Review: Friction Forces

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Review: Friction Forces
Phy 2053 Announcements
Contact between bodies with a relative velocity produces friction
Exam 1
1.
Feb 18, 8:20 – 10:10 pm
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Please get there at least 10 minutes early, and preferably 20 minutes
Will cover material from sections 1.1 – 5.3 of Serway/Vuille
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Room assignments
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If your last name begins with A through P, you should go to Carleton 100
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If your last name begins with R through Z, you should go to Pugh 170
You be allowed one handwritten formula sheet (both sides), 8 ½” x 11” paper
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Exam conflicts: Anyone with exam conflicts, send email to [email protected]
and [email protected] by no later than Friday, Feb 6!!
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Friction is proportional to the normal force
Static friction: the direction of the frictional force is opposite
ƒs ≤ µ n
Kinetic friction: the direction of the frictional force is opposite
the direction of motion
the direction of the applied force,
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Include the reason for the conflict
ƒk = µ n
Prof. Chan is out of town from Feb 5 – Feb 14. His office hours are cancelled for this
period, but he will be reading e-mail.
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I will be out of town from Feb 11 – Feb 13 and Feb 17-19. Office hours also cancelled,
but I will be reading e-mail
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I will have special office hours on Monday Feb 9 from 10-12 am and Monday Feb 16 10-12 am
Review: Energy and Work
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Professors out of town:
2.
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Mechanical Energy
•Kinetic (associated with motion)
•Potential (associated with position
Work:
Work-Kinetic Energy Theorem
Wnet = KEf − KEi = ΔKE
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W ≡ (F cos θ)Δx
Work Can Be Positive or Negative
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When work is done by a net force on an
object and the only change in the object
is its speed, the work done is equal to
the change in the object’s kinetic
energy
1
2
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Kinetic Energy: KE = mv 2
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Units: 1 Joule = 1 N m = 1 kg m2/s2
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A force is conservative if work done on
object moving between two points is
independent of the path the object takes
between the points
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units follow from above definitions
Two Kinds of Forces
Conservative and Non-Conservative
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The work depends only upon the initial and final
positions of the object
Any conservative force can have a potential
energy function associated with it
Examples of conservative forces include:
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Gravity
Spring force
Electromagnetic forces
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Speed will increase if work is positive
Speed will decrease if work is negative
An object’s kinetic energy can also be
thought of as the amount of work the
moving object could do in coming to rest
A force is nonconservative if the work it does
on an object depends on the path taken by the
object between its final and starting points.
Examples of nonconservative forces
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kinetic friction and air drag
•The blue path is shorter than
the red path
•The work required is less on
the blue path than on the red
path
•Friction depends on the path
and so is a non-conservative
force
1
Problem 5-18
Work and Potential Energy
On a frozen pond, a 10 kg sled is given a kick that imparts
to it an initial speed of v0 = 2.0 m/s. The coefficient of
kinetic between the sled and the ice is μk = 0.1. Use the
Work-energy theorem to find the distance the sled moves
before coming to rest.
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For every conservative force a potential
energy function can be found
Evaluating the difference of the function
at any two points in an object’s path
gives the negative of the work done by
the force between those two points
Example will be gravity
Image Credit: http://www.snowmobileforum.com/snowmobile-still-shots/8148-sled-car.html
Work and Gravitational Potential Energy
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Conservation of Mechanical Energy
PE = mgy
In any isolated system of objects interacting only
through conservative forces, the total mechanical
energy of the system remains constant.
Won −book = PEi − PE f = mgyi − mgy f = mg ( yi − y f )
Units of Potential Energy, Work,
and Kinetic Energy
are the same=joules
Ei = E f
Work-Energy Theorem
KEi + PEi = KE f + PE f
Wnc = (KEf − KEi )
+(PEf − PEi ) = 0
If nonconservative forces are present, then the full
Work-Energy Theorem must be used instead of the
equation for Conservation of Energy
(conservative)
Conservation of Energy
KEi + PEi = KE f + PE f
Wnc = (KEf − KEi ) +(PEf − PEi )
Springs: Force
Problem Solving with Conservation of Energy
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Define the system- Verify only conservative forces
present
Select the location of zero gravitational potential
energy
¾ Do not change this location while solving problem
Identify two points the object of interest moves
between
¾ At one point information is given
¾ At other point you want to find out something
Apply the conservation of energy equation to the
system
Hooke’s Law gives the force
F=-kx
k is the ‘spring constant’
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F is the restoring force
F in the opposite direction of x
k depends on how the spring
was formed, material from
which it was made, thickness
of the wire, etc.
Fapplied
xmax
2
Springs: Work
F varies with x: F = - k x
W=Fparallel Δx is only valid if F constant.
For varying forces,
we can approximate with series of steps
Work is sum of areas of rectangles = area
under curve.
Linear spring is a simple case:
A=½Bh
W = ½ xmax Fmax
= ½ k x2
Potential Energy in a Spring
1
PE s = kx 2
2
Elastic Potential Energy
„ related to the work required
to compress spring from its
equilibrium position to some
final, arbitrary, position x
Work = Potential Energy
Initial and Final
Kinetic Energies=0
Area unde
r cu
rve
= work done on spring
Springs and Gravity
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Wnc = (KEf – KEi) + (PEgf – PEgi) +
(PEsf – PEsi)
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PEg is the gravitational potential energy
PEs is the elastic potential energy
associated with a spring
PE will now be used to denote the total
potential energy of the system
Conservation of Energy: Spring + Gravity
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The PE of the spring is added to both sides
of the conservation of energy equation
(KE + PE g + PE s )i = (KE + PE g + PE s )f
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PEg is the gravitational potential energy
PEs is the elastic potential energy associated
with a spring
PE will now be used to denote the total
potential energy of the system
The same problem-solving strategies apply
3
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