Transcript energy

WORK, POWER, ENERGY
QOTD: Write a list of 10 examples your idea of
work.
 Demo : create a work equation using a spring
scale, string and a book.
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WHAT IS WORK?
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Work is done only when a force moves an object
A force acting on an object and causing it to
move a distance is work
Not every force is work..if you push against the
wall it does not move..that is not work!
Work = force X distance
Work is measured in Joules
If you pick up a bag of groceries and walk across
the room the work is picking up the groceries
not the walking.
 The
object must move some distance as a result of
your force
 The force you exert must be in the same direction
as the objects motion.
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Ie: the groceries
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You walk
WHAT’S WORK?
A scientist delivers a speech to an
audience of his peers.
 A body builder lifts 350 pounds
above his head.
 A mother carries her baby from
room to room.
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A father pushes a baby in a carriage.
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A woman carries a 20 kg grocery
bag to her car?
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WHAT’S WORK?
A scientist delivers a speech to an
audience of his peers. No
 A body builder lifts 350 pounds
above his head. Yes
 A mother carries her baby from
room to room. No
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A father pushes a baby in a carriage. Yes
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A woman carries a 20 kg grocery
bag to her car? No
6
Work can be determined by calculating
 Force used x distance moved = amount of work
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Therefore what is the formula for work?
Work = force x distance
 Joule – is the SI unit for work.
 Newton = force
 Meters = distance
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Therefore if you exert:
 1 Newton of force for 1 meter of distance
= 1 joule of work or 1N/m
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Work is done when a force is exerted through a distance.
A student lifts a bag of books that weighs 135 N. If the bag
is lifted .75 m, how much work does the student do?
F = 135 N d = .75 m
W = Fd
W = (135 N)( .75 m)
W = 101.25 J
Negative Work
If the object moves in the direction opposite the direction of the force
(for instance if force and displacement are in opposite directions)
then the work is negative: W < 0.
The energy of the system is reduced.
A +24 N force is applied to an object that moves 10 m
in the same direction during the time that the force is
applied. How much work is done to the object?
http://www2.franciscan.edu/academic/mathsci/
mathscienceintegation/MathScienceIntegation1011.htm#item1015
Find the equation for POWER
1. Attach a string and spring scale to a large book.
2. Pull the book .5m slowly. Use a stopwatch to determine time .
3. Record the time and distance on a data table.
4. Repeat 1- 3 – but this time pull the book faster.
5. Repeat 1-3 even faster.
Force-N
distance -m
time- s
POWER
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Power tells you how fast something is
happening..how fast the work is being done
Power = work/time or Power = Force X Distance
Time
Power is measured in watts (W)
One watt is equal to 1 joule per second of work divide
joules/seconds
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Power – the rate at which energy is transferred.
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P=W
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t
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1 Watt (W) = 1 J/s
P = power
W = work
t = time
Watts
Joules
seconds
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HOW MUCH POWER MUST A MOTOR HAVE TO OPERATE A PUMP
THAT RAISES
1500 KG OF WATER EVERY MINUTE A DISTANCE OF 12 M?
1. m = 1500 kg
t = 60 s d = 12 m
 2. Equations
P = W/t
W = Fd
F = mg
 3. Plug and chug
F = mg = (1500 kg)(9.8 m/s2) = 14,700 N
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W = Fd = (14,700 N)(12 m) = 1.76 x 105 J
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P = W/t = (1.76 x 105 J)/(60 s) = 2940 W
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http://www.physicsclassroom.com
What is Energy?
It turns out that energy is so fundamental, like space and
time, that there is no good answer to this question. However,
just like space and time, that doesn't stop us from doing very useful calculations with
Energy
We may not be able to define energy, but because it is a
conserved property of nature, it's a very useful idea.
POTENTIAL ENERGY
Potential Energy (PE):
Stored energy due to position
Examples:
rock on a cliff, battery, food,
gasoline, stretched rubber band, apple
hanging in a tree
Gravitational Potential Energy
A barbell of mass "m" is lifted vertically upwards a distance "h" by an
outside force. How much work does that outside force do on the
barbell?
Fapp
mg
W = Fdparallel
Since a = 0, Fapp = mg
W = (mg) dparallel
Since F and d are in the same direction ...and dparallel = h
W = (mg) h
W = mgh
Gravitational Potential Energy
But we know that in general,
Eo + W = Ef.
If our barbell had no energy to begin
with, Eo = 0, then W = Ef
But we just showed that we did
W=mgh to lift the barbell... so mgh=Ef
The energy of a mass is increased by
an amount mgh when it is raised by a
height "h".
Gravitational Potential Energy
The name for this form of energy is
Gravitational Potential Energy (GPE).
GPE = mgh
One important thing to note is that while changes in gravitational potential energy are
important, their absolute value is not.
