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Phy 2053 Announcements
By now, you should be familiar (and
comfortable) with:
Exam 1
1.
Feb 18, 8:20 – 10:10 pm
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If your last name begins with R through Z, you should go to Pugh 170
Exam conflicts: Anyone with exam conflicts,
[email protected] and [email protected]
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send
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email
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2.
Include the reason for the conflict
There are still lots of Student Solution Manuals available at the Reitz Union
Book store
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Webassign useful information - the final answer usually requires 3
significant figures, and you should keep at least that many significant
figures in intermediate steps to get the right answer.
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Two objects with masses of 3.00 kg and
5.00 kg are connected by a light string
that passes over a frictionless pulley, as
in the Figure. Determine (a) the tension
in the string, (b) the acceleration of
each object, and (c) the distance each
object will move in the first second of
motion if both objects start from rest.
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The coefficient of friction μ (‘mu’) depends
on the surfaces in contact
The direction of the frictional force is
opposite the direction of motion
The coefficients of friction are nearly
independent of the area of contact
3 kg
5 kg
Friction Forces
Contact between bodies with a relative
velocity produces friction
„ Friction is proportional to the normal
force
„ The force of static friction is generally
greater than the force of kinetic friction
Accelerating and equilibrium situations
Using free-body diagrams
Example #4-38
Draw free body
diagrams
Apply Newton’s Laws
separately to each
object
The magnitude of
the acceleration of
both objects will be
the same
The tension is the
same in each
diagram
Solve the
simultaneous
equations
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Objects behave as particles
Neglect masses of strings, ropes, pulleys,
springs
Applications of Newton’s Laws
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Two objects connected by a massless string
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Inertia, mass, Σ F = ma, action/reaction
Assumptions (for now)
1.
to:
Webassign homework #3 due on Wednesday by midnight
2.
Newton’s Laws 1, 2, and 3
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If your last name begins with A through P, you should go to Carleton 100
You be allowed one handwritten formula sheet (both sides)
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Please get there at least 10 minutes early, and preferably 20 minutes
Room assignments
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Static Friction ƒs
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Static friction acts to keep the
object from moving
If F increases, so does ƒs
If F decreases, so does ƒs
ƒs ≤ µ n where n = normal
force vector
uur uur
f s = -F
1
Kinetic Friction, ƒk
The force of kinetic
friction acts when the
object is in motion
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ƒk = µ n
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Direction of ƒk opposite
to motion: opposes
motion
Variations of coefficient
of friction with speed
will be ignored
Fig. 4-19, p.102
Chapter 5.1-5.2
Block on a Ramp
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Energy and Work
Axes are rotated as
usual on an incline
The direction of
impending motion
would be down the
plane
Friction acts up the
plane
Mechanical Energy
•Kinetic (associated with motion)
•Potential (associated with position)
„Chemical Energy
„Electromagnetic Energy
„Nuclear Energy
Energy can be transformed from one form to another
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Opposes the motion
Draw free body
diagram
Yada Yada Yada
But not destroyed– “Energy is conserved”
(advanced physics: ‘E=mc2’)
Work/Energy can be used in place of Newton’s laws to
solve certain problems more simply
Work
W ≡ (F cos θ)Δx
F is the magnitude of the net force
„ Δ x is the magnitude of the
object’s displacement r
„ θ is the angle between F and
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This gives no information about
„ the time it took for the
displacement to occur
„ the velocity or acceleration of
the object
Work is a scalar quantity
Work is zero when force and
displacement are perpendicular
e. g., carrying a bucket of water
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r
Δx
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Displacement is
horizontal
Force is vertical
cos 90° = 0
W ≡ (F cos θ)Δx
So no work
done!
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Work Can Be Positive or Negative
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Units of Work
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In SI system
„ Newton • meter = Joule
„N • m = J
2 / s2
„ J = kg • m
US Customary
„ foot • pound
„ ft • lb
„ no special name
Two Kinds of Forces
Conservative and Non-Conservative
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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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Kinetic Energy
Work done on box is
positive when lifting the
box
Work is negative if
lowering the box
„ The force would still be
upward, but the
displacement would be
downward
OR
Box does positive work on
student when lowered
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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Energy associated with the motion
of an object
KE =
1
mv 2
2
Scalar quantity with the same
units as work
Work is related to kinetic energy
Work-Kinetic Energy Theorem
Wnet = KEf − KEi = ΔKE
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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
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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
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Work and Potential Energy
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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
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