Download Today • Announcements: • F=ma • Electric Force • Work, Energy and

Today
• Announcements:
– The average on the first exam was 31/40
– Exam extra credit is due by 8:00 am Friday
February 20th.
• F=ma
• Electric Force
• Work, Energy and Power
ISP209s7 Lecture 10
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Exam 1
60
Number
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10
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Score
ISP209s7 Lecture 10
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Newton’s Second Law of Force
F=ma
• Force is equal to mass times acceleration.
• For a given force, the amount of acceleration is
inversely proportional to the mass.
• Force causes acceleration.
• If you observe acceleration, there must be a force
acting.
ISP209s7 Lecture 10
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A new Force!
• Charge is a property of matter. It is measured
in Coulombs C.
• Like charges repel, unlike charges attract.
• Coulomb’s Law of Electric Force
-
+
r12
kQ1Q2
F=
2
r12
k = 8.99 E 9 N ! m
ISP209s7 Lecture 10
2
C
2
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Why?
• Coulomb’s law looks like Newton’s Law of
gravity. Why?
• Why does charge come in two types and
mass only came in one type?
• Why do we always get r2? I hate squares.
• Why is k = 8.99E9 Nm2/C2 so much bigger
than G = Nm2/kg2?
Two possible answers:
(1) I can’t tell you until you are older. (2) I don’t know.
ISP209s7 Lecture 10
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Energy
• Energy is the ability to do work
• Energy comes in two forms
– Kinetic (KE) – energy of motion
– Potential (PE) – energy of position
• There are many variants on these type main
types, e.g. chemical, nuclear, thermal, …
ISP209s7 Lecture 10
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Energy and Power
• Energy is the ability to do work: Work = force x
distance = F d
1 2
KE = mv
• Energy comes in two forms
2
m - mass
– Kinetic (KE) – energy of motion
v - velocity
– Potential (PE) – energy of position
Gravitational GPE = m (gh); g = 9.81 m/s2 on Earth,
h height
• Power (measured in W = J/s) is the rate of change (or
use) of energy
ISP209s7 Lecture 10
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Work: Using a Force to Move Something
In common English, work refers to any kind of effort
you put into performing a task, whether physical or
mental.
In physics, work is done whenever an object is pushed
or pulled through a distance; there must be both force
and motion.
work = force × distance = Fd
ISP209s7 Lecture 10
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Work and Energy: A simple Example
• Slowly lift your book some height h and then
lower it.
• You did work on the book while lifting it; the book
did work on you while you lowered it.
• The raised book has an increased ability to do
work, and does this work as you lower it.
• What if you lift your book some height h and then
drop it? Can it still “do work”?
ISP209s7 Lecture 10
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Work and Energy: A simple Example
It accelerates downward,
acquiring kinetic energy
as it loses height.
Work requires motion
You could have the dropped book do work by driving a
thumbtack into the floor.
ISP209s7 Lecture 10
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Quantitative Look at Energy
• An object’s energy is defined as the amount
of work it can do.
• Therefore, the gravitational potential energy
(GPE) of an object is its weight multiplied by
its height, GPE = mgh
• The kinetic energy (KE) of an object in
motion can be derived from Newton’s laws
• KE = 1/2 * MV2
ISP209s7 Lecture 10
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Quantitative Look at Energy
GPE when you let it
drop is the same as its
KE just before it hits
the floor.
ISP209s7 Lecture 10
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Quantitative Look at Energy
If you add the
gravitational energy and
the kinetic energy at any
point in the book’s fall,
you will find that the
sum stays the same.
Energy is conserved.
ISP209s7 Lecture 10
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An Aside on Semantics
A “system” is a distinct collection of objects
and/or fields that are interacting in some way.
Any system having the ability to do work is said
to have energy.
A system with energy need not do work, but a
system that does work must have had energy.
