Chapter 7 - Conservation of Energy and Momentum
Transcript of Chapter 7 - Conservation of Energy and Momentum
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UNIT 3Momentum & Energy
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EFFICIENCY
Efficiency is the ratio of useful energy or work
output to the total energy or work output.
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EFFICIENCY
A model rocket engine contains explosives storing
3.5*10^3J of chemical potential energy. The stores
energy is transformed into gravitational potential
energy at the top of a rockets flight path. Calculate
how efficiently the rocket transforms storedchemical energy into gravitational potential energy
if the 0.500kg rocket is propelled to a height of
1.00*10^2m.
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EFFICIENCY
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CHAPTER 17CONSERVATION OF
ENERGY AND MOMENTUM
Law of conservation of energy: Energy can not becreated or destroyed, or may only be transformed.
Thus, the total energy of an isolated system must
be constant over time.
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ENERGY TRANSFORMATIONS
Youve talked about kinetic, potential, and
gravitational energyall mechanical energies. Now
we will talk about what happens to the energy after
youve done work on the object.
If you shoot a hockey puck down an ice surface,
what will eventually happen?
It has lost the mechanical energy that weve given
it!
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CONSERVATIVE AND NON-
CONSERVATIVE FORCES
If you lift a book one meter above a table and
release it, what happens?
If you push a book across a table, will itautomatically return to its original spot?
What are we doing work against in the first case?
And the second?
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CONSERVATIVE AND NON-
CONSERVATIVE FORCES
Now, if you lift the book one meter above the table,
and then carry it across the room, have you done
more work on the book than in the first case?
If you push the book from one side to the other, and
then push it back to its original position, have you
done more work than before?
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CONSERVATION OF MECHANICAL
ENERGY
When all of the work done throughout a process is
done by conservative forces, the total mechanical
energy of the system before the process is equal to
the total mechanical energy at the end of the
process.
Ek + Eg + Ee= Ek + Eg + Ee
k = kinetic
g = gravitational
e = elastic
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CONSERVATION OF MECHANICAL
ENERGY
What kind of energy transformation is happening if
you drop a rock?
What happens the total energy?
What is happening to the different energies
throughout the process?
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CONSERVATION OF MECHANICAL
ENERGY
A skier is gliding along with a speed of 2.00m/s at
the top of a ski hill, 40.0m high. The skier then
begins to slide down the icy (frictionless) hill.
a. What will be the skiers speed at a height of 25.0m?
b. At what height will the skier have a speed of 10.0m/s?
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CONSERVATION OF MECHANICAL
ENERGY
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CONSERVATION OF MECHANICAL
ENERGY
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CONSERVATION OF MECHANICAL
ENERGY
Homework problems: pg. 287, #1-4
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ELASTIC POTENTIAL ENERGY AND
KINETIC ENERGY
Youve leaned what elastic potential energy is and
how to express it when stored in a stretched or
compressed spring:
Now, what are some practical examples of
transforming elastic potential energy into kinetic
energy?
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ELASTIC POTENTIAL ENERGY AND
KINETIC ENERGY
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ELASTIC POTENTIAL ENERGY AND
KINETIC ENERGY
A low friction cart with a mass of 0.25kg travels
along a horizontal track and collides head on with a
spring that has a spring constant of
155N/m. If the spring was compressed by 6.0cm,
how fast was the cart initially travelling?
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CONSERVATION OF TOTAL ENERGY
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CONSERVATION OF TOTAL ENERGY
A system is any object or group of objects.
An internal force is any force exerted on any objectin the system due to another object in the system.
An external force is any force exerted by an object
that is not a part of the system on an object withinthe system.
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CONSERVATION OF TOTAL ENERGY
An open system can exchange both matter and
energy with its surroundings.
A closed system can exchange energy, but notmatter, with its surroundings.
An isolated system can not exchange energy or
matter with its surroundings - nothing can enter orleave.
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CONSERVATION OF TOTAL ENERGY
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CONSERVATION OF TOTAL ENERGY
You often hear that a system lost energy. Since
the energy can not be created or destroyed, what
happens to the energy?
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CONSERVATION OF TOTAL ENERGY
We can now state the law of conservation of energy
mathematically:
The work done by non-conservative forces is the
difference between the final mechanical energy andthe initial mechanical energy of a system.
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CONSERVATION OF TOTAL ENERGY
A roller-coaster with a mass of 200.0kg is moving to the right at a
speed of 4.00m/s at point A, 15.00m above the ground. The
car then heads down the slope towards point B, 6.00m above
the ground. If 3.40*10^3J of work are done by friction between
points A and B, determine the speed of the car at point B.
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CONSERVATION OF TOTAL ENERGY
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CONSERVATION OF TOTAL ENERGY
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CONSERVATION OF TOTAL ENERGY
Example: A 65.0kg skydiver steps out from a hot air
balloon that is 5.00*10^2m above the ground. After
free-falling a short distance, she deploys her
parachute, finally reaching the ground with a
velocity of 8.00m/s.
a. What is the gravitational potential energy
of the skydiver, relative to the ground,
before she jumps?b. What is the kinetic energy just before she
lands on the ground?
c. How much work did the non-conservative
frictional force do?
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CONSERVATION OF TOTAL ENERGY
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CONSERVATION OF TOTAL ENERGY
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CONSERVATION OF MOMENTUM
Elastic collisionskinetic energy is conserved.
Inelastic collisionskinetic energy is not
conserved.
Newtons third law of motion states that for every
action force on object B due to object A, there is a
reaction force equal in magnitude (but opposite
direction) acting on object A due to object B.
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CONSERVATION OF MOMENTUM
So how do we derive the conservation of
momentum law from Newtons third law? We use
the impulse-momentum theorem!
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CONSERVATION OF MOMENTUM
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CONSERVATION OF MOMENTUM
The conservation of momentum law states that the
total momentum of two objects before a collision is
the same as the total momentum of the same two
objects after the collision.
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CONSERVATION OF MOMENTUM
We all know that systems are rarely perfectly
isolated, and that immediately after a collision,
frictional forces and interactions with other objects
change the momentum of the objects.
So is this law still useful?
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CONSERVATION OF MOMENTUM
Yes! We can still use the conservation of
momentum law to describe a system from the
instant before to the instant after a collision.
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CONSERVATION OF MOMENTUM
A 1.75*10^4kg boxcar is rolling down a track toward
a stationary boxcar that has a mass of 2.00*10^4kg.
Just before the collision, the first boxcar is moving
east at 5.45m/s. When the boxcars collide, they
lock together and continue down the track. What isthe velocity of the two boxcars after the collision?
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CONSERVATION OF MOMENTUM
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CONSERVATION OF MOMENTUM
A 0.250kg billiard ball moving at 5.00m/s collides
head-on with a stationary, 0.800kg steel ball. If the
billiard ball bounces directly backwards at 2.62m/s,
was the collision elastic?
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REAL LIFE EXAMPLES
What are some examples that make this important
for everyday events?
Homework: pg. 327 # 2,7,8
pg. 332 # 38, 42, 44, 46, 49