Download PHY131H1F - Class 11 - University of Toronto Physics

PHY131H1F - Class 11
Today:
• Conservative and
Nonconservative Forces
• Potential Energy
• Conservation of Energy
Clicker Question
A cart rolls up a frictionless incline. It starts
with speed vi, but stops near the top. As it rolls
up the ramp, its kinetic energy is transformed to
A. stopping energy.
B. gravitational potential energy.
C. energy of motion.
D. internal thermal energy.
E. energy of rest.
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Class 11 Preclass Quiz on MasteringPhysics
 This was due this morning at 8:00am
 72% of students got the first true/false question.
 A nonconservative force permits a two-way conversion
between kinetic and potential energies.
FALSE
 A potential energy function can be specified for a
nonconservative force.
FALSE
 A conservative force permits a two-way conversion between
kinetic and potential energies.
TRUE
 The work done by a nonconservative force depends on the
path taken.
TRUE
 The work done by a conservative force depends on the path
taken.
FALSE
 A potential energy function can be specified for a
conservative force.
TRUE
Class 11 Preclass Quiz on MasteringPhysics
 This was due this morning at 8:00am
 67% of students got the second true/false question.
 The total mechanical energy of a system, at any one instant,
is either all kinetic or all potential energy. FALSE (although
it could be)
 The total mechanical energy of a system is constant only if
conservative forces act. TRUE
 The total mechanical energy of a system is equally divided
between kinetic and potential energy.
FALSE (although
it could be)
 Mechanical energy can be dissipated to nonmechanical
forms of energy.
TRUE
 The total mechanical energy of a system is constant only if
nonconservative forces act.
FALSE (always false)
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Class 11 Preclass Quiz Student Comments
 “FYI, the answer to the last question is posted online on
yahoo since two years ago.
https://ca.answers.yahoo.com/question/index?qid=20131003
213113AAT6UcS”
Yahoo!
Answers can
help you get
this part of
your mark.
…but it’s not
going to help
you with this
part!
Class 11 Preclass Quiz Student Comments
 “I say that Could you please differentiate between what
conservative and non-conservative forces are? Some
examples would be helpful perhaps :)”
 Harlow answer: Yes will do!
 “Do you believe in me?”
 Harlow answer: Yes I do! You can do this!
 (at 2:42 am) “I have a CHM138 midterm in about, let's see,
15 hours. Please wish me luck.”
 Harlow answer: Good luck!
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Class 11 Preclass Quiz Student Comments
 “i trust in physics, but i'd never tie a bowling ball to the end of
a string and let it go to see if it would hit me in an attempt to
test a theorem, just sayin'. my mom paid a lot of money for
my teeth”
Conservative and Nonconservative Forces
• A conservative force stores any work done against it, and
can “give back” the stored work as kinetic energy.
• For a conservative force, the work done in moving between
two points is independent of the path.
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Conservative and Nonconservative Forces
• Because the work done by a
conservative force is path
independent, the work done in
going around any closed path is
zero:
𝐹 ∙ 𝑑𝑟 = 0
Conservative and Nonconservative Forces
• A nonconservative force does not store work
done against it, the work done may depend on
path, and the work done going around a closed
path need not be zero.
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Conservative and Nonconservative Forces
• Examples of conservative forces include:
• Gravity
• The electric force
• The force of an ideal spring
• Nonconservative forces include:
• Kinetic Friction
• Pushing force of a human or animal
• Automobile engine
Potential Energy
 Consider two
particles A and B
that interact with
each other and
nothing else.
 There are two ways
to define a system.
 System 1 consists
only of the two
particles, the forces
are external, and the
work done by the
two forces change
the system’s kinetic
energy.
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Potential Energy
 System 2 includes
the interaction
within the system.
 Since Wext = 0, we
must define an
energy associated
with the interaction,
called the potential
energy, U.
 When internal
forces in the system
do work, this
changes the
potential energy.
Potential Energy
• The change in potential energy is defined as
the negative of the work done by a
conservative force acting over any path
between two points:
B
U AB    F  dr
A
– Potential energy change is independent of path.
– Only changes in potential energy matter.
– We’re free to set the zero of potential energy at
any convenient point.
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Gravitational Potential Energy
Gravitational Potential Energy
• Gravitational potential energy stores the work
done against gravity:
U  mg y
– Gravitational potential energy increases linearly
with height y.
– This reflects the constant gravitational force near
Earth’s surface.
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Last class at the end I asked:
• Which has more energy, a desk on the top floor
of a building, or a desk on the ground floor?
• Technically, neither (a desk is a desk)!!
• But, if you count the gravitational interaction
between the Earth and the desk, then the system
of the Earth+desk on top floor has more energy
than the system of the Earth+desk on bottom
floor.
• Potential energy is the interaction energy of at
least two things!
Clicker Question
A car starts with speed vi, but the driver puts on
the brakes and the car slows to a stop. As the
car is slowing down, its kinetic energy is
transformed to
A. stopping energy.
B. gravitational potential energy.
C. energy of motion.
D. internal thermal energy.
E. energy of rest.
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Kinetic Energy: The energy of motion
𝐾=
1
𝑚𝑣 2
2
Potential Energy: The
energy of position
𝑈 = 𝑚𝑔𝑦
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Internal Energy: The energy of
microscopic thermal vibrations
𝐸𝑖𝑛𝑡 ∝ 𝑇
Mechanical Energy
• Mechanical Energy is defined as the sum of the
kinetic plus potential energy:
Emech = K + U
• When the only forces doing work on an object are
all conservative, then the mechanical energy is
conserved.
Ef = Ei
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Another way of looking at freefall:
vi
vf
QUESTION:
I hold a ball at a distance of 5 m
above the ground and release it from
rest.
How fast is it going just before it
hits the ground?
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A small child slides down the four frictionless slides A–D.
Each has the same height, and the child always starts
from rest. Rank in order, from largest to smallest, her
speeds vA to vD at the bottom.
A.
B.
C.
D.
E.
vC > vA = vB > vD
vC > vB > vA > vD
vD > vA > vB > vC
vA = vB = vC = vD
vD > vA = vB > vC
NOTE: The Zero of Potential Energy
 You can place the origin of your coordinate system, and thus
the “zero of potential energy,” wherever you choose and be
assured of getting the correct answer to a problem.
 The reason is that only ΔU has physical significance, not Ug
itself.
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QUESTION:
Zainab runs forward with her sled at
2.0 m/s. She hops at the top of a
very slippery slope. The slope is
7.0° below the horizontal, and
extends down a total vertical
distance of 5.0 m. What is her
speed at the bottom?
A child is sliding down a playground
slide at constant speed.
While sliding, the energy transformation
is
A. U → K
B. U → Eint
C. K → U
D. K → Eint
E. There is no transformation
because energy is conserved.
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Elastic Potential
Energy
 Consider a before-and-after
situation in which a spring launches
a ball
 The compressed spring has
“stored energy,” which is then
transferred to the kinetic energy of
the ball
−𝑥i
𝑥f = 0
We define the elastic
potential energy U of
a spring to be:
U  12 kx 2
A spring-loaded gun shoots a plastic ball
with a speed of 4 m/s. If the spring is
compressed twice as far, the ball’s speed
will be
A. 1 m/s.
B. 2 m/s.
C. 4 m/s.
D. 8 m/s.
E. 16 m/s.
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Before Class 12 on Monday
• Please finish reading Wolfson Chapter 7
• Something to think about:
• A red marble is balanced on the top of a smooth hill.
A blue marble sits at the bottom of a smooth valley.
Which marble is in equilibrium? What is the
difference between these two situations?
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