide 8
∫ ⋅=b
a
ldFW
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Mechanics Lecture 9, Slide 9
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Mechanics Lecture 9, Slide 10
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ff
Mechanics Lecture 9, Slide 11
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“Heat” is just the kinetic energy of the atoms!
Mechanics Lecture 9, Slide 12
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“Heat” is just the kinetic energy of the atoms!
Mechanics Lecture 9, Slide 13
This is how the conservative “fundamental forces”(gravity, electromagnetism...) give rise to nonconservative macroscopic forces
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Example: A block of mass 12 kg has an initial velocity of 1.0 m/s to the right as it slides across the floor with a coefficient of kinetic friction
k = 0.45. How far does it travel
before coming to rest? Solve via:a) 2nd law and kinematics equationsb) Work-energy theorem
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H
N1
mg
N2
mg
µ mg
must be negative
m
Mechanics Lecture 9, Slide 15
Conservative and Nonconservative Forces
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A block of mass m, initially held at rest on a frictionless ramp a vertical distance H above the floor, slides down
the ramp and onto a floor where friction causes it to stop a distance r from the bottom of the ramp. The coefficient
of kinetic friction between the box and the floor is µk. What is the macroscopic work done on the block by
friction during this process?
A) mgH B) –mgH C) µk mgD D) 0
D
m
CheckPoint
Mechanics Lecture 9, Slide 16
H
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What is the macroscopic work done on the block by friction during this process?
A) mgH B) –mgH C) µk mgD D) 0
B) All of the potential energy goes to kinetic as it slides down the ramp, then the friction does
negative work to slow the box to stop
C) Since the floor has friction, the work done by the block by friction is the normal force times
the coefficient of kinetic friction times the distance.
Mechanics Lecture 9, Slide 17
CheckPoint
D
m
H
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A block of mass m, initially held at rest on a frictionless ramp a vertical distance H above the floor, slides down
the ramp and onto a floor where friction causes it to stop a distance D from the bottom of the ramp. The coefficient
of kinetic friction between the box and the floor is µk. What is the total macroscopic work done on the block by
all forces during this process?
A) mgH B) –mgH C) µk mgD D) 0
CheckPoint
Mechanics Lecture 9, Slide 18
D
m
HtotWK =∆
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What is the total macroscopic work done on the block by all forces during this process?
A) mgH B) –mgH C) µk mgD D) 0
D) total work is equal to the change in kinetic energy. since the box starts and ends at rest, the
change in kinetic energy is zero.
Mechanics Lecture 9, Slide 19
CheckPoint
D
m
HtotWK =∆
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Potential Energy vs. Force
Mechanics Lecture 9, Slide 20
dx
xdUxF
)()( −=
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Suppose the potential energy of some object U as a function of x looks like the plot shown below.
Where is the force on the object biggest in the –x direction?
A) (a) B) (b) C) (c) D) (d)
U(x)
x
(a) (b) (c) (d)
CheckPoint
Mechanics Lecture 9, Slide 21
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Suppose the potential energy of some object U as a function of x looks like the plot shown below.
Where is the force on the object biggest in the –x direction?
A) (a) B) (b) C) (c) D) (d)
U(x)
x
(a) (b) (c) (d)
CheckPoint
Mechanics Lecture 9, Slide 22
dx
xdUxF
)()( −=
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Suppose the potential energy of some object U as a function of x looks like the plot shown below.
Where is the force on the object zero?A) (a) B) (b) C) (c) D) (d)
U(x)
x
(a) (b) (c) (d)
Flashcard Question
Mechanics Lecture 9, Slide 23
dx
xdUxF
)()( −=
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Suppose the potential energy of some object U as a function of x looks like the plot shown below.
Where is the force on the object in the +x direction?A) To the left of (b) B) To the right of (b) C) Nowhere
U(x)
x
(a) (b) (c) (d)
Flashcard Question
Mechanics Lecture 9, Slide 24
dx
xdUxF
)()( −=
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HW Example
● What is work done by tension before the incline?● What is the speed of the block before the incline?● What is the work done by friction after traveling up the incline?● What is the work done by gravity after traveling up the incline?● How far does the block travel before coming to rest?
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Homework Example
● How far will you get with some initial speed?● If you have the minimum speed 11,068 m/s required,
what is your speed when you reach the moon?● Which effects minimum speed? m
earth, r
earth, m
ship?
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HW Example: Potential Energy in Earth-Moon System
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HW Example: Potential Energy in Earth-Moon System