Transcript ch. 6 work and energy ppt

Chapter 6
work & energy
Physical science ~ mr.e ~ SRCS
Chapter 6:
WORK
AND ENERGY
Around 1637, Fermat wrote his Last Theorem in the margin of his copy of the
Arithmetica next to Diophantus' sum-of-squares problem:[14]
. it is impossible to separate a cube into two cubes, or a fourth power into two
fourth powers, or in general, any power higher than the second, into two like
powers. I have discovered a truly marvelous proof of this, which this margin is
too narrow to contain.[15]
This theorem was first conjectured by Pierre de Fermat in 1637, famously in the
margin of a copy of Arithmetica where he claimed he had a proof that was too
large to fit in the margin.
No successful proof was published until 1995 despite the efforts of countless
mathematicians during the 358 intervening years.
The unsolved problem stimulated the development of algebraic number theory
in the 19th century and the proof of the modularity theorem in the 20th.
It is among the most famous theorems in the history of mathematics and prior to
its 1995 proof was in the Guinness Book of World Records for "most difficult
math problems".
This lecture will help you understand:
•
•
•
•
•
•
•
Energy and Work
Work-Energy Theorem
Conservation of Energy
Power
Machines
Efficiency
Sources of Energy
Rube Goldberg Napkin Machine - YouTube
Honda Commercial Rube Goldberg
Work
Augie March - The Cold Acre - YouTube
Work
Work
• defined as the product of force exerted on an
object and the distance the object moves (in the
same direction as the force)
• is done only when the force succeeds in moving
the body it acts upon
• equation: work = force  distance
W = Fd
Work
Two things must be present
where work is done:
• application of F
• movement of something by
that force
Work done on the barbell is the
average force multiplied by the
distance through which the
barbell is lifted.
Work
What are the Units for Work?
Best way to figure this out?
Formula!
W=Fd
W=Nxm
(read: “Newton-meters”)
Here’s a question:
According to the scientific
definition of work, am I
actually accomplishing any?
Work
CHECK YOUR NEIGHBOR
If you push against a stationary brick wall for several minutes,
you do no work on the wall.
A.
B.
C.
D.
True.
False.
It depends.
Which prison system do I
belong to?
Work
CHECK YOUR ANSWER
If you push against a stationary brick wall for several minutes,
you do no work on the wall
A.
B.
C.
D.
True.
False.
It depends.
Which prison system do I
belong to?
Explanation:
You may do work on your
muscles, but not on the wall.
Work
actually accomplishing any?
Back to the Units for Work…
W=Fd
W=Nxm
A Newton-meter is also
known as a joule (J)
Work
One joule in everyday life is approximately:
• the energy required to lift a quarter pounder patty (w/out
cheese)…what distance?
Work
One joule in everyday life is approximately:
• the energy required to lift a small apple one
metre straight up. (A mass of about 102 g )
• the energy released when that same apple falls
one metre to the ground.
• the energy released as heat by a person at rest,
every 17 seconds.
• the kinetic energy of a 50 kg human moving
very slowly (0.2 m/s)—20cm/s.
• the kinetic energy of a tennis ball moving at
23 km/h (14 mph).
Work
More joules in everyday life…
Kilojoule
• One kilojoule per second (1000 watts) is approximately the
amount of solar radiation received by one square meter of the
Earth in full daylight.[8]
Work
More joules in everyday life…
Terajoule
• The terajoule (TJ) is equal to one trillion (1012) joules. About 63
terajoules were released by the atomic bomb that exploded
over Hiroshima.[10]
• The International Space Station, at completion, with a mass of
450,000kg and orbital velocity of 7.7 km/s,[11] will have a kinetic
energy of roughly 13 terajoules.
Work
More joules in everyday life…
Petajoule
• The petajoule (PJ) is equal to 1015
joules. 210 PJ is equivalent to
about 50 megatons of TNT. This is
the amount of energy released by
the Tsar Bomba, the largest manmade nuclear explosion ever.
More joules in
everyday life…
Exajoule
• The exajoule (EJ) is
equal to 1018 joules.
The 2011 Tōhoku
earthquake and
tsunami in Japan
manifested 1.41 EJ
of energy
• in the United States
used per year is
roughly 94 EJ.
Work
Work
More joules in everyday life…
Zettajoule
• The zettajoule (ZJ) is equal to 1021 joules. Annual global energy
consumption is approximately 0.5 ZJ
Work
More joules in everyday life…
Yottajoule
• The yottajoule (YJ) is equal to 1024 joules. This is approximately
the amount of energy required to heat the entire volume of
water on Earth by 1 °Celsius.
Work
The quantity of work done is equal to the amount of
force  the distance moved in the direction in which
the force acts.
Work falls into two categories:
• work done against another force
Powerlifter Shane Hamman
http://www.youtube.com/watch?v=xAYAvLSwQGw
• work done to change the speed of an object
Spiderman 2 (2004) Peter Stops The Train!
Work
CHECK YOUR NEIGHBOR
Work is done in lifting a barbell. How much work is done in lifting
a twice-as-heavy barbell the same distance?
A.
B.
C.
D.
Twice as much.
Half as much.
The same.
Depends on the speed of the lift.
Work
CHECK YOUR ANSWER
Work is done in lifting a barbell. How much work is done in lifting
a twice-as-heavy barbell the same distance?
A.
B.
C.
D.
Twice as much.
Half as much.
The same.
Depends on the speed of the lift.
Explanation:
This is in accord with work = force  distance. Twice the force for the
same distance means twice the work done on the barbell.
Work
CHECK YOUR NEIGHBOR
You do work when pushing a cart. If you push the cart twice as
far with the same constant force, then the work you do is
A.
B.
C.
D.
less than twice as much.
twice as much.
more than twice as much.
zero.
Work
CHECK YOUR ANSWER
You do work when pushing a cart. If you push the cart twice as
far with the same constant force, then the work you do is
A.
B.
C.
D.
less than twice as much.
twice as much.
more than twice as much.
zero.
Power
Define WORK again…
Which aspect is left out?
Here’s a hint (riddle):
This thing all things devours:
Birds, beasts, trees, flowers;
Gnaws iron, bites steel;
Grinds hard stones to meal;
Slays king, ruins town,
And beats high mountain down.
Power
Which accomplishes more WORK…Does it make a
difference if I walk
or run upstairs?
Why not?
Then why are you more tired when running up the stairs as opposed to merely
walking up the stairs? Does one require more E? Let’s see…
Power
Power is the rate at which work is performed or
energy is converted
(AKA: measure of how fast work is done)
What are the Units for Power?
What is the formula for Power?
Power  work done
time interval

P = Work accomplished/t taken
Which uses more E? Doing something fast or doing
the same thing slow? Why?
W/t
P = J/s

Power
How much energy is required to lift a quarter pounder patty
(w/out cheese) one m? How about lifting the same patty
one m in 1 second?
If lifting with 1 N of F a distance
of 1 m expends 1 J of E…1 J
expended in 1 second = 1 Watt
P=W/t
P=Fxd/t
P=Nxm/s
P = J/s
1 J/s = 1 watt
I converted the steam engine from a
“prime mover of marginal efficiency
into the mechanical workhorse of the
Industrial Revolution"
Power
The
development of the steam
engine provided a
1 horsepower is equivalent to 7465.5
watts.
Hp So if you took
reason to horse
compare
horses with that of
a 1-horsepower
and put the
it on aoutput
treadmill,of
it could
operate
a generator that
producing
a continuous
watts.
the engines
could
replace746them.
• "Watt found by experiment in 1782 that a 'brewery horse' was able to
produce 32,400 foot-pounds per minute." James Watt and Matthew
Boulton standardized that figure at 33,000 the next year.[7]
• Most observers familiar with horses and their capabilities estimate that
Watt was either a bit optimistic or intended to underpromise and
overdeliver; few horses can maintain that effort for long. Regardless,
comparison with a horse proved to be an enduring marketing tool.
~12 hp
One unit of
mechanical
horsepower is
approximately
equivalent to 745.7
watts.
Power
Surfer Rides 90 Foot Wave, Sets New...
A healthy human can produce about 1.2 hp briefly and
sustain about 0.1 hp indefinitely; trained athletes
can manage up to about 2.5 hp briefly and 0.3 hp
for a period of several hours…
Usain Bolt 9.58 100m New
World Record Berlin [HQ]
Power
CHECK YOUR NEIGHBOR
A job can be done slowly or quickly. Both may require the same
amount of work, but different amounts of
A.
B.
C.
D.
energy.
momentum.
power.
impulse.
Power
CHECK YOUR ANSWER
A job can be done slowly or quickly. Both may require the same
amount of work, but different amounts of
A.
B.
C.
D.
energy.
momentum.
power.
impulse.
Comment:
Power is the rate at which work is done.
This is an example of stored E (Potential E)…for our purposes,
definition has a mechanical E spin…
Energy
Energy
• defined as that which produces changes in matter
• (AKA the ability to do what?)
