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Chapter 4 Lecture
Conceptual
Integrated Science
Second Edition
Momentum
and Energy
© 2013 Pearson Education, Inc.
This lecture will help you understand:
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Momentum
Impulse
Impulse–Momentum Relationship
Conservation of Momentum
Work
Energy
Power
Potential Energy
Kinetic Energy
The Work–Energy Theorem
Kinetic Energy and Momentum
Conservation of Energy
Machines
Efficiency
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Momentum
Momentum is inertia in motion, defined as the
product of mass and velocity:
Momentum = mass x velocity
p=mxv
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Momentum
Momentum = mass  velocity
or
Momentum = mass  speed (when direction is unimportant)
Momentum = mv
•
mass or high velocity  high momentum
High mass and high velocity  higher momentum
•
•
Low mass or low velocity  low momentum
Low mass and low velocity  lower momentum
•
High
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Momentum
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Momentum
CHECK YOUR NEIGHBOR
A moving object has
A.
B.
C.
D.
momentum.
energy.
speed.
all of the above
Explain your answer to your neighbor.
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Momentum
CHECK YOUR NEIGHBOR
When the speed of an object is doubled, its
momentum
A. remains unchanged in accord with the
conservation of momentum.
B. doubles.
C. quadruples.
D. decreases.
Explain your answer to your neighbor.
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Impulse
• Impulse is the product of force and contact time.
– Equation for impulse:
Impulse = force  time = Ft
• Great force for long time  large impulse
• Same force for short time  smaller impulse
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Impulse
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.
increased by four times.
decreased by half.
Explain your answer to your neighbor.
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Impulse–Momentum Relationship
• The greater the impulse exerted on something,
the greater will be its change in momentum.
• The change in momentum of an object is equal
to the force applied to it multiplied by the time
interval during which the force is applied.
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Impulse–Momentum Relationship
• Equation:
Impulse = change in momentum
or
Force  time =  momentum
• Greater force, greater change in
velocity  greater change in momentum
• Same force for short time  smaller change in momentum
• Same force for longer
time  more change in
momentum
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Impulse–Momentum Relationship
• Impulse may be viewed as causing momentum
change, or momentum change may be viewed
as causing impulse.
• It doesn’t matter which way you think about it, as
long as you know that impulse and change of
momentum are always linked.
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Impulse–Momentum Relationship
• Cases of momentum changes
– Increasing momentum: Apply the greatest
force for the longest time (impulse) to produce
the maximum increase in momentum.
Examples:
• Long-range cannons have long barrels for
maximum range.
• A golfer follows through while teeing off.
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Impulse–Momentum Relationship
CHECK YOUR NEIGHBOR
Compared to a cannonball shot from a cannon
with a short barrel, a cannonball shot from a
cannon with a long barrel emerges with greater
speed because the cannonball receives a greater
A.
B.
C.
D.
average force.
impulse.
both of the above
neither of the above
Explain your answer to your neighbor.
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Impulse–Momentum Relationship
• Cases of momentum changes (continued)
– Decreasing momentum: The impulse with the
longer time that decreases momentum has a
smaller force.
Examples:
• Driving into a haystack versus a brick wall
• Jumping into a safety net versus onto solid
ground
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Impulse–Momentum Relationship
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Impulse–Momentum Relationship
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Impulse–Momentum Relationship
• By hitting the haystack instead of a wall, you
extend the time of contact.
• The longer contact time therefore provides you
with a lesser force acting on you.
• The reverse is also true.
• Short contact time gives you a higher force.
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Impulse–Momentum Relationship
• Whether you hit the wall or the haystack, your
momentum will be decreased by the same
amount.
• This means that the impulse required to stop you
is the same.
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Impulse–Momentum Relationship
CHECK YOUR NEIGHBOR
A fast-moving car produces vastly different results
when it hits a haystack than when it hits a cement
wall. But, in both cases, the car experiences
A.
B.
C.
D.
the same change in momentum.
the same impulse.
the same force.
both the same change in momentum and the
same impulse.
Explain your answer to your neighbor.
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Impulse–Momentum Relationship
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
Explain your answer to your neighbor.
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Impulse–Momentum Relationship in Sports
• When the boxer
moves away (rides
the punch), he
extends the time and
diminishes the force.
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Impulse–Momentum Relationship in Sports
• If the boxer moves
into the punch, the
time is reduced and
he must withstand a
greater force
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Impulse–Momentum Relationship in Sports
• Imparting a large
impulse to the bricks
in a short time
produces
considerable force.
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Conservation of Momentum
• In every case, the momentum of a system
cannot change unless it is acted on by external
forces.
• A system has the same momentum both before
and after the interaction occurs. When the
momentum does not change, we say it is
conserved.
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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.
– Equation form:
(Total momentum)before = (Total momentum)after
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Conservation of Momentum
• The momentum before firing is zero
• After firing, the net momentum is still zero
– Because the momentum of the cannon is
equal and opposite to the momentum of the
cannonball
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Conservation of Momentum
• A) external force acts
on the 8 ball,
increasing its p
• B) external force acts
on the cue-ball, and
its p decreases
• C) no external force
acts on the cue-ballplus-8-ball, and the p
is conserved (it’s just
transferred)
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Conservation of Momentum
• Collisions
– When objects collide in the absence of
external forces,
Net momentum before collision = Net momentum after collision
Examples:
• Elastic collisions
• Inelastic collisions
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Conservation of Momentum
• An elastic collision is defined as a collision in
which objects collide without permanent
deformation or the generation of heat.
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Conservation of Momentum
• Moving ball A strikes ball B, which was initially at
rest.
• Ball A comes to rest, and ball B moves away with
a velocity equal to the initial velocity of ball A.
• Momentum is transferred from ball A to ball B.
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Conservation of Momentum
• An inelastic collision is a collision in which
colliding objects don’t rebound, but become
tangled or coupled together, generating heat.
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Conservation of Momentum
CHECK YOUR NEIGHBOR
Freight car A is moving toward identical freight car
B, which is at rest. When the cars collide, they
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
Explain your answer to your neighbor.
© 2013 Pearson Education, Inc.
Work
• Work
– is defined as the product of the force exerted on an
object and the distance the object moves (in the same
direction as the force).
– is done only when a force succeeds in moving the
body it acts upon.
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Work
• Two things enter where
work is done:
– Application of force
– Movement of something by
that force
• The work done on the
object is the average force
multiplied by the distance
through which the object is
moved.
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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
Explain your answer to your neighbor.
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Work
• The quantity of work done is equal to the amount
of force times the distance moved in the
direction in which the force acts.
–W=Fxd
• Units for work are in joules (J)
• Work falls into two categories:
– Work done against another force
– Work done to change the speed of an object
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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
It depends on the speed of the lift.
Explain your answer to your neighbor.
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Work
CHECK YOUR NEIGHBOR
You do work when you push 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.
Explain your answer to your neighbor.
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Energy
• Energy is defined as that which produces
changes in matter.
• The effects of energy are observed only when it
is being transferred from one place to another
or
transformed from one form into another.
• Unit for energy: joule
• Both work and energy are measured in joules.
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Power
• Power is a measure of how quickly work is done
or
the rate at which energy is changed from one
form into another.
• Equation for power:
Power = work done
time interval
Units for power: joule per second, or watt
(One watt = 1 joule of work per second)
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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.
Explain your answer to your neighbor.
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Potential Energy
• Potential energy is 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
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Potential Energy
• The amount of gravitational potential energy
possessed by an elevated object is equal to the
work done against gravity in raising it.
• The work done on an object equals the force
required to move it upward times 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 an
object through height h is the product mgh.
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Potential Energy
• Equation for gravitational potential energy:
PE = weight  height
or
PE = mgh
Examples of gravitational potential energy:
• Water in an elevated reservoir
• The elevated ram of a pile driver
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Potential Energy
• Which diagram has the greatest potential
energy?
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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
There is not enough information.
Explain your answer to your neighbor.
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Kinetic Energy
• Kinetic energy is the energy of a moving body.
• Equation for kinetic energy:
Kinetic energy = 1/2 mass  speed2
or
Kinetic energy = 1/2 mv2
• Small changes in speed  large changes in kinetic
energy
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Kinetic Energy
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Kinetic Energy
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Kinetic Energy
CHECK YOUR NEIGHBOR
Must a car with momentum have kinetic energy?
A. Yes, due to motion alone
B. Yes, when motion is nonaccelerated
C. Yes, because speed is a scalar and velocity is
a vector quantity
D. No
Explain your answer to your neighbor.
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The Work–Energy Theorem
• When work is done on an object to change its kinetic
energy, the amount of work done is equal to the change
in kinetic energy.
• Equation for the work–energy theorem:
Net work = change in kinetic energy
– If there is no change in an object's energy, then no
work is done.
– The theorem applies to potential energy: For a barbell
held stationary, no further work is done, so there is no
further change in energy.
– The theorem applies to decreasing energy: The more
kinetic energy something has, the more work is
required to stop it.
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The Work–Energy Theorem
CHECK YOUR NEIGHBOR
Consider a problem that asks for the distance
needed for a fast-moving crate sliding across a
factory floor to come 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.
Explain your answer to your neighbor.
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The Work–Energy Theorem
CHECK YOUR NEIGHBOR
The work done in braking a moving car to a stop is
the force of tire friction times the stopping distance.
If the initial speed of the car is doubled, the
stopping distance will be
A.
B.
C.
D.
actually less.
about the same.
twice.
none of the above
Explain your answer to your neighbor.
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Kinetic Energy and Momentum
• Comparison of kinetic energy and momentum
– Both depend on mass and velocity.
• Momentum depends on mass and speed.
• KE depends on mass and the square of its speed.
– Momentum is a vector quantity.
Kinetic energy is a scalar quantity.
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Conservation of Energy
• Conservation is defined in everyday language as
"to save"—in physics, to "remain unchanged."
• Law of conservation of energy:
– In the absence of external work input or
output, the energy of a system remains
unchanged. Energy cannot be created or
destroyed.
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Conservation of Energy
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Conservation of Energy
• Will all the Energy be transferred or converted
completely to the new type of Energy?
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Conservation of Energy
• 6CO2 + 6H2O + sunlight  C6H12O6 + 6O2
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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 goes to warming the bow.
10 joules goes to warming the target.
10 joules is mysteriously missing.
Explain your answer to your neighbor.
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Machines
• A machine is 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.
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Machines
• Equations:
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
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Machines
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Machines
• Pulleys allow you to
exert a small force
through a large
distance to lift a
heavy object
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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 100-centimeters length of rope she
pulls downward, the crate rises
A.
B.
C.
D.
50 centimeters.
45 centimeters.
25 centimeters.
none of the above
Explain your answer to your neighbor.
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Machines
• A. A machine that does work with only one
movement is a simple machine.
Machines
• B. Lever—bar that is free to pivot about a fixed
point called the fulcrum
– 1. Input arm is part of the lever on which effort
force is applied.
– 2. Output arm is part of the lever that exerts
the resistance force.
Machines
– 3. Three classes of levers based on positions of effort
force, resistance force, and fulcrum
• a. First-class lever—fulcrum is located between the effort and
resistance forces; multiplies and changes direction of force
• b. Second-class lever—resistance force is located between
the effort force and fulcrum; always multiplies force
• c. Third-class lever—effort force is between the resistance
force and fulcrum; doesn’t multiply force but does increase
distance over which force is applied
Machines
– 4. Calculating ideal mechanical advantage
(IMA) of a lever—IMA equals length of input
arm divided by length of output arm
Machines
• C. Grooved wheel with a rope, simple chain, or
cable running along the groove is a pulley,
which is a modified first-class lever.
– 1. A fixed pulley is attached to something that doesn’t
move; force is not multiplied but direction is changed;
IMA = 1.
– 2. A movable pulley has one end of the rope fixed and
the wheel free to move; multiplies force; IMA = 2.
Machines
– 3. Block and tackle—system of pulleys
consisting of fixed and movable pulleys; IMA
= number of ropes supporting resistance
weight
Machines
• D. Wheel and axle—machine with two wheels
of different sizes rotating together; modified lever
form
– 1. IMA = radius of wheel divided by the radius
of axle
– 2. Gears are a modified form of the wheel and
axle.
Machines
• E. Inclined Plane—sloping surface that reduces
the amount of force required to do work
– 1. IMA = length of slope (effort distance)
divided by height of slope (resistance
distance)
– 2. Less force is required if a ramp is longer
and less steep.
Machines
• F. Screw—inclined plane wrapped in a spiral
around a cylindrical post
Machines
• G. Inclined plane with one or two sloping sides is
a wedge.
Machines
• H. Compound machine—uses a combination of
two or more simple machines
Efficiency
• Efficiencyis how effectively a device transforms
or transfers useful energy.
– Equation for efficiency:
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.
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Efficiency
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Efficiency
CHECK YOUR NEIGHBOR
A certain machine is 30% efficient. This means the
machine converts
A. 30% of the energy input to useful work—70%
of the energy input will be wasted.
B. 70% of the energy input to useful work—30%
of the energy input will be wasted.
C. as strange as it may seem, both of the above
D. none of the above
Explain your answer to your neighbor.
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