Transcript Work and Energy - russballard.com

Work and Energy
Russ Ballard
Science Department
Kentlake High School
Slippery Concepts
• Mostly our definitions will work.
• Sometimes they do not.
• Think of pushing a heavy
object that does not move.
• Is work being done?
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Slippery Concepts
• Can we have negative work?
• How do we define work and
energy?
• Can we transform energy into
different forms?
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Lecture Concepts
1. Work done by a constant
force.
2. Work done by a variable
force.
3. Work-Energy Theorem.
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Lecture Concepts
4. Potential Energy.
5. Conservation of energy.
6. Power
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Objective 1
• To be able to
–Define mechanical work
–Compute the work done in
various situations.
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Work & Constant Force
• The work done by a constant
force in moving an object is
equal to the product of the
magnitudes of the
displacement and the
component of the force parallel
to the displacement.
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Work & Constant Force
• W = Fd (cos )
• SI units are N m or joule (J)
●
• Work is a scalar quantity.
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Teaching Note
• If you carry a book across the
room is any work done?
• Explain your reasoning.
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Example 5.1
•
A student holds her physics
textbook, which has a mass of 1.5
kg, out of a second story window.
•
a. How much work is done holding
it?
•
b. How much work is done on it
when it has fallen 3.0 meters?
a. 0
b. +44J
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Draw Free-Body Diagrams
F
d
W = Wmax
F
d
W > 0 but < Wmax
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Draw Free-Body Diagrams
F
d
W=0
F
W<0
d
F
W = -Wmax
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Coefficient of Friction
• f k = μ kN
• μ k = fk = mg sin  = tan 
N mg cos 
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Teaching Note in 5.3
• Friction does negative work
• Weight does positive work
• Net work is zero only when
forces are equal and opposite.
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Example 5.3
• A 0.75 kg block slide down a ramp with
uniform velocity. Base = 1.2 m, angle = 20o.
• a. how much work is done by friction?
• b. what is the net work done on the block?
• c. discuss work done if ramp is adjusted to
cause acceleration.
• a. -3.2 J
• b. +3.2J
• c. component in x > friction.
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Objective 2
• To be able to
–differentiate work done by a
constant and variable force
–compute work done by a spring
force.
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Work and Variable Force
• If you pull on a spring it pulls
back.
• The relationship to the distance
pulled and pull of the spring is
nearly linear.
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Work and Variable Force
• Fs = -kx
• Why is kx negative?
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Work and Variable Force
• We will generally be limited to
constant or average force
situations.
• Work done is stretching a
spring
• W= ½ kx2
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Teaching Note
• Constant acceleration is not
present in variable forces.
• Why?
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Teaching Note
• If you use a bow vs. a spring.
• It is not possible to derive an
expression for the bow.
• Why?
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Example 5.4
• A 0.15kg mass is suspended from a
vertical spring and descends a
distance of 4.6 cm, after which is
hangs at rest. An additional mass of
0.50 kg is hung from the first. What is
the total extension of the spring.
• .20 m or 20 cm
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Problem Hint
• The important quantity in
computing work is the
displacement difference x, or
net change in length of the
spring.
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Objective 3
• To be able to
–explain the work-energy theorem
–apply it in solving problems.
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Work-Energy Theorem
• Kinetic energy
KE = ½ mv2
• Units are the joule (J)
• Energy of motion.
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Work-Energy Theorem
• Wnet = KE
• W = Fd = mgh = ½ mv2 = KE
• Work is the measure of the
transfer of kinetic energy.
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Teaching Note
• Kinetic energy is a positive
quantity.
• In the previous problem you
can find the acceleration.
• Then use a kinematics
equation to find the velocity.
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Example 5.5
• A shuffleboard player pushes a 0.25 kg
puck, initially at rest, in a way that causes a
constant horizontal force of 6.0 N to act on it
through a distance of 0.50 m (neglect
friction)
• a. what are the kinetic energy and speed of
the puck when the force is removed?
• b. How much work would be required to
bring the puck to rest?
• a. 4.9 m/s
• b. -3.0J
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Problem Hint
• You have to calculate the
actual KE.
• You cannot use the change of
velocity.
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Example 5.6
• In a football game, a 140-kg guard runs
with 4.0 m/s and a 70-kg free safety
moves at 8.0 m/s.
• a. both players have the same kinetic
energy
• b. safety has twice as much
• c. guard has twice as much
• d. safety has four times as much
• Explain your answer
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Example 5.7
• A car is traveling at 5.0 m/s speeds up
to 10 m/s, with an increase of kinetic
energy that requires work. Then the
speed goes up 15 m/s, requiring work.