Gravitational Potential Energy
You can define any height to be the zero
for height...and therefore the zero for
GPE.
0.5 m
But whichever height you choose to call
zero, changes in heights will result in
changes of GPE. For example, the floor
level can be considered zero energy or
the ladder level can be zero.
0m
0.5 m
0m
GRAVITATIONAL PE
Gravitational PE (GPE):
Energy stored by objects that are above the
earth’s surface (objects that can fall)
Depends on mass, acceleration and height
GPE increases with height
GRAVITATIONAL PE
GPE = mass  gravity  height
GPE = m g h = weight  height
GPE = m (kg)  9.8 m/s2  h (m)
j = 1 Nm
What is the change of GPE for a 5.0 kg object which is raised from the
floor to a final height of 2.0m above the floor?
answer
9
As an object falls, its GPE always _____.
A
increases
B
decreases
C
stays the same
answer
10
What is the change of GPE for a 8.0 kg object which is lowered from an
initial height of 2.0 m above the floor to a final height of 1.5m above the
floor?
answer
11
What is the change in height of a 2.0 kg object which gained 16 J of GPE?
answer
12
GPE=mg
h = GPE
h = 16/(2
h = 0.82m
KINETIC ENERGY
Kinetic Energy (KE):
Energy in the form of motion
Depends on mass and velocity of
moving object.
Object in motion has ability to do work
http://www.youtube.com/watch?featur
e=player_detailpage&v=0ASLLiuejAo
Kinetic Energy
The energy an object has by virtue of its motion
is called its kinetic energy. The symbol we will
be using for kinetic energy is KE.
Like all forms of energy, it is measured in
Joules (J).
The amount of KE an object has is given by:
KE = 1/2 mv2
KINETIC ENERGY
KE = ½ mass  velocity2
KE = m  V2
2
(j) = (kg)  (m/s)
1 j = 1 kg m/s
As an object falls, its KE always _____.
A
decreases
B
increases
C
stays the same.
answer
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A ball falls from the top of a building to the ground below. How does
the kinetic energy (KE) compare to the potential energy (PE) at the top
of the building?
A
KE = PE
B
KE > PE
C
KE < PE
D
It is impossible to tell.
answer
14
What is the kinetic energy of a 12 kg object with a velocity of 10 m/s?
answer
15
What is the mass of an object which has 2400 J of KE when traveling at
6.0 m/s?
answer
16
17
A 3 kg object has 45 J of kinetic energy. What is its velocity?
If the speed of a car is doubled, the KE of the car is:
A
quadrupled
B
quartered
C
halved
D
doubled
answer
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Which graph best represents the relationship between the KE and the
velocity of an object accelerating in a straight line?
C
A
KE
KE
v
v
B
D
KE
KE
v
v
answer
19
20
The data table below lists mass and speed for 4 objects. Which 2 have
the same KE?
A
B
B and D
C
A and C
D
B and C
answer
A and D
Elastic Potential Energy
Energy can be stored in a spring, this energy is called
Elastic Potential Energy.
Robert Hooke first observed the relationship between the
force necessary to compress a spring and how much the
spring was compressed.
Hooke's Law
Fspring = -kx
k represents the spring constant and is measured in N/m.
x represents how much the spring is compressed and is measured as you would
expect, in meters.
The - sign tells us that this is a restorative force.
(if you let the spring go once it is compressed, it
will go back to its original position)
Elastic Potential Energy
(F= -kx)
The work needed to compress a spring is equal to the area under its force vs. distance
curve.
Area of a triangle = 1/2 b h
W = 1/2 (x)(F)
W = 1/2 (x)(kx)
W = 1/2kx2
Elastic Potential Energy
The energy imparted to the spring by this work must be stored in the Elastic Potential
Energy (EPE) of the spring:
EPE = 1/2 k x2
Like all forms of energy, it is measured in Joules (J).
Determine the elastic potential energy stored in a spring whose spring
constant is 250 N/m and which is compressed 8 cm.
EPE = 0.5 kx2
EPE = 0.5 (250)(0.082)
answer
21
EPE = 0.8 J
What is the spring constant of a spring that is compressed 5 cm and has
0.65 J of elastic potential energy stored in it?
answer
22
EPE = 0.5 kx2
k = EPE/0.5x2
k = 0.65 / 0.5 (0.052)
k = 520 N/m
How much does a spring with a spring constant of 500 N/m need to be
compressed in order to store 1.75 J of elastic potential energy?
answer
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A 3 kg mass compresses a spring 2.5 cm. What is the spring constant?
answer
24
F
F
F
k
k = 1176 N/m
The same 3 kg mass compresses the same spring 2.5 cm. How much elastic
potential energy is stored in the spring?
answer
25
LAW OF CONSERVATION OF ENERGY
The law of Conservation of Energy:
Energy cannot be created or destroