Phy 2053 Announcements
Exam 1
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Feb 17 Wednesday, 8:20 – 10:10 pm
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Please get there at least 10 minutes early
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Covers Chapters 1 - 5 (includes Lecture on Feb 11 Th)
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Room assignments
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If your last name begins with A through O, you
should go to Carleton 100
If your last name begins with P through Z, you
should go to McCarty C 100
You will be allowed one handwritten formula sheet
(both sides)
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Sample exam from last year posted on website.
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Previous exams & solutions available at Target copy.
Review: Energy and Work
Work done by a force F on an object:
W ≡ (F cos θ)∆x
Can Be Positive
or Negative
Kinetic Energy:
1
2
KE = mv
2
Work-Kinetic Energy Theorem
Wnet = KEf − KEi = ∆KE
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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
•
Speed will increase if work is positive
•
Speed will decrease if work is negative
Units of Work and KE
W ≡ (F cos θ)∆x
1
2
KE = mv
2
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In SI system
„ Newton • meter = Joule
„N • m = J
2 / s2
„ J = kg • m
Food calorie = 4184 J
Work and Friction
W ≡ (F cos θ)∆x
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Work can be done by friction.
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Friction opposite to ∆x Î negative W
Wnet = KEf − KEi = ∆KE
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The kinetic energy lost to friction by an
object goes into heating both the
object and its environment
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Some energy may be converted into
sound
Kinetic and potential energy
Potential energy can only be associated with conservative
forces.
Conservative and nonconservative forces
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Two general kinds of forces
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Conservative
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Work and energy associated with the force
can be recovered
Example: gravitation, spring
Nonconservative
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The forces are generally dissipative and
work done against it cannot easily be
recovered
Example: friction
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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.
Example: kinetic friction
•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
Conservative and Non-Conservative Forces
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A force is conservative if its work done
on object moving between two points
is independent of the path the object
takes between the points
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The work depends only upon the initial
and final positions of the object
Examples:
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Gravity
Spring force
Electromagnetic forces
Work and Potential Energy
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For every conservative force a potential
energy function can be found
Difference of potential energy at any two
points = - (work done by the force between
those two points)
Potential energy is associated with the
position of the object within some system
Example: gravity
Gravitation Potential Energy
∆PE = mgy
• Units: Joules (same as KE and work)
• Only depends on y, does not depend on x
Conservation of Mechanical Energy
In any isolated system of objects interacting
only through conservative forces, the total
mechanical energy of the system remains
constant.
Ei = E f
KEi + PEi = KE f + PE f
A diver drops (does not jump) from a board 10
m above the water. If he weights 700 N, what
is his speed just as he hits the water?
Gravitation Potential Energy
∆PE = mgy
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A location where the
gravitational potential
energy is zero must be
chosen
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The choice is arbitrary
since the change in the
potential energy is the
important quantity
Once the position is
chosen, it must remain
fixed for the entire
problem
Problem 5.46 (modified) A child of mass m starts
from rest and slides without friction from a height
h along a curved waterslide. She is launched
from a height h/5 into the pool. Find the max
height y after she leaves the waterslide.