Effects of Mechanical energy observed only when
• it is being transferred from one place to another
or
• it is being transformed from one form to another
Both work and energy are measured in joules.
Mechanical Energy
Two Types
• E due to an object’s POSITION
or
• E due to its MOVEMENT
What do we call E of position?
What do we call E of motion?
Potential Energy
Example: potential energy of 10-N ball is the same in
all 3 cases because work done in elevating it
is the same. Why?
Potential Energy
Potential Energy
is defined as stored energy due to position, shape, or
state. In its stored state, energy has the potential for
doing work.
Examples:
Drawn bow
Stretched rubber band
Raised ram of a pile driver…..others?
How did the object get that E?
Gravitational Potential Energy
The amount of gravitational potential energy
possessed by an elevated object is equal to the work
done against gravity in raising it.
Work done equals force
required to move it upward 
the vertical distance moved
(W = Fd). The upward force
when moved at constant
velocity is the weight, mg, of
the object. So the work done
in lifting it through height h is
the product mgh.
Gravitational Potential Energy
Equation for gravitational potential energy:
PE = weight  height
Try your hand at the
or
text questions in the
blue box on p. 88…
PE = mgh
Gravitational potential energy examples:
Water in an elevated reservoir
The elevated ram of a pile driver
How derived? 1st formula?
F=ma so F= mg
Substitute: PE = Fxd
= mgxh or mgh
Potential Energy
CHECK YOUR NEIGHBOR
Does a car hoisted for repairs in a service station have increased
potential energy relative to the floor?
A.
B.
C.
D.
Yes.
No.
Sometimes.
Not enough information.
Potential Energy
CHECK YOUR ANSWER
Does a car hoisted for repairs in a service station have increased
potential energy relative to the floor?
A.
B.
C.
D.
Yes.
No.
Sometimes.
Not enough information.
Comment:
And if the car were twice as heavy, its increase in potential energy
would be twice as much.
Kinetic Energy
…is defined as the energy of a moving body; that is, the KE of
an object is equal to the W required to bring it to that speed
from rest or the amount of W that object can do while being
brought to rest.
Equation for kinetic energy:
Kinetic energy = 1/2 mass  speed2
or
KE = 1/2 mv2
small changes in speed  large changes in KE
(In fact if you double the speed of an object, you _____ the KE? Why?
Kinetic Energy
How did we get this formula?
Consider:
F = ma
(mult. by d)
F d = mad
(d= ½ at2)
Fd = ma (½ at2)
Fd = ½ m a2t2 (a=v/t or v=at)
Fd = ½ mv2
KE = ½ mv2
Try your hand at the
text questions in the
blue box on p. 89…
KE = 1/2 mv2
The story of kinetic and potential energy
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).
Do you see a
correlation
between the
data and the
formula?
KE = ½ mv2
d increased by what factor? Why?
The Work-Energy Theorem
CHECK YOUR NEIGHBOR
The work done in braking a moving car to a stop is the force of
tire friction  stopping distance. If the initial speed of the car is
doubled, the stopping distance is
A.
B.
C.
D.
actually less.
about the same.
twice.
None of the above.
The Work-Energy Theorem
CHECK YOUR ANSWER
The work done in braking a moving car to a stop is the force of
tire friction  stopping distance. If the initial speed of the car is
doubled, the stopping distance is
A.
B.
C.
D.
actually less.
about the same.
twice.
None of the above.
Try your hand at the
text questions in the
blue box on p. 90…
Explanation:
Twice the speed means four times the kinetic energy and four times the
stopping distance.
Work-Energy Theorem
When work is done on an object to change its KE,
the amount of work done is equal to the change in KE.
Equation for work-energy theorem:
Net work = change in KE
• If there is no change in object’s energy, then no work is
done on the object.
• Applies to potential energy:
For a barbell held stationary, no further work is done  no
further change in energy.
• Applies to decreasing energy:
The more kinetic energy something has  the more work is
required to slow it or stop it
The Work-Energy Theorem
CHECK YOUR NEIGHBOR
Consider a problem that asks for the distance a fast-moving crate
slides across a factory floor in coming to a stop. The most useful
equation for solving this problem is
A.
B.
C.
D.
F = ma.
Ft = mv.
KE = 1/2mv2.
Fd = 1/2mv2.
The Work-Energy Theorem
CHECK YOUR ANSWER
Consider a problem that asks for the distance a fast-moving crate
slides across a factory floor in coming to a stop. The most useful
equation for solving this problem is
A.
B.
C.
D.
F = ma.
Ft = mv
KE = 1/2mv2.
Fd = 1/2mv2.
Comment:
The work-energy theorem is the physicist’s favorite starting point
for solving many motion-related problems.
Conservation of Energy with a Simple Pendulum
Conservation of Energy
Conservation of Energy Demo with a Bowling Ball
Example: energy transforms without net loss or net
gain in the operation of a pile driver
Consider:
How do we know?
Impulse =  p
F t=  mv (divide by 2)
F t=  mv
2
2
(mult. By v)
v x ½ Ft = ½ mv x v
½ Ftv = ½ mv 2
½ Ft x d/t = ½ mv 2 (parse v; cancel t’s)
½ Fd= ½ mv 2
(mult. by 2)
Fd = mv2
(fill in units)
N x m = kg x m2/s2 (parse unit)
N x m = kg x m/s2 x m (Subst. concepts)
Fd = Fd
Work = Work
Kinetic Energy and Momentum
Comparison of Kinetic Energy and Momentum
• Both depend on mass and velocity—
Momentum depends on mass and velocity. (m x v)
KE depends on mass and the square of its velocity
• Momentum is a vector quantity. (m____ & d_____)
• Kinetic energy is a scalar quantity. (just m______)
Kinetic Energy
CHECK YOUR NEIGHBOR
Must a car with momentum have kinetic energy?
A.
B.
C.
D.
Yes, due to motion alone.
Yes, when motion is nonaccelerated.
Yes, because speed is a scalar and velocity is a vector quantity.
No.
Kinetic Energy
CHECK YOUR ANSWER
Must a car with momentum have kinetic energy?
A.
B.
C.
D.
Yes, due to motion alone.
Yes, when motion is nonaccelerated.
Yes, because speed is a scalar and velocity is a vector quantity.
No.
Explanation:
Acceleration, speed being a scalar, and velocity being a vector quantity,
are irrelevant. Any moving object has both momentum and kinetic
energy.
Conservation of Energy
Conservation defined in
• everyday language as “ to save”
• physics as to “remain unchanged”
In other words…if you don’t
clean your room (Einput)…it
will become a mess…
Law of conservation of energy
• In the absence of external work input or output, the total
energy of a system remains unchanged.
• Energy cannot be created or destroyed. (merely transformed)
What did Einstein
seemingly combine
when he formed his
famous formula E =
mc2?
The laws of
conservation of
mass…& E!
Conservation of Energy
PE = 10J
KE = ~
?
if KE of impact is ~8J
KE of heat was…~ J
Technically, the PE of the string changes to KE (bow, arrow & string), sound
(bow, arrow, string,& target) and heat (the target and arrow are slightly warmer
upon impact)! No E is truly LOST—just put into a less usable form…
A situation to ponder…
CHECK YOUR NEIGHBOR
Suppose the potential energy of a drawn bow is 50 joules, and
the kinetic energy of the shot arrow is 40 joules. Then
A.
B.
C.
D.
energy is not conserved.
10 joules go to warming the bow.
10 joules go to warming the target.
10 joules is mysteriously missing.
A situation to ponder…
CHECK YOUR ANSWER
Suppose the potential energy of a drawn bow is 50 joules, and
the kinetic energy of the shot arrow is 40 joules. Then
A.
B.
C.
D.
energy is not conserved.
10 joules go to warming the bow.
10 joules go to warming the target.
10 joules is mysteriously missing.
Explanation:
The total energy of the drawn bow, which includes
the poised arrow, is 50 joules. The arrow gets 40
joules and the remaining 10 joules warms the bow—
still in the initial system.
Conservation of Energy
Fill in the values for the PE & KE at each position. Assume
a PE of 4000J at the start (LEFT).
Conservation of Energy
Draw
something
falling off the
cliff. Fill in
the values
for the PE &
KE at each
position
(start, ¼, ½,
¾, end).
Assume a
PE of 4000J
at the start
(LEFT).
PE=4000J
KE=
PE=
KE=
PE=
KE=
PE=
KE=
PE=
KE=
Machines
Principle of a machine
• conservation of energy concept:
work input = work output
• input F input d = output F output d
• (force  distance)input = (force  distance)output
How could this
demonstration become a
venture into the local
hospital?
Machines
Machine—a device for multiplying force or changing
the direction of force.
No machine can
• put out more energy than is put into it.
• create energy; it can only transfer or transform
energy.
Simple Machines Song
Machines
Equation:
work input = work output
(force  distance)input = (force  distance)output
Example: a simple lever
small input force over a long distance  large output
force over a short distance
The Lever, a
Simple
Machine
Components of a Lever System
• Fulcrum: axis of rotation of the system.
