Download Energy Sub-Unit Notes

Momentum/Energy Unit- Energy Sub-Unit
Regents Physics
3.2.1 Introduction to Work & Energy
Definitions
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energy: __________________________________________________________
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Example #2 – Flat Ground
A box is pushed with a force of 100 newtons across a frictionless surface for a
distance of 10 meters. How much work is done on the box?
Unit: ________________________
work: _____________________________________________________________
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requires: ______________________
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Unit: ________________________
100 N
10 m
Equation
Example #1 – No Motion
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A student is trying to push a heavy crate across the floor, but it does not move.
Is work being done ‘on the crate’?
Example #3 – Incline
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A box is pulled up a 3.0 meter long plane that is inclined at 20° using a force of
10 newtons. How much work is done in moving the box?
10 N
3.0 m
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Example #4 – Force on an Angle
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3)
A 100 newton block is placed on a frictionless 30° incline.
A sled is pulled a horizontal distance of 4.0 meters across a frictionless,
horizontal surface using a force of 15 newtons at an angle of 30° above the
horizontal. How much work is done on the sled?
15N
30°
30°
4.0 m
a.
Draw the weight and normal force vectors acting on the block.
b.
Determine the force needed to move the block up the plane at a constant
velocity.
c.
If the block is moved 2.0 meters along the plane using this force, how much
work is done on the block?
PRACTICE
1)
2)
If 2000 joules of work are done in moving an object a distance of 500 meters,
determine the average force that must be exerted on the object.
Calculate the amount of work done in pulling an object 4.0 meters up a 60°
frictionless incline if the force directed along the plane is 30 newtons.
Momentum/Energy Unit- Energy Sub-Unit
Regents Physics
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kinetic energy: _____________________________________________________
3.2.2 Work/Energy Principle
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Definitions – Types of Energy
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depends on mass and velocity
Equation
potential energy: __________________________________________________
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can be in a ___________________ or _____________________
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gravitational PE is stored in gravitational fields
Equation
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Example #3
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A 5.0 kilogram toy car is moving at 2.0 meters per second. What is the kinetic
energy of the toy car?
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internal energy: ___________________________________________________
elastic PE is stored in elastic objects (springs)
Equation
Variable
Example #1
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A 30 kilogram object is positioned 2.0 meters above the surface of the Earth.
What is the gravitational potential energy of the object?
Work/Energy Principle
When work is done ‘on a system’ there is a net gain of one or more types of energy by that
system. Energy types can change within a system at any time.
if ________________ changes
Example #2
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The length of a spring with a spring constant of 100 newtons per meter is
changed by 4.0 centimeters. What is the elastic potential energy stored in the
spring?
if ________________ changes
WORK
W = Fd = ΔET
if ________________ changes
if ________________ changes
Gravitational PE
Elastic PE
Kinetic Energy
Internal Energy
3|Page
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Scenario #1
A car is moving along a flat surface with an increasing speed. What type(s) of
energy are changing?
PEg
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PES
KE
Q
a.
What are the initial and final kinetic energies of the object?
b.
How much work needed to be done on the object?
X = no change
↑ = increase
↓ = decrease
? = can’t be determined
2)
Determine the amount of work needed to move a 5.0 newton object from a 1.5 meter
high shelf to a 4.0 meter high shelf.
PES
KE
Q
3)
A 3.0 kilogram object is pushed with a force of 2.0 newtons over a distance of 6.0
meters. How much kinetic energy is gained by the object?
4)
Determine the change in the length of a spring with a spring constant of 50 newtons
per meter when 400 joules of work are done on it.
X = no change
↑ = increase
↓ = decrease
? = can’t be determined
Scenario #4
A car is moving on a flat surface toward a wall and is stopped by a spring on its
front. What type(s) of energy are changing?
PEg
•
Q
X = no change
↑ = increase
↓ = decrease
? = can’t be determined
A 2.0 kilogram object that is initially at rest is accelerated to a speed of 5.0 meters per
second.
Scenario #3
A car is applying its brakes and slowing down as it moves down a slope. What
type(s) of energy are changing?
PEg
•
KE
1)
Scenario #2
A car is moving up an incline with constant speed. What type(s) of energy are
changing?
PEg
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PES
PRACTICE
PES
KE
Q
X = no change
↑ = increase
↓ = decrease
? = can’t be determined
Scenario #5
A rocket flies upward with an increasing velocity [ignore air resistance]. What
type(s) of energy are changing?
PEg
PES
KE
Q
X = no change
↑ = increase
↓ = decrease
? = can’t be determined
Momentum/Energy Unit- Energy Sub-Unit
Regents Physics
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Review Questions
3.2.2 – Use equations to calculate work; force; distance; PE; and/or KEin
75 joules of work are done in lifting a 2.5 kilogram object. What change in
height will the object experience?
frictionless systems Identify/sketch graphs that related variables involved with
energy calculations.
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How much work is done on an object if 35 newtons of force are applied to it as
it is moved 10 meters?
[3.05m]
[35J]
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What is the spring constant of a spring that requires 0.4 joules of work to be
compressed a distance of 0.2 meter?
What amount of kinetic energy does a 4.0 kilogram object have when moving
at 3.0 meters per second?
[20N/m]
[18J]
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A 10 newton force is applied to an object at an angle of 30° above horizontal.
If the object is moved a distance of 2.0 meters horizontally along a frictionless
surface using this force, what amount of kinetic energy is gained by the object?
How much work is needed to change the speed of a 2.0 kilogram object from
4.0 meters per second to 10 meters per second?
[84J]
[17J]
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Sketch the approproate shape for each of the graphs below.
A 5.0 kilogram object initially at rest is moved 4.0 meters across a frictionless
surface with a force of 20 newtons.
o
What amount of kinetic energy does the object gain?
PE
[80J]
o
KE
h
PES
v
x
What final speed will the object have?
.
[5.6m/s]
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[direct;
3.2.3 Conservation of Energy
Law of Conservation of Energy
The total amount of energy in a closed system must remain constant – energy is never created
or destroyed.
Example #2 – Skier
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A skier begins at rest at the top of a snowy, frictionless hill. He slides down the
hill and after reaching the bottom slides across a long stretch of unpacked snow.
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Equation
At which point is the total energy completely potential / kinetic /
internal?
v=0
Example #1 – Cliff Diver
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A 500 newton cliff diver climbs to a height of 50 meters above the water.
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50 m
PE
v=0
What is his total energy at the
top of his climb?
unpacked snow
KE
Total Mechanical Energy = ___________________
25 m
PE
KE
Example #2 – Carts and Hills
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0m
PE
KE
What is his potential energy at
the point where he is 40
meters above the water’s
surface? What is his kinetic
energy at that point?
A 4.0 kilogram cart operating on a frictionless track has a speed of 5.0 meters per
second while at the top of a 2.0 meter high hill.
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What is the cart’s total energy at the top of the hill?
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What is the cart’s speed at the bottom of the hill?
5.0 m/s
2.0 m
Momentum/Energy Unit- Energy Sub-Unit
Regents Physics
PRACTICE
Example #3 – Spring Toy
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1)
A spring toy with a mass of 2.0 grams has a spring with a spring constant of 120
newtons per meter. The toy is compressed 4.0 centimeters.
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An astronaut standing on the Earth throws a 0.2 kilogram wrench into the air with an
initial speed of 2.0 meters per second
a.
What potential energy will the wrench have when it reaches its maximum
height?
b.
Compare the maximum height that the wrench would reach on Earth to the
maximum height that it would reach on the Moon where acceleration due
2
to gravity is 1.62 meters per second .
How much energy can be stored in the toy’s spring?
h
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What maximum height will the spring toy reach if it is released?
Example #4 – Pendulum
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Label points at which potential and kinetic energies are maximum/minimum.
2)
A 3.0 kilogram cart that is moving at 4.0 meters per second moves to the top of a 0.5
meter high hill. What kinetic energy will the cart have when it reaches the top of the
hill?
0.5 m
7|Page
3.2.4 Work to Overcome Friction
Example #2 – Missing KE
Energy “Loss”
In the real world potential energy is not completely converted into kinetic
energy when objects lose height.
Energy can never truly be destroyed, but it can be converted into non-mechanical forms
(mainly heat) that are not ‘useful’
ET  PE  KE  Q
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We now consider problems in which Q ≠ 0.
A 4.0 kilogram object begins at rest at the top of an incline that is 2.0 meters
above the ground and slides down to the bottom. The object reaches a speed of
5.0 meters per second at the bottom of the hill.
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Determine the total energy of the object at the top of the incline.
Example #1 – Lifting a Load
In the real world it takes more energy to lift a load than the gain in potential
energy would suggest.
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5200 joules of work are done in lifting a 50 kilogram object a distance of 10
meters.
o
2.0 m
Determine the amount of potential energy gained by lifting this object
the given height.
5.0 m/s
o
Determine the amount of energy used to overcome friction as the
block slides down the incline.
Example #3 – Constant Velocity
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How much energy must have been used to overcome friction?
In the real world we must constantly add energy to a system (do work) to
keep things moving at a constant speed.
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A 2.0 kilogram object is pulled along a flat surface at a constant speed with a
force of 30 newtons.
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Calculate the amount of work done in moving the object 4.0 meters.
o
How much work must have done against friction in moving this object?
Momentum/Energy Unit- Energy Sub-Unit
Regents Physics
PRACTICE
1)
A 50 newton cart that begins at rest at the top of a 3.0 meter high hill reaches a
kinetic energy of 120 joules as it reaches the bottom of the hill. How much internal
energy is generated as the cart moves down the hill?
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A 4.0 kilogram object moving at 15 meters per second is slowed down to a
speed of 6.0 meters per second by a friction force of 20 newtons.
o
How much internal energy is produced during this change?
[378J]
o
What distance will the object travel during this motion?
[18.9m]
2)
A 3.0 kilogram block is dropped from a height of 10 meters. If air resistance does 200
joules of work on the block as it falls, what kinetic energy will the block have as it
reaches the ground?
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500 joules of energy are used in lifting a 10 kilogram object a distance of 3.0
meters. What amount of work is done by friction in this system?
[205.7J]
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A 6.0 newton object is lifted a distance of 10 meters. If 100 joules of work are
done by friction during this lift, what is the total amount of energy expended as
the object is lifted?
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A 2.0 kilogram object at rest at the top of a frictionless 4.0 meter high hill is
allowed to slide to the bottom. What speed will the object reach at the bottom
of the hill?
Review Questions
3.2.3 – Use the principle of Conservation of Energy to determine changes in KE;
PE; internal energy; speed and /or height.
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How much work is needed to accelerate a 5.0 kilogram object moving at 3.0
meters per second on a frictionless surface to a speed of 10 meters per
second?
[160J]
[227.5J]
[6.3m/s]
9|Page
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A 5.0 kilogram object at the top of a 2.0 meter high hill gains 15 joules of
kinetic energy as it slides to the bottom of the hill. How much work was done
by friction as the object slid down the hill?
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A 500 newton per meter spring is compressed a distance of 0.06 meter then
used to shoot a 0.02 kilogram object along a horizontal surface. The object is
launched with a speed of 6.0 meters per second.
o
Determine the amount of energy stored in the spring.
[0.9J]
[83.1J]
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A spring with a spring constant of 1000 newtons per meter is used to launch a
3.0 kilogram object vertically. The spring is compressed 0.10 meter before the
launch.
o What amount of energy will be stored in the spring before launch?
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Determine the kinetic energy of the object at launch.
[0.36J]
[5J]
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What amount of internal energy is generated in this system?
How high will the object go?
[0.54J]
[0.17m]
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A ball slides down from rest starting at point A on the frictionless track shown
below.
A
C
D
B
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At which point is gravitational potential energy a maximum? _______
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At which point is kinetic energy a maximum? ________
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Compare the ball’s speed at point C to its speed at point D. ________
[A; B; C < D]
Momentum/Energy Unit- Energy Sub-Unit
Regents Physics
Example #3 – Elevator Motor
3.2.5 Mechanical Power
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Definitions
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A motor pulls an 800 newton elevator upward with an average velocity of 3.0
meters per second.
power: the rate at which…
o
_______________________________________________
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_______________________________________________
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Unit: ________________________
Equation
Example #1 – Power Plant
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A power plant produces 200 mega joules of energy in 30 seconds. What is the
power output of the plant?
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What power must be supplied by the motor?
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How can the demand for power be reduced?
PRACTICE
1)
A 50 kilogram student who is capable of generating 700 watts of power climbs a set of
stairs that is 6.5 meters high.
a.
Calculate the amount of work that the student needs to do in order to climb
the stairs.
b.
Determine the amount of time that it will take for the student to climb the
stairs.
Example #2 – Dog Sled
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A team of dogs pull a sled with an average force of 3000 newtons across a
distance of 200 meters in 75 seconds. What is their power output during this
time?
11 | P a g e
2)
Compare the power output of a man lifting a 300 newton weight 2.0 meters in 2.0
seconds to the power output of a woman lifting a 100 newton weight 1.5 meters in
0.5 seconds.
Review Questions
3.2.3 – Use equations to determine power; work; time; force; and/or distance.
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What amount of power is generated in a system that uses 35 joules of energy
in 10 seconds?
[3.5W]
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What is the power output of a motor that applies 75 newtons of force in lifting
an object 5.0 meters in 2.5 seconds?
[150W]
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What is the power generated by a person who pulls a rope with a force of 100
newtons, lifting an object with an average speed of 3.5 meters per second?
[350W]
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A 3000 watt motor is used to drive a boat. How long will it take the motor to
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use 6.0 x 10 joules of energy?
[2000s]