Transcript Lecture 4

Lecture 4
• Momentum and
Impulse
• Energy and Work
• Potential Energy
• Kinetic Energy
Momentum
• Momentum: Inertia in motion
– Directly related to the magnitude of an
object’s velocity and its mass.
– Momentum = mass x velocity
– Momentum = mv
Momentum and Force
• Force causes an acceleration.
• Acceleration = a change in an object’s
velocity = a change in its momentum.
Momentum and Time
• How long a force is applied will also determine
how much the momentum of an object changes.
– Applying a force for twice the time produces twice the
change in momentum.
Momentum and Impulse
• Impulse = Force x time
• Impulse = Change in Momentum
• Force x time = Change in Momentum
Ft = Δ (mv)
Momentum and Impulse
• Compare the momentum of a 1 kg cart
moving at 10 m/s with that of a 2 kg cart
moving at 5 m/s.
• For the same force, which cannon imparts
a greater impulse to a cannonball – a long
cannon or a short one?
Impulse Changes Momentum
• In order to increase the
momentum of an object,
apply the greatest force
for as long as possible.
Impulse Changes Momentum
• Extending the time of an impact reduces the
force of an impact.
Impulse Changes Momentum
Impulse Changes Momentum
• Imparting a large impulse on objects in a
short time produces considerable force.
To bring a super tanker to a stop, its engines are typically
cut off about 25 km from port. What makes the momentum
of a supertanker so enormous that it needs considerable
time to stop.
1.
2.
3.
4.
Because they travel at a
high velocity.
Because of the Earth’s
gravitational pull on the
tanker.
Because of the
enormous mass of the
tanker.
Because of the density
of the tanker.
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Momentum and Impulse
• A few equations to remember:
–Momentum = mv
–Impulse = Ft = Δ mv
A 0.15 kg baseball moving at a speed of 40 m/s is caught.
What is the momentum of the ball before it is brought to
rest?
1.
2.
3.
4.
5.
6.
4 kg·m/s
4N
6 kg·m/s
6N
15 kg·m/s
15 N
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A 0.15 kg baseball moving at a speed of 40 m/s is caught.
How much impulse acts on the ball when it has been
caught and brought to rest?
1.
2.
3.
4.
12 kg·m/s
6 kg·m/s
0 kg·m/s
4 kg·m/s
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0%
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Automobiles were previously manufactured to be
as rigid as possible, where as today’s autos are
designed to crumple upon impact. Why?
1.
2.
3.
4.
Increases the amount of time
the car is brought to rest
which reduces the force of
impact.
Shortens the amount of time
the car is brought to rest
which reduces the force of
impact.
The force of impact remains
the same, but the impulse of
the impact is reduced.
None of the above. They’re
just saving on manufacturing
material costs.
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If a boxer increases the duration of impact to 3
times as long by riding with the punch. By how
much is the force of the impact reduced?
1.
2.
3.
1/3 the amount of force.
1/9 the amount of force.
The amount of force
cannot be changed
because the change in
momentum is the same.
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If a boxer moves into the punch and decreases the
duration of the impact by half, then how much is
the force of the impact changed?
1.
2.
3.
4.
4 times as much
Twice as much
Half as much
No change
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Which has a greater momentum? A 50,000 kg
train locomotive traveling at 1 m/s or a 1 kg
squirrel traveling at 50,000 m/s.
1. The train
locomotive.
2. The squirrel.
3. They have the
same momentum.
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Energy
• The universe is composed of both matter
and energy.
– Matter is substance
– Energy is the mover of substance
Energy
• Energy: the property of a system that
enables it do work (produce changes on
another system).
– When work is done by one system on
another, energy is transferred.
– We usually only observe energy when it is
being transferred or being transformed.
Energy and Work
• Whenever work is
done:
1) Application of a
force
2) Movement of
something by that
force
Energy and Work
Work = Force X Distance
W = Fd
Units of work: Newton-meter (N·m) or
Joules (J).
• Units of Energy: Joules (J).
– Heating 1g of water one degree C = 4.2 J
– 1 nutritional Calorie = 4.2 kilojoules (KJ)
– 1 kilowatt-hour = 3.6 megajoules (MJ)
– Recommended human diet = 9 megajoules (MJ)
– 1 large pizza = 16 megajoules (MJ)
– 1 gallon of gasoline = 120 megajoules (MJ)
– 1 ton of TNT = 4.2 gigajoules (GJ)
Mass-Energy Equivalence
Matter is a condensed form of energy.
1 gram of mass = 89.9 Terajoules.
1 gram of mass = energy released by 21.5 kilotons of TNT
or the combustion of 568,000 gallons of gasoline.
Potential Energy
• Potential Energy (PE): stored energy or the
potential for doing work.
• Examples:
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Stretched Springs
Chemical energy in fuels and food
Electric potential or voltage
Buildup of stress along a fault in Earth’s crust
Gravitational potential energy
• Whenever work is done, energy is exchanged.
Potential Energy
• Gravitational Potential Energy (PE): the
potential energy due to elevated positions.
• Amount of PE possessed by an elevated
object = work done against gravity in lifting
it.
Potential Energy
• Gravitational Potential Energy = weight X
height
PE = mgh
(weight = mg)
(h = height)
Potential Energy
• The PE of an elevated object does not depend
on the path taken to get it there. Only vertical
distance matters.
Kinetic Energy
• Kinetic Energy (KE): the energy of
motion.
– Depends on the mass of an object as well as
its velocity.
Kinetic energy = ½ mass X velocity2
KE = ½ mv2
Potential and Kinetic Energy
Work-Energy Theorem
• KE of a moving object is equal to:
– the work required to bring it from rest to a
speed.
– the work the object can do while being
brought to rest.
Work-Energy Theorem
• Work = Change in Kinetic Energy.
Work = ΔKE
Fd = ΔKE
• If there is no change in an object’s energy,
then no net work was done on it.
• If you push a crate horizontally with 100 N
across 10 m, and the friction between the
crate and the floor is a steady 70 N, how
much KE is gained by the crate?
• For the same force, why does a longer
cannon impart more speed to a
cannonball?
Energy Transformations
The 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.
Energy Transformations
Energy Transformations
What is the ultimate source of energy
stored in fossil fuels such as coal?
Efficiency
• In any energy transformation, some
energy is dissipated to thermal energy
(heat).
• Efficiency = useful energy output / total
energy input.
Power
• Power: the measure of how fast work is done.
Power = work done / time interval
• Example: An engine that delivers twice the
power can accomplish twice the amount of work
in the same amount of time.
– Greater power = greater acceleration
Power
• Power is also the rate at which energy is changed from
one form to another.
• Unit of power: joule per second or the watt (W).
– 1 W of power is used when 1 J of work is done in 1
second (J/s).
– 1 W of power represents 1 J of energy that is
converted each second (J/s).
Power
• The human heart
uses slightly more
than 1 W of power in
pumping blood.
• 3 main engines of a
space shuttle can
develop 33,000 MW
of power when fuel is
burned at a rate of
3,400 kg/s.
The Grand Coulee Dam can produce up to approximately
7,080 Megawatts or power.