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Conceptual Physics
Fundamentals
Chapter 5:
MOMEMTUM AND ENERGY
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley
This lecture will help you
understand:
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Momentum
Impulse
Impulse Changes Momentum
Bouncing
Conservation of Momentum
Collisions
Energy
Work
Potential Energy
Work-Energy Theorem
Conservation of Energy
Power
Machines
Efficiency
Sources of Energy
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Momentum and Energy
“Human history becomes more and more a
race between education and catastrophe.”
—H. G. Wells
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley
Momentum
Momentum
• a property of moving things
• means inertia in motion
• more specifically, mass of an object multiplied by
its velocity
• in equation form: mass velocity
(momentum = mv)
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Momentum
example:
• A moving boulder has more
momentum than a stone rolling at
the same speed.
• A fast boulder has more momentum
than a slow boulder.
• A boulder at rest has no momentum.
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Momentum
CHECK YOUR NEIGHBOR
A moving object has
A.
B.
C.
D.
momentum.
energy.
speed.
all of the above
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Momentum
CHECK YOUR ANSWER
A moving object has
A.
B.
C.
D.
momentum.
energy.
speed.
all of the above
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Momentum
CHECK YOUR NEIGHBOR
When the speed of an object is doubled, its momentum
A.
B.
C.
D.
remains unchanged in accord with the conservation of
momentum.
doubles.
quadruples.
decreases.
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Momentum
CHECK YOUR ANSWER
When the speed of an object is doubled, its momentum
A.
B.
C.
D.
remains unchanged in accord with the conservation of
momentum.
doubles.
quadruples.
decreases.
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Impulse
Impulse
• product of force and time (force
• in equation form: impulse = Ft
time)
example:
• A brief force applied over a short time interval produces a
smaller change in momentum than the same force applied over
a longer time interval.
or
• If you push with the same force for twice the time, you impart
twice the impulse and produce twice the change in momentum.
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Impulse Changes Momentum
The greater the impulse exerted on
something, the greater the change in
momentum.
• in equation form: Ft = (mv)
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Impulse Changes Momentum
CHECK YOUR NEIGHBOR
When the force that produces an impulse acts for twice as
much time, the impulse is
A.
B.
C.
D.
not changed.
doubled.
quadrupled.
halved.
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Impulse Changes Momentum
CHECK YOUR ANSWER
When the force that produces an impulse acts for twice as
much time, the impulse is
A.
B.
C.
D.
not changed.
doubled.
quadrupled.
halved.
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Impulse Changes Momentum
• Case 1: increasing momentum
– apply the greatest force for as long as possible and
you extend the time of contact
– force can vary throughout the duration of contact
examples:
• golfer swings a club and follows through
• baseball player hits a ball and follows through
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Impulse Changes Momentum
CHECK YOUR NEIGHBOR
A cannonball shot from a cannon with a long barrel will
emerge with greater speed because the cannonball
receives a greater
A.
B.
C.
D.
average force.
impulse.
both of the above
neither of the above
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Impulse Changes Momentum
CHECK YOUR ANSWER
A cannonball shot from a cannon with a long barrel will
emerge with greater speed because the cannonball
receives a greater
A.
B.
C.
D.
average force.
impulse.
both of the above
neither of the above
Explanation:
The force on the cannonball will be the same for a short- or long-barreled cannon.
The longer barrel provides for a longer time for the force to act, and therefore, a
greater impulse. (The long barrel also provides a longer distance for the force to
act, providing greater work and greater kinetic energy of the cannonball.)
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Impulse Changes Momentum
• Case 2: decreasing momentum over a long time
– extend the time during which momentum is
reduced
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Impulse Changes Momentum
CHECK YOUR NEIGHBOR
A fast-moving car hitting a haystack or a cement wall
produces vastly different results.
1. Do both experience the same change in momentum?
2. Do both experience the same impulse?
3. Do both experience the same force?
A.
B.
C.
D.
yes for all three
yes for 1 and 2
no for all three
no for 1 and 2
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Impulse Changes Momentum
CHECK YOUR ANSWER
A fast-moving car hitting a haystack or hitting a cement wall
produces vastly different results.
1. Do both experience the same change in momentum?
2. Do both experience the same impulse?
3. Do both experience the same force?
A.
B.
C.
D.
yes for all three
yes for 1 and 2
no for all three
no for 1 and 2
Explanation:
Although stopping the momentum is the same whether done slowly or
quickly, the force is vastly different. Be sure to distinguish between
momentum, impulse, and force.
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Impulse Changes Momentum
CHECK YOUR NEIGHBOR
When a dish falls, will the change in momentum be less if it
lands on a carpet than if it lands on a hard floor? (Careful!)
A.
B.
C.
D.
no, both are the same
yes, less if it lands on the carpet
no, less if it lands on a hard floor
no, more if it lands on a hard floor
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Impulse Changes Momentum
CHECK YOUR ANSWER
When a dish falls, will the change in momentum be less if it
lands on a carpet than if it lands on a hard floor? (Careful!)
A.
B.
C.
D.
no, both are the same
yes, less if it lands on the carpet
no, less if it lands on a hard floor
no, more if it lands on a hard floor
Explanation:
The momentum becomes zero in both cases, so both change by the same
amount. Although the momentum change and impulse are the same, the force is
less when the time of momentum change is extended. Be careful to distinguish
between force, impulse, and momentum.
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Impulse Changes Momentum
examples:
when a car is out of control, it is better to hit a
haystack than a concrete wall
physics reason: same impulse either way, but extension
of hitting time reduces the force
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Impulse Changes Momentum
example (continued):
in jumping, bend your knees when your feet make
contact with the ground because the extension of
time during your momentum decrease reduces the
force on you
in boxing, ride with the punch
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Impulse Changes Momentum
• Case 3: decreasing momentum over a short time
– short time interval produces large force
example: Karate expert splits a
stack of bricks by bringing her
arm and hand swiftly against
the bricks with considerable
momentum. Time of contact is
brief and force of impact is huge.
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Bouncing
Impulses are generally greater when objects
bounce.
example:
Catching a falling flower pot from a shelf with your
hands. You provide the impulse to reduce its
momentum to zero. If you throw the flower pot up
again, you provide an additional impulse. This “double
impulse” occurs when something bounces.
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Bouncing
Pelton wheel designed to “bounce” water when it
makes a U-turn when it impacts the curved
paddle
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Conservation of Momentum
Law of conservation of momentum:
In the absence of an external force, the
momentum of a system remains unchanged.
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Conservation of Momentum
examples:
• When a cannon is fired, the force on cannonball
inside the cannon barrel is equal and opposite to
the force of the cannonball on the cannon.
• The cannonball gains momentum, while the
cannon gains an equal amount of momentum in
the opposite direction—the cannon recoils.
When no external force is present, no external
impulse is present, and no change in
momentum is possible.
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Conservation of Momentum
examples (continued):
• Internal molecular forces within a baseball come in
pairs, cancel one another out, and have no effect
on the momentum of the ball.
• Molecular forces within a baseball have no effect
on its momentum.
• Pushing against a car’s dashboard has no effect
on its momentum.
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Collisions
For all collisions in the absence of external
forces
• net momentum before collision equals net
momentum after collision
• in equation form:
(net mv)before = (net mv)after
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Collisions
Collisions
• elastic collision
– occurs when colliding objects rebound without
lasting deformation or any generation of heat
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Collisions
Collisions
• inelastic collision
– occurs when colliding objects result in
deformation and/or the generation of heat
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Collisions
example of elastic collision:
single car moving at 10 m/s collides with another car of
the same mass, m, at rest
From the conservation of momentum,
(net mv)before = (net mv)after
(m 10)before = (2m V)after
V = 5 m/s
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Collisions
CHECK YOUR NEIGHBOR
Freight car A is moving toward identical freight car B that is
at rest. When they collide, both freight cars couple
together. Compared with the initial speed of freight car A,
the speed of the coupled freight cars is
A.
B.
C.
D.
the same.
half.
twice.
none of the above
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Collisions
CHECK YOUR ANSWER
Freight car A is moving toward identical freight car B that is
at rest. When they collide, both freight cars couple
together. Compared with the initial speed of freight car A,
the speed of the coupled freight cars is
A.
B.
C.
D.
the same.
half.
twice.
none of the above
Explanation:
After the collision, the mass of the moving freight cars has doubled. Can you see
that their speed is half the initial velocity of freight car A?
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Momemtum Video
Conservation of momentum in space
http://www.youtube.com/watch?v=4IYDb6K5
UF8
Physics class room explanation
http://www.physicsclassroom.com/class/mo
mentum/u4l2b.cfm
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Energy
A combination of energy and matter make
up the universe.
Energy
• mover of substances
• both a thing and a process
• observed when it is being transferred or being
transformed
• a conserved quantity
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Energy
• property of a system that enables it to do work
• anything that can be turned into heat
example: electromagnetic waves from the Sun
Matter
• substance we can see, smell, and feel
• occupies space
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Work
Work
• involves force and distance
• is force distance
• in equation form: W = Fd
Two things occur whenever work is done:
• application of force
• movement of something by that force
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Work
CHECK YOUR NEIGHBOR
If you push against a stationary brick wall for several
minutes, you do no work
A.
B.
C.
D.
on the wall.
at all.
both of the above
none of the above
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Work
CHECK YOUR ANSWER
If you push against a stationary brick wall for several
minutes, you do no work
A.
B.
C.
D.
on the wall.
at all.
both of the above
none of the above
Explanation:
You may do work on your muscles, but not on the wall.
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Work
examples:
• twice as much work is done in lifting 2 loads 1- story
high versus lifting 1 load the same vertical distance
reason: force needed to lift twice the load is twice as much
• twice as much work is done in lifting a load 2 stories
instead of 1 story
reason: distance is twice as great
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Work
example:
• a weightlifter raising a barbell from
the floor does work on the barbell
Unit of work:
Newton-meter (Nm)
or Joule (J)
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Work
CHECK YOUR NEIGHBOR
Work is done in lifting a barbell. How much work is done in
lifting a barbell that is twice as heavy the same distance?
A.
B.
C.
D.
twice as much
half as much
the same
depends on the speed of the lift
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Work
CHECK YOUR ANSWER
Work is done in lifting a barbell. How much work is done in
lifting a barbell that is twice as heavy 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.
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Work
CHECK YOUR NEIGHBOR
You do work when pushing a cart with a constant force. If
you push the cart twice as far, then the work you do is
A.
B.
C.
D.
less than twice as much.
twice as much.
more than twice as much.
zero.
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Work
CHECK YOUR ANSWER
You do work when pushing a cart with a constant force. If
you push the cart twice as far, then the work you do is
A.
B.
C.
D.
less than twice as much.
twice as much.
more than twice as much.
zero.
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Potential Energy
Potential Energy
• stored energy held in readiness with a potential
for doing work
example:
• a stretched bow has stored energy that can do work
on an arrow
• a stretched rubber band of a slingshot has stored
energy and is capable of doing work
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Potential Energy
Gravitational potential energy
• potential energy due to elevated position
example:
• water in an elevated reservoir
• raised ram of a pile driver
• equal to the work done (force required to move it
upward the vertical distance moved against
gravity) in lifting it
• in equation form: PE = mgh
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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
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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:
If the car were twice as heavy, its increase in potential energy
would be twice as great.
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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
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Kinetic Energy
Kinetic Energy
• energy of motion
• depends on the mass of the object and its speed
• include the proportional constant 1/2 and KE =
1/2 mass speed squared
• If object speed is doubled
kinetic energy is
quadrupled
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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
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Kinetic Energy
CHECK YOUR ANSWER
Must a car with momentum have kinetic energy?
A.
B.
C.
D.
yes, due to motion alone
yes, when momentum 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.
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Kinetic Energy
Kinetic energy and work of a moving object
• equal to the work required to bring it from rest to
that speed, or the work the object can do while
being brought to rest
• in equation form: net force distance =
kinetic energy, or Fd = 1/2 mv2
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Work-Energy Theorem
Work-energy theorem
• gain or reduction of energy is the result of work
• in equation form: work = change in kinetic
energy (W = KE)
• doubling speed of an object requires 4 times the
work
• also applies to changes in potential energy
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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)
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Work-Energy Theorem
CHECK YOUR NEIGHBOR
Consider a problem that asks for the distance of a fastmoving crate sliding across a factory floor and then 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.
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Work-Energy Theorem
CHECK YOUR ANSWER
Consider a problem that asks for the distance of a fastmoving crate sliding across a factory floor and then 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.
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Work-Energy Theorem
CHECK YOUR NEIGHBOR
The work done in bringing 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
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Work-Energy Theorem
CHECK YOUR ANSWER
The work done in bringing 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.
Explanation:
Twice the speed means four times the kinetic energy and four
times the stopping distance.
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Conservation of Energy
Law of conservation of energy
• Energy cannot be created or destroyed; it may
be transformed from one form into another, but
the total amount of energy never changes.
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Conservation of Energy
example: energy transforms without net loss or net
gain in the operation of a pile driver
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Conservation of Energy
A situation to ponder…
Consider the system of a bow and arrow.
In drawing the bow, we do work on the
system and give it potential energy. When
the bowstring is released, most of the
potential energy is transferred to the arrow
as kinetic energy, and some as heat to the
bow.
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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 are mysteriously missing.
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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 are 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.
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Kinetic Energy and Momentum
Compared
Similarities between momentum and kinetic
energy
• both are properties of moving things
Difference between momentum and kinetic
energy
• momentum is a vector quantity and therefore is
directional and can be cancelled
• kinetic energy is a scalar quantity and can never
be cancelled
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Kinetic Energy and Momentum
Compared
• velocity dependence
– momentum depends on velocity
– kinetic energy depends on the square of
velocity
example: An object moving with twice the velocity of
another with the same mass, has twice the
momentum but 4 times the kinetic energy.
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Power
Power
• measure of how fast work is done
• in equation form:
Power = work done
time interval
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Power
example:
• A worker uses more power running up the stairs than
climbing the same stairs slowly.
• Twice the power of an engine can do twice the work
of one engine in the same amount of time, or twice
the work of one engine in half the time or at a rate at
which energy is changed from one form to another.
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Power
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
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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.
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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.
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Video
Energy, Work and Power
http://www.youtube.com/watch?v=pDK2p1QbPKQ&feature
=related
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Machines
Machine
• device 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
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Machines
Principle of a machine
• conservation of energy concept:
work input = work output
• input force input distance =
output force output distance
• (force distance)input = (force distance)output
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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
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Machines
• pulley
– operates like a lever with equal arms—
changes the direction of the input force
example:
this pulley arrangement can allow a load to be
lifted with half the input force
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Machines
• operates as a system of pulleys (block and tackle)
• multiplies force
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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
1-meter length of rope she pulls downward, the crate rises
A.
B.
C.
D.
50 centimeters.
45 centimeters.
25 centimeters.
none of the above
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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
1-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.
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Efficiency
Efficiency
• percentage of work put into a machine that is
converted into useful work output
• in equation form:
efficiency = useful energy output
total energy input
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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.
both of the above
none of the above
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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.
both of the above
none of the above
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Sources of Energy
Sources of energy
Sun
example:
• Sunlight evaporates water; water falls as rain; rain
flows into rivers and into generator turbines; then
back to the sea to repeat the cycle.
• Sunlight can transform into electricity by
photovoltaic cells.
• Wind power turns generator turbines.
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley
Sources of Energy
Concentrated energy
• nuclear power
– stored in uranium and plutonium
– byproduct is geothermal energy
• held in underground reservoirs of hot water to
provide steam that can drive turbogenerators
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley
Sources of Energy
• dry-rock geothermal power is a producer of
electricity
– Water is put into cavities in deep, dry, hot
rock. Water turns to steam and reaches a
turbine, at the surface. After exiting the
turbine, it is returned to the cavity for reuse.
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley