Clicker question (from a former midterm…) - U of T...
Transcript of Clicker question (from a former midterm…) - U of T...
PHY131 Class 10 Notes 10/19/2015
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PHY131H1F– Class 10
Today:
• Energy
• Work
• Work as an integral
• Kinetic Energy
• Power
Clicker question
(from a former midterm…)
PHY131 Class 10 Notes 10/19/2015
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Class 10 Preclass Quiz on MasteringPhysics
This was due this morning at 8:00am
91% of students answered correctly: If a graph depicts force
versus position, the work done is equal to the area under
the curve.
82% of students answered correctly: A vector 𝐶 has a
magnitude 𝐶. Then the scalar product of the vector with
itself is 𝐶 ∙ 𝐶 = 𝐶2.
77% of students answered correctly: If the net work done on
an object is zero, the object’s kinetic energy remains the
same.
90% of students answered correctly: Person B does twice
the work of person A, and in one-half of the time. Person B
has four times the power output of person A.
Class 10 Preclass Quiz Student Comments
“The whole energy of the earth is increasing because of the
continuous sunlight, right?”
Harlow answer: Actually, no. The earth, just like the Sun,
radiates its energy out into space. The sun radiates visible
light, but the Earth, which is at a lower temperature, radiates
infrared light. But the Earth radiates exactly as much power
as it absorbs from the Sun. The whole energy of the Earth is
a constant.
About 100 comments such as: “none of us have had
integration yet”
Harlow answer: I understand this. But you must learn a bit
of integration for this course.
PHY131 Class 10 Notes 10/19/2015
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Calculus in a nutshell
http://hyperphysics.phy-astr.gsu.edu/hbase/math/derint.html
Class 10 Preclass Quiz Student Comments
“Is Work a scalar quantity or vector quantity?”
Harlow answer: Work, like all forms of energy, is a scalar
quantity. It has no direction associated with it. But it can be
positive or negative.
[lengthy description of confusion about the Power:Climbing
example on page 102, then] “... wait a minute... Do watts
always have 'per second' included within it?”
Harlow answer: correct. Watt is a short-form for
Joules/second
“Is there ever a time when you can use the equation for
work= F∆x without having to integrate?”
Harlow answer: Yes, if the force is constant!
“I had to do a lot of WORK in this chapter.. didn't like it but i
POWERED through it..”
“Brain is currently 待机-ing.... Please hold while it tries to
reboot.”
PHY131 Class 10 Notes 10/19/2015
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Last class I asked:“A pendulum bob swings back and forth on the end of a
string, describing a circular arc. Does the tension
force in the string to any work?”
Answer: NO!
The tension force always acts perpendicular to
infinitesimal displacement of the bob. In this case,
tension is not speeding the bob up or slowing down, it
is only turning it. So it does zero work.
Big Idea Chapters 6, 7 and 9 introduce the principles of
conservation of energy and conservation of
momentum. These concepts give us new useful ways
of analyzing motion.
Some quantities stay the same while other things
around them change.
For example, when a dish falls to the floor and
shatters, if you add up the mass of all the pieces, it will
be the same as the mass of the original dish. This is
“Conservation of Mass”: Mf = Mi.
Similarly, we have “Conservation of Energy” (Ef = Ei)
and “Conservation of Momentum” ( 𝑝𝑓 = 𝑝𝑖): two new
principles which we will use to solve problems.
PHY131 Class 10 Notes 10/19/2015
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• Energy is a property of an object, like age or
height or mass.
• Every object that is moving has some Kinetic
Energy.
• Objects in a gravitational or electric field may
also have Potential Energy.
• Energy has units, and can be measured.
• Energy is relative; kinetic energy of car is
different for an observer in the car than it is for
an observer standing on the side of the road.
What is “energy”?
• involves force and distance.
• is force distance.
• in equation form: W F Δx
Two things occur whenever work is done:
• application of force
• movement of something by that force
SI Unit of work:
newton-meter (N·m)
or joule (J)
The most basic form
of energy: Work
PHY131 Class 10 Notes 10/19/2015
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Work can be positive, zero or
negative
• When the force and the distance are in the same
direction, you are helping the motion with the
force, so the work done on the object is positive.
• The force is adding energy to the object +
environment.
F
Δx
• Maybe this force
is speeding the
object up.
Work can be positive, zero or
negative
• When the force and the distance are at right
angles, you are not helping the motion with the
force, so the work is zero.
• This force is not changing the energy of the
object.
F• This force won’t
speed the object
up or slow it
down. Δx
PHY131 Class 10 Notes 10/19/2015
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Class 10 Preclass Quiz Student Comments
“If there is no displacement in the direction of your force,
there is ZERO work hahahahah.
“There is a term describing this saying a person is doing
efficient-less job called "无用功“
Work can be positive, zero or
negative
• When the force and distance are in opposite
directions, you are hindering the motion with the
force, so the work done on the object is
negative.
• This force is reducing the energy of the object.
F• Maybe this
force is
slowing the
object down.
Δx
PHY131 Class 10 Notes 10/19/2015
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• Justin is doing a bench press, and he slowly
pushes the bar up a distance of 0.30 m while
pushing upwards on the bar with a force of 200 N.
The bar moves with a constant velocity during this
time.
• During the upward push, how much work does
Justin do on the bar?
A. 60 J
B. 120 J
C. 0 J
D. -60 J
E. -120 J
Discussion Question
• Justin is doing a bench press, and he slowly
lowers the bar down a distance of 0.30 m while
pushing upwards on the bar with a force of 200 N.
The bar moves with a constant velocity during this
time.
• During the downward lowering, how much work
does Justin do on the bar?
A. 60 J
B. 120 J
C. 0 J
D. -60 J
E. -120 J
Discussion Question
PHY131 Class 10 Notes 10/19/2015
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• Justin is doing a bench press, and he slowly
lowers the bar down a distance of 0.30 m while
pushing upwards on the bar with a force of 200 N.
He then pushes it up slowly the same distance of
0.30 m back to its starting position, also pushing
upwards on the bar with a force of 200 N.
• During the complete downward and upward
motion, how much total work does Justin do on
the bar? A. 60 J
B. 120 J
C. 0 J
D. -60 J
E. -120 J
Discussion Question
Simple Machines
• Devices for multiplying forces or changing the
direction of forces
• Cannot create energy but can transform energy
from one form to another, or transfer energy
from one location to another
• Cannot multiply work or energy
PHY131 Class 10 Notes 10/19/2015
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• (Force distance)input (force distance)output
Principles of a simple machine:
• Conservation of energy concept:
Work input work output
• Input force input distance
Output force output distance
Simple Machines
Simplest machine:
• Lever
– rotates on a point of support called the
fulcrum
– allows small force over a large distance and
large force over a short distance
PHY131 Class 10 Notes 10/19/2015
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Pulleys
This arrangement operates
like a lever with equal
arms— changes the
direction of the input force:
This arrangement
can allow a load to
be lifted with half the
input force:
Work as a scalar product
• The work done by a constant force is the
scalar-product of the force and the
displacement.
W = F r cosθ
𝑊 = 𝐹 ∙ 𝑟
PHY131 Class 10 Notes 10/19/2015
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The Work Done by a Variable Force
To calculate the work done on an object by a force that is
not constant, we use an integral:
We must evaluate the integral either geometrically, by
finding the area under the cure, or by actually doing the
integration.
𝑊 = 𝑥1
𝑥2
𝐹𝑥𝑑𝑥
A particle moving along the x-axis experiences the force
shown in the graph.
How much work is done on the particle by this force as it
moves from x = 0 to x = 2 m?
A. 0.0 J
B. 1.0 J
C. 2.0 J
D. 4.0 J
E.−2.0 J
PHY131 Class 10 Notes 10/19/2015
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Kinetic Energy• Energy of motion
• Depends on the mass of the object and square of
its speed:
If object speed is doubled kinetic energy is
quadrupled.
𝐾 =1
2𝑚𝑣2
Demonstration
• In terms of WORK and ENERGY,
describe what is happening to the ball
as it goes from A to B to C?
A spring-loaded toy gun is used to shoot a ball of mass m
straight up in the air. The spring has spring constant k. The
ball has speed vB at point B.
PHY131 Class 10 Notes 10/19/2015
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Work and Kinetic Energy• If an object starts from rest and there is a net
force doing work on it, the work done will be
equal to the final kinetic energy of the object.
• In equation form:
𝐹𝑑 =1
2𝑚𝑣2
The Work – Kinetic Energy Theorem:
• The work done by the net force on an
object as it moves is called the “net work”,
Wnet.
• The the net work causes the object’s
kinetic energy to change by:
ΔK = Wnet.
PHY131 Class 10 Notes 10/19/2015
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A particle moving along the x-axis experiences the force
shown in the graph. The particle starts at rest at x = 0.
What is the kinetic energy of the particle when it reaches
x = 2 m?
A. 0.0 J
B. 1.0 J
C. 2.0 J
D. 4.0 J
E.−2.0 J
Work-Energy Theorem• Applies to decreasing speed:
– reducing the speed of an object or bringing it to a halt
Example: Applying the brakes to slow a moving car, work is done on it (the friction force supplied by the brakes distance).
PHY131 Class 10 Notes 10/19/2015
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(A) I did positive work on the box, friction did negative work on the
box, there was net positive work done on the box.
(B) I did positive work on the box, friction did negative work on the
box, there was net negative work done on the box.
(C) I did positive work on the box, friction did negative work on the
box, there was net zero work done on the box.
(D) I did zero work on the box, friction did negative work on the
box, there was net positive work done on the box.
(E) I did zero work on the box, friction did positive work on the box,
there was net zero work done on the box.
Clicker Question. (From 2013 final exam)
Yesterday in my office I pushed a box, initially at rest, across the
rough floor to the other side of my office, where it now rests. Which
statement below is true concerning this motion of the box?
Power• Measure of how fast work
is done
• In equation form:
Power =
work done
time interval
Unit of power
• joule per second, called the
watt after James Watt,
developer of the steam
engine
• 1 joule/second 1 watt
• 1 kilowatt 1000 watts
PHY131 Class 10 Notes 10/19/2015
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Power
• 1 kWh is the amount of energy used by a
power of 1kW over 1 hour
• 1 kWh = 1000 J/s * 60 min/hour * 60 s/min
• 1 kWh = 3.6 million Joules
[Chart downloaded Oct.16 2015 from http://www.ontario-hydro.com/index.php?page=current_rates ]
• The unit of power is the
watt, which is defined as
1 watt = 1 W = 1 J/s
• Energy is measured by
Ontario Hydro in kWh
“kiloWatt hours”.
ExampleYour clothes dryer uses 5000 Watts and you need
to run it for 1 hour to dry your clothes. If you run it
during “on peak” time, such as between 7 and
11am on a weekday, the cost is 16 cents/kWh.
If you run it during “off peak” on the weekend the
price for Ontario Hydro electricity is 8 cents/kWh.
How much money do you save per load by doing
your laundry on the weekend?
PHY131 Class 10 Notes 10/19/2015
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Before Class 11 on Wednesday:
• Please read Chapter 7, sections 7.1-7.3
• Preclass quiz due Wednesday by 8:00am
• Complete MasteringPhysics.com Problem Set 4
due tonight at 11:59pm: Material: Uncertainties
and sections 5.1-5.3.
• Something to think about: Which has more
energy, a desk on the top floor of a building, or a
desk on the ground floor?