ISP209s7 Lecture 10
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Some Forms of Energy
Kinetic energy: energy of motion
Gravitational energy: energy associated with a raised
Object (aka “potential energy”)
Elastic energy: energy of a stretched or deformed object
Thermal energy: energy in the form of heat due to the
random microscopic motion of atoms and molecules
ISP209s7 Lecture 10
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Forms of Energy
Electromagnetic energy – energy associated with electric
and magnetic fields
Radiant energy – energy of electromagnetic waves such
as light, infrared, and X-rays
Chemical energy – energy involved in chemical reactions
Nuclear energy – energy involved in nuclear reactions
ISP209s7 Lecture 10
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The Law of Conservation of Energy
Experiments have found that energy is always
conserved, although it may change its form.
• The total energy of all the participants in any process
remains unchanged throughout that process.
• That is, energy cannot be created or destroyed.
Energy can be transformed (changed from one form to
another), and it can be transferred (moved from one
place to another), but the total amount always stays the
same.
ISP209s7 Lecture 10
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The Work-Energy Principle
Another way of stating the conservation of
energy is what the book calls
The work-energy principle:
Work is an energy transfer. Work reduces the
energy of the system doing the work and
increases the energy of the system on which
work is done, both by an amount equal to the
work done.
ISP209s7 Lecture 10
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Transformations of Energy
What happens after
it hits the floor?
Where is all that energy now?
It’s gone into heat – both your book and the floor
are now slightly warmer.
ISP209s7 Lecture 10
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Transformations of Energy
One way to visualize energy
transformations is through the use of an
energy flow diagram. The one below is for
the dropped book.
ISP209s7 Lecture 10
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Some Example Problems
Examples:
• A mass of 1.0 kg is raised 1.0 m. How much work was
done?
W = ΔGPE = mgΔh = 1.0 kg x 9.81m/s^2 x 1.0 m = 9.81 J
• A 90.0 kg ISP209 professor walks up two flights of
stairs. How much did his/her potential energy
increase? DATA 1 flight of stairs = 3.00 m
ΔGPE = 90.0 kg x 9.81m/s2 x 2 flights x (3 m/flight) = 5.29 kJ
ISP209s7 Lecture 10
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Conservation of Energy
In nature certain quantities are “conserved”. Energy is one of
these quantities. Charge is another.
Example: Ball on a hill
A 1.00 kg ball is rolled toward a hill with an initial speed of 5.00
m/s. If the ball roles without friction, how high, h, will the ball go?
1 2
KE = mv
2
PE = mgh ; g = 9.80
m
s2
1 2
v 2 (5 m / s )2
mv = mgh " h =
=
= 1.28 m
2
2 g 2 ! 9.80 m
s2
ISP209s7 Lecture 10
-22-
Work
• Work = Force x distance
• Work is a scalar and is measured in Joules, J
• Bill pushes on a wall with 10 N for 33 s. If the wall
does not move, how much work is done on the wall?
• Work = 10.0 N x 0.0 m = 0.0 N
• How does that make sense? Work has a strict
definition. If the kinetic or potential energy of the
wall did not change, no work was done on the wall.
• Work changes energy from one form to another.
ISP209s7 Lecture 10
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Power
• Power is the rate of change of energy
• Power = (change in energy)/(change in
time)
• Power is a scalar and is measured in watts.
• Light bulbs are measured in watts
• Sun (a big light bulb) - 3.827×1026 W
ISP209s7 Lecture 10
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Information
• Horsepower 746 W = 1 horsepower
In fourteen hundred and ninety-two
Columbus sailed the ocean blue.
And if you divide by two
You get watts in a horsepower too
• Food energy is measured in kcal
– 1 food cal = 4.184 J
– 1 Calorie = 1 kcal (what we call calories are
actually kilocalories)
ISP209s7 Lecture 10
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Example Problem
How many kcal are burned by doing 1500 J of work?
DATA: The human body is 10% efficient in
converting food energy to work.
#
1 cal &
1
!!
cal = energy '
' $$
4.184 J % efficiency "
1 cal & 1 #
1500 J '
'$
! = 3590.cal = 3.59 kcal
4.184 J % 0.1 "
ISP209s7 Lecture 10
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