• A. W1 > W2
• B.W1 = W2
• C. W2 > W1
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Objective 4
• To be able to
–explain how potential energy
depends on position
– compute values of gravitational
potential energy.
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Potential Energy
• Potential is stored energy.
• Normally thought to be mechanical
in nature.
• Work is also a change in potential
energy.
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Potential Energy
• It has two expressions.
• U = ½ kx2
• U = mgh
• U= potential energy.
• Units are joule (J)
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Example 5.8
• A 0.50kg ball is thrown vertically upward with
an initial velocity of 10 m/s.
• a. What is the change in the ball’s kinetic
energy between the start and its maximum
height?
• a. -25 J
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Example 5.8
• b what is the change in the ball’s potential
energy between the maximum height and
the launch point?
• b. +25 J
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Teaching Note
• Potential energy is also a
scalar quantity.
• But it can be positive or
negative.
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Teaching Note
• You can pick the zero point.
• Change in potential energy is
independent of path.
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Objective 5
• To be able to
–distinguish between
conservative and
nonconservative forces
– explain their effects on the
conservation of energy.
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The Conservation of Energy
• When something is conserved
it is constant.
• The total energy in the
universe is conserved or is
constant.
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The Conservation of Energy
• A force is said to be
conservative if the work done
on an object is independent of
the object’s path.
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The Conservation of Energy
• If it the path influences that the
amount of work done then it is
nonconservative.
• A long path will result in the
total work not equal to a
change in potential energy.
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The Conservation of Energy
• A conservative force allows all
of the energy to be conserved
to potential energy.
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The Conservation of Energy
• Nonconservative force does
not.
• A force is conservative if the
work done by or against it in
moving an object through a
round trip is zero.
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Conservation of Total
Mechanical Energy
• Etotal = KE + U
• KEi + Ui = KEf + Uf
• KE = - U
This only works when
nonconservative forces do no
work.
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Example 5.9
• A painter on a scaffold drops a 1.50kg can of
paint from a height of 6.0m
• a. what is the kinetic energy of the can when
it is at a height of 4.00m?
• b. with what speed will the can hit the
ground? (neglect air resistance).
• a. 29.4 J
• b. 10.8 m/s
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Example 5.11
• A 0.30kg mass sliding on a horizontal
frictionless surface with a speed of 2.5
m/s, strikes a light spring, which has a
spring constant of 3.0 x 103 N/m.
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Example 5.11
• a. What is the total mechanical energy
of the system?
• b. What is the kinetic energy(K1) of the
mass when the spring is compressed a
distance x1 = 1.0cm? (assume no
energy loss).
• a. 0.94 J
• b. 0.79 J
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Total Energy and
Nonconservative Forces
• Friction is a nonconservative
force.
• If nonconservative forces are
present mechanical energy is
not conserved.
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Example 5.12
• A skier with a mass of 80-kg starts from rest
and skis down a slope from an elevation of
110m. the speed of the skier at the bottom of
the slope is 20 m/s
• A. show that the system is nonconservative
• B. how much work is done by the
nonconservative force of friction?
• a. 8.6 x 104 J vs. 1.6 x 104 J
• b. -7.0 x 104 J
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Review of Concepts
• Constant force work
W = Fd cos 
• Variable force work requires
advanced math.
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Review of Concepts
• Kinetic Energy
KE = ½ mv2
• Potential Energy
PE = mgh
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Review of Concepts
• Conservation of energy.
• Total energy of the universe is
conserved.
• Total energy kinetic plus
potential is constant.
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Review of Concepts
• Mechanical systems have
friction.
• Friction causes a loss of
mechanical energy.
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Review of Concepts
• Power is work over time.
• P = W = Fd = Fv
t
t
• Efficiency relates output to
energy (work) input.
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Formulas
• Work W = Fd cos 
• Hooke’s Law Fs = -kx
• Work (spring) W = ½ kx2
• Kinetic Energy KE = ½ mv2
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Formulas
• Work Energy Theorem
Wnet = Kf – Ki = K
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Formulas
• Elastic spring Potential
U = ½ kx2
• Gravitational Potential Energy
U = mgh
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Formulas
• Conservation of Mechanical
Energy
½ mvi2 + Ui = ½ mvf2 + Uf
• Efficiency (percent)
 = Wout (x 100%)
Win
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Credits
• Problems
–Prentice Hall College Physics
Willson and Buffa
• Diagrams
–Holt Physics Serway & Faughn
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