Transcript Work and Energy Unit Chapter 9

Work and Energy Unit
Chapter 9
Energy can change from one
form to another without a net
loss or gain.
LAW OF CONSERVATION OF ENERGY!!!
(You will learn to identify these
transformations)
9.1 Work
think!
Suppose that you apply a 60-N horizontal force to a 32 kg
package, which pushes it 4 meters across a mailroom floor.
How much work do you do on the package?
9.1 Work
think!
Suppose that you apply a 60-N horizontal force to a 32-kg
package, which pushes it 4 meters across a mailroom floor.
How much work do you do on the package?
Answer:
W = Fd = 60 N × 4 m = 240 J
9.7 Conservation of Energy
Total Mechanical
Energy
Total Mechanical
Energy
Same energy
transformation applies
Non-mechanical
Energy (dissipated)
The 2 J of heat can be called nonuseful work (work that is not part of the
object’s total mechanical energy).
Dissipated energy (DE) is amount of energy
transferred away from the total mechanical
energy. More DE means less KE, which
reduces TME, which means less speed!
10 J of PE does 8 J
useful work on the
arrow and 2 J of
non-useful work on
the molecules that
compose the bow
and string and
arrow. The arrow
has 8 J of KE as a
result.
9.7 Conservation of Energy
Total Mechanical
Energy
Total Mechanical
Energy
Non-mechanical
Energy (dissipated)
The 2 J of heat can be called nonuseful work (work that is not part of the
object’s total mechanical energy).
Dissipated energy (DE) is amount of energy
transferred away from the total mechanical
energy. More DE means less KE, which
reduces TME, which means less speed!
Energy
I can define
energy
• The ability to do work or
cause change
• Can be transferred into
other forms
• Is conserved (can neither
be created nor
destroyed)
• SI Unit is Joules
• Force times distance the
force is applied (W = Fd)
Work
I can define work. • When work is done, energy
is transferred, stored or
Positive work?
used
Negative work?
• SI Unit is Joules
• Positive work is work done
in the direction of motion.
• Negative work does work
against the object (in a
direction opposite of
motion)
Watch the transfer of KE and PE.
What happens to the PE when the skier moves down the hill?
What happens to the KE and TME when the skier travels over the
unpacked snow?
What work is done?
6.1 Work
= force × distance
a) Did the weightlifter do work on the
barbell and weights?
b) Is the weightlifter currently doing
work on the barbell and weights?
c) Explain two ways that the work done
by the weightlifter be increased.
1.
2.
9.1 Work
= force × distance
Did the weightlifter do work on the barbell and
weights?
•Yes, when he first lifted them above his head.
Is the weightlifter currently doing work on the
barbell and weights?
No, the barbell and weights are not moving.
•Explain two ways that the work done by the
weightlifter be increased.
1) Increase the weight on the ends of the barbell
2) Increase the distance over which the weightlifter
pushes the barbell and weights.
9.1 Work
While the weight lifter is holding a
barbell over his head, he may get
really tired, but he does no work on
the barbell.
Work may be done on the muscles
by stretching and squeezing them,
but this work is not done on the
barbell.
When the weight lifter raises the
barbell, he is doing work on it.
9.1 Work
When the
object
moves.
When is work done on an object?
When is work not done on an object?
When the object
does not move.
Ramp Work: Force and Distance
• To test the relationship between force and
distance when using a ramp of different
lengths
• Use the equation W = Fd
9.1 Work
Work has the same units as energy
Joules
Newton x meter
J
Nxm
•One joule (J) of work is done when a
force of 1 N is exerted over a distance
of 1 m (lifting an apple over your
head).
Kinetic
Energy
What is kinetic energy?
What are the forms of KE?
• The energy of motion
• KE = ½m x v2
• Different forms of KE
(mechanical, electrical,
thermal, electromagnetic
or light)
Kinetic Energy
KE increases
with mass
KE
increases
with speed
WIND ENERGY
• Atmospheric pressure differences cause
air particles to move.
SOUND ENERGY
• Energy caused by compression of air
particles.