• Load: the Fresistance
• Effort: the Fapplied
• Effort Arm – The distance from an applied force to the
fulcrum. (The moment arm of the force.)
• Resistance Arm – The distance from the resistance to the
fulcrum. (The moment arm of the resistance.)
First Class Lever
effort
load
force
arm
resistance arm
fulcrum
First Class: The fulcrum is between the effort & the load…
Second Class Lever
force arm
resistance arm
load
effort
fulcrum
Second Class: The load is between the effort and the fulcrum.
Third Class Lever
resistance arm
force
arm
load
applied force
fulcrum
Third Class: The effort is between the load and the fulcrum.
Classes of Levers
How to keep the classes straight:
1. First Class: The fulcrum is between the effort
& the load…
2. Second Class: The load is between the effort
and the fulcrum.
3. Third Class: The effort is between the load
and the fulcrum.
Notice how the letters form f, l, e…
…FL e: “florida education” in that order (1 2 3)
Torque Produced in Lever Systems
•
Two Torques
What does this mean?
1. Torque produced by the applied force
2. Torque produced by the resistance
•
The direction in which a lever system moves
is dependent on the relative lengths of the
force and resistance arms as well as the
At the
end of the day…the
of Work a lever can
magnitudes
of force amount
and resistance.
do remains the same…but one can use them to
multiply the d & the F; just remember, what you gain
in F (lesser F [easier]) you lose in d (longer d)
Test what happens to F & d as fulcrum
changes…
.
At the end of the day…the amount of Work a lever can do remains the
same…but one can use them to multiply the d & the F; just remember,
what you gain in F (lesser F [easier]) you lose in d (longer d)
Classify: which lever class
Classify: which lever class
Classify: which lever class
Classify: which lever class
Classify: which lever class
Classify: which lever class
Mechanical Advantage
This is the effectiveness of a lever at moving a
resistance. It is a calculated value:
Mechanical
Advantage
=
ForceArm
Re sis tan ceArm
Because of their different configurations, the
mechanical advantage of a first class lever can favor
the force or resistance depending on the placement
of the fulcrum. A second class lever always favors
the force arm. A third class lever always favors the
resistance arm.
applied force
resistance
force
arm
resistance arm
fulcrum
The fulcrum in a first class lever system can often vary in position to favor the
force arm or the resistance arm.
force arm
resistance arm
resistance
applied
force
fulcrum
In a second class lever system, the mechanical advantage favors the force arm.
(The force arm will always be longer.)
resistance arm
force
arm
resistance
applied force
fulcrum
The mechanical advantage of a third class lever system favors the resistance arm.
(The resistance arm is always longer.)
Machines
CHECK YOUR NEIGHBOR
In an ideal pulley system, a woman lifts a 100-N crate by pulling a
rope downward with a force of 25 N. For every one-meter length
of rope she pulls downward, the crate rises
A.
B.
C.
D.
50 centimeters.
45 centimeters.
25 centimeters.
None of the above.
Machines
CHECK YOUR ANSWER
In an ideal pulley system, a woman lifts a 100-N crate by pulling a
rope downward with a force of 25 N. For every one-meter length
of rope she pulls downward, the crate rises
A.
B.
C.
D.
50 centimeters.
45 centimeters.
25 centimeters.
None of the above.
Explanation:
Work in = work out; Fd in = Fd out.
One-fourth of 1 m = 25 cm.
Efficiency
Efficiency
• how effective a device transforms or transfers useful
energy
• equation: Efficiency  work done  100%
energy used
a machinewith low efficiency  greater amount of
energy wasted as heat
Some energy is always dissipated as heat, which means
that no machine is ever 100% efficient.
Efficiency
CHECK YOUR NEIGHBOR
A certain machine is 30% efficient. This means the machine will
convert
A.
B.
C.
D.
30% of the energy input to useful work—70% of the energy input will
be wasted.
70% of the energy input to useful work—30% of the energy input will
be wasted.
As strange as it may seem, both of the above.
None of the above.
Efficiency
CHECK YOUR ANSWER
A certain machine is 30% efficient. This means the machine will
convert
A.
B.
C.
D.
30% of the energy input to useful work—70% of the energy input will
be wasted.
70% of the energy input to useful work—30% of the energy input will
be wasted.
As strange as it may seem, both of the above.
None of the above.
Sources of Energy
Energy sources
Sun
Examples:
• Sunlight evaporates water; water falls as rain; rain
flows into rivers and into generator turbines; then
back to the sea to repeat the cycle.
• Solar energy can transform into electricity by
photovoltaic cells.
• Solar energy indirectly produces wind that can power
turbines and generate electricity.