ELECTRICAL ENERGY
• Energy of moving charged particles.
THERMAL ENERGY
• The energy of moving and vibrating
molecules
• Sometimes called heat.
LIGHT or
RADIANT ENERGY
• Energy that travels in waves as
electromagnetic radiation and/or as
photons.
9.5 Kinetic Energy
When you throw a ball, you do work on it to give it speed as
it leaves your hand. The moving ball can then hit something
and push it, doing work on what it hits.
WORK
9.5 Kinetic Energy
If the speed of an object is doubled, its kinetic
energy is quadrupled (22 = 4).
• It takes four times the work to double the speed.
• An object moving twice as fast takes four times as much
work to stop and will take four times as much distance to
stop.
Kinetic Energy
• How does KE increase or decrease?
Increase or decrease the velocity or the
mass!!!!
Double the velocity, Quadruple the KE!!!!!
Prove it: Calculate the KE of a 2500 kg car traveling at
20 m/s and at 40 m/s
• KE at 20 m/s
• (500,000 J)
KE at 40 m/s
(2,000,000 J)
Kinetic Energy
More mass, same speed, more KE.
Double the mass, double the KE
Prove it: Calculate the KE of a 100 kg cart and a 200 kg
cart, each traveling at 15 m/s
• 100 kg cart at 15 m/s
m/s
• (11,250 J)
200 kg cart at 15
(22,500 J)
• Stored energy or the
energy of position
Potential Energy
What is potential • Gravitational PE is based
energy?
on height and mass
• Gravitational PE is mass
How does GPE
x gravity x height (GPE
change?
= mgh)
• Increases in height
cause increases in
stored energy
9.4 Potential Energy
Gravitational Potential Energy
•Energy is stored in an object as the result of increasing its
height.
•Work is required to elevate objects against Earth’s gravity.
•Example: Water in an elevated reservoir and the raised ram
of a pile driver have gravitational potential energy.
9.4 Potential Energy
The amount of gravitational potential energy possessed by
an elevated object is equal to the work done against gravity
to lift it.
PE = mgh
What is the gravitational PE of a 10.0 kg object at 4.00 m
above the ground?
mg is weight (in newtons) [mass (kg) x gravity (m/s2)]
10 kg x 9.8 m/s2 x 4 m = 392 J
9.4 Potential Energy
The potential energy of the 100-N boulder with respect to the ground below
is 200 J in each case.
a. The boulder is lifted with 100 N of force.
9.4 Potential Energy
The potential energy of the 100-N boulder with respect to the ground below
is 200 J in each case.
a. The boulder is lifted with 100 N of force.
b. The boulder is pushed up the 4-m incline with 50 N of force.
9.4 Potential Energy
The potential energy of the 100-N boulder with respect to the ground below
is 200 J in each case.
a. The boulder is lifted with 100 N of force.
b. The boulder is pushed up the 4-m incline with 50 N of force.
c. The boulder is lifted with 100 N of force up each 0.5-m stair.
9.4 Potential Energy
think!
You lift a 100-N boulder 1 m.
a. How much work is done on the boulder?
b. What power is expended if you lift the boulder in a time of 2 s?
c. What is the gravitational potential energy of the boulder in the lifted
position?
• Other forms of PE
(Chemical PE, Elastic
Other forms of PE
PE, Electric PE,
What are the
Magnetic PE, Nuclear
forms of potential
PE)
energy?
• Changes in position in a
force field changes the
PE (gravitational fields,
magnetic fields and
electric fields)
9.4 Potential Energy
Elastic Potential Energy—potential to do work
•Energy stored in a stretched or compressed spring or
material.
•When a bow is drawn back, energy is stored and the bow can
do work on the arrow.
•These types of potential energy are elastic potential energy.
CHEMICAL POTENTIAL
ENERGY
• Energy due to the bond position between
molecules (stored during bonding).
• Potential chemical energy is released from
chemical reactions (burning, for example).
• Fuels, Food, Batteries, for example.
9.4 Potential Energy
Name three examples of
potential energy.
Difference between kinetic
energy and potential energy
Kinetic energy
Potential energy
The energy of
motion
The energy of
position or stored
energy
Mechanical
Energy
What is
mechanical
energy?
• The sum of the KE and
PE in a system: (total
ME = KE + PE)
• Describes energy
associated with the
motion of objects
• The KE and GPE are
conserved for moving
objects (neglecting
friction, drag, vibrations
and sound)
Mechanical Energy = PE + KE
• The total mechanical energy = 100 J
100 J = 100 J PE + 0 J KE
100 J = 50 J PE + 50 J KE
100 J = 0 J PE + 100 J KE
Non-Mechanical
Energy
What is nonmechanical
energy?
• Energy not associated
with the motion of objects
• Typical examples are
vibrations, sound and
heat
• Referred to as dissipated
energy or waste energy
• Can be “observed” at the
molecular level
• Path of energy transfer
that reduces the KE of
the object
Starter 1-10
•
•
•
•
Energy transfers
Energy transfers into different forms
PE transfers to KE
When you fall, your PE decreases and your
KE increases
• Half way down PE = KE
• As the person falls, the PE and KE flip
• Energy is not destroyed (start and end with
10,000 J)
Starter 1-10
•
•
•
•
•
•
•
Gravity is involved (GPE-- gravitational PE)
Max KE can never exceed the Max PE
As PE decreases, KE increases
PE stored is used when object is in motion
No energy is “lost” from PE to KE
The farther the diver falls, the greater the KE
Energy transforms from PE to KE from point
A to point B
Starter 1-10
• As the KE increases, the PE decreases
• As the diver hits the bucket, all PE has been
transferred to KE
• Work produces energy
• Energy changes throughout the dive
• At the top of the platform, all GPE and no KE
• The diver always possesses 10,000 J of
energy (energy is conserved)
• Inverse relationship between PE and KE
Starter 1-10
• Energy is constantly changing as the diver
falls
• No energy is lost during the dive; it transfers
from PE to KE
• All PE has been transferred to KE
• The PE decreases
• 2500 J change in PE or KE
• As the PE decreases, the KE increase
(gravitational PE)
• PE is inversely related to KE
Total Mechanical Energy
• Total mechanical energy = kinetic energy + potential
energy
• TME = KE + PE
• 100 J = 0 J + 100 J
• At rest, no KE, no motion
• 100 J = 50 J + 50 J
• In motion, 50 J of PE transferred, object now has 50 J of
KE.
• 100 J = 100 J + 0 J
• In motion, no potential energy (100 J transferred to KE)
• In each case, the total mechanical energy is the same.
As the PE decreases, the KE increases.
Indicate where:
•KE is at a minimum and maximum
•GPE is at a minimum and maximum
•The speed is greatest
•The speed is least
•Energy is being stored and released
1. Explain how energy
transforms and is
conserved as the
pendulum swings back
and forth
2. What happens as
the KE increases?
3. What happens as
the GPE increases?
Positions 1 and 5 are at
the same height
KE min
KE min
PE max
PE max
V = 0 m/s
V = 0 m/s
transformation
of PE to KE
KE max
(release)
PE min
V = maximum
transformation
of KE to PE
(storage)
Analyzing KE and PE
farthest
Distance
(from
motion
detector)
closest
time
Power
What is power?
• The rate at which energy
is transferred or work is
done (work per second)
• SI Unit is Watts
(Joules/second)
• The faster the energy is
used, the greater the
power
• More powerful if
– more work is done in
same time
– same work is done in less
time
9.2 Power
Jet engine vs. lawn mower engine
Both receive ½ gallon of fuel (same energy, same
work)
•A high-power jet engine does work rapidly, uses ½ gallon in 1
second.
•The low-powered lawn mower engine does work slowly, using ½
gallon in 30 minutes.
vs.
9.2 Power
P = w/t
Power is the rate at which work is done.
The unit of power is the joule per second, also known as
the watt.
One watt (W) of power is expended when one joule of
work is done in one second.
One kilowatt (kW) equals 1000 watts.
One megawatt (MW) equals one million watts.
Power
• When you run 3 km rather than
walk, you use the energy more
quickly because your body
demands more energy per unit
time.
• When you compare the amount of
energy required to operate an
electric dryer vs. a laptop
computer, the electric dryer
demands more energy per unit
time.
• More energy per unit time means
more power is required!
Needs
5500 J/s
Needs 50
J/s
Power
100 W incandescent
light bulb
How much electrical
energy per second?
100 joules per
second.
Power vs. Work
When carrying a load up some stairs, you do the
same amount of work whether you walk or run
up the stairs.
Whether you walk 3 km or run 3 km, you do the
same amount of work (your weight x distance),
burn roughly the same amount of calories, and
use the same amount of energy.
So what is power?
Power
• Consider a person climbing stairs.
• Name two ways that the person can double
their power when moving.
• Do twice the work in the same amount of time
(climb a second flight of stairs in the same
time)
• Do the same amount of work in half the time
(climb one flight of stairs in half the time).
9.2 Power
The three main engines of the
space shuttle can develop
33,000 MW of power when
fuel is burned at the
enormous rate of 3400 kg/s.
9.2 Power
think!
If a forklift is replaced with a new forklift that has twice the
power, how much greater a load can it lift in the same amount
of time? If it lifts the same load, how much faster can it
operate?
9.2 Power
think!
If a forklift is replaced with a new forklift that has twice the
power, how much greater a load can it lift in the same amount
of time? If it lifts the same load, how much faster can it
operate?
Answer:
The forklift that delivers twice the power will lift twice the load
in the same time, or the same load in half the time.
Role of friction and drag in work
• Does work against the
moving object (negative
work in opposite direction
of motion)
• Or it takes work (energy)
to overcome friction or
drag
Work – Energy
Theorem
What is the
relationship between
work and kinetic
energy (work-energy
theorem)?
• Work done changes the
energy. If a car has
34,000 J of KE, 34,000 J
of work was done on the
car to speed it up, and
braking will require
34,000 J of negative
work due to friction to
bring the car to rest
9.6 Work-Energy Theorem
Due to friction, energy is transferred both into the floor and
into the tire when the bicycle skids to a stop.
a. An infrared camera reveals the heated tire track on the
floor.
http://www.batesville.k12.in.us/physics/phy
net/mechanics/energy/braking_distance.ht
m
9.6 Work-Energy Theorem
Due to friction, energy is transferred both into the floor and
into the tire when the bicycle skids to a stop.
a. An infrared camera reveals the heated tire track on the
floor.
b. The warmth of the tire is also revealed.
kinetic energy is transformed into thermal energy, sound and
vibrations, which represent work done to slow the bike (Fd)
Work – Energy
Theorem
What is the
relationship between
work and kinetic
energy (work-energy
theorem)?
http://www.youtube.com/watch?v=Z_nHIBnfts
http://www.youtube.com/watch?v=WjvVbX
Dy20w
http://www.youtube.com/watch?v=0mR89s
T0YfA
http://www.youtube.com/watch?v=u_89NXUio9w
9.6 Work-Energy Theorem
The work-energy theorem states that whenever
work is done, energy changes.
Work = ∆KE
Work equals the change in
kinetic energy.
Calculating Stopping Distance
• Fd = ½ mv2
• What is the stopping distance for a 650 kg
car that is traveling 5 m/s if 4,500 N of
braking force is applied?
• d = ½ mv2
F
• d = 1.8 m
• Calculate the stopping distance for the
same car that travels at 10 m/s.
• 7.2 m.
Calculating Stopping Distance
• Calculate the stopping distance for the
same car that travels at 10 m/s.
• 7.2 m.
• How does this stopping distance compare
with the stopping distance at 5 m/s?
• It is four times greater!
• Double the speed, quadruple the stopping
distance.
Calculate Stopping Distance
• Fd = ½ mv2
-Calculate the difference in stopping distance for a car that travels at 30 km/h
and the same car that travels 60 km/h. Assume that the mass of the car is
800 kg and the braking force is 5000 N. Show your work and analyze your
results. (Note: you must first convert km/h to m/s)
How does speed influence stopping distance?
9.6 Work-Energy Theorem
A car moving at twice the speed of another has four times as
much kinetic energy, and will require four times as much work
to stop.
The frictional force is nearly the same for both cars, so the
faster one takes four times as much distance to stop.
Kinetic energy depends on speed squared.
9.6 Work-Energy Theorem
Typical stopping distances for cars equipped with
antilock brakes traveling at various speeds. The work
done to stop the car is friction force × distance of
slide.
9.6 Work-Energy Theorem
Typical stopping distances for cars equipped with
antilock brakes traveling at various speeds. The work
done to stop the car is friction force × distance of
slide.
9.6 Work-Energy Theorem
Typical stopping distances for cars equipped with
antilock brakes traveling at various speeds. The work
done to stop the car is friction force × distance of
slide.
9.6 Work-Energy Theorem
think!
When the brakes of a car are locked, the car skids to a stop.
How much farther will the car skid if it’s moving 3 times as
fast?
9.6 Work-Energy Theorem
think!
When the brakes of a car are locked, the car skids to a stop.
How much farther will the car skid if it’s moving 3 times as
fast?
Answer:
Nine times farther. The car has nine times as much kinetic
energy when it travels three times as fast:
9.6 Work-Energy Theorem
For moving objects such as cars:
The more kinetic energy it has, the more work is required to
stop it.
Twice as much kinetic energy means twice as much work.
Brakes do work on wheels (you do work by pushing the brake
pedal). When a car brakes, the work is the friction force
(supplied by the brakes) multiplied by the distance over which
the friction force acts.
KE is transformed by work (friction) into thermal energy, sound
energy and larger-scale vibrations.
9.7 Conservation of Energy
The law of conservation of energy states that energy
cannot be created or destroyed. It can be
transformed from one form into another, but the
total amount of energy never changes.
For any system in its entirety—as simple
as a swinging pendulum or as complex as
an exploding galaxy—there is one quantity
that does not change: energy.
Energy may change form, but the total
energy stays the same.
9.7 Conservation of Energy
When energy is transformed, it is conserved, meaning that it
will change form without losing its original amount of energy.
9.7 Conservation of Energy
When the woman leaps from the
burning building, the sum of her PE
and KE remains constant at each
successive position all the way down
to the ground.
9.7 Conservation of Energy
Elastic potential energy
will become the kinetic
energy of the arrow
when the bow does
work on the arrow.
As you draw back the arrow in a bow, you
do work stretching the bow.
The bow then has potential energy.
When released, the arrow has kinetic
energy equal to this potential energy.
It delivers this energy to its target.
9.7 Conservation of Energy
Everywhere along the path of the pendulum bob, the sum of
PE and KE is the same. Because of the work done against
friction, this energy will eventually be transformed into heat.
Non-useful work can also be called non-useful energy!
9.7 Conservation of Energy
• Why does a tennis ball eventually stop
bouncing?
• Eventually, all of the total mechanical energy is
transformed into non-useful energy (heat,
sound, movement of fibers)
50 J
PE
New height less than before means less PE
stored 35 J PE
20 J PE
50 J
KE
Bounce!
35 J KE
Bounce!
20 J KE
(bounce and so
on!)
Slides showing transformation of
KE and PE
• Source:
http://www.physicsclassroom.com/mmedia
/index.cfm
Watch how KE and gravitational PE
transform
Where is the KE at the maximum?
Where is the PE at the maximum?
How is PE stored?
Watch the change in height vs. the
change in speed!
How does the change in height affect KE and PE?
What happens to KE and TME when the
brakes are applied? What work is being
done?
Watch the transfer of KE and PE.
What happens to the PE when the skier moves down the hill?
What happens to the KE and TME when the skier travels over the
unpacked snow?
What work is done?
Same work, more force, less
displacement (from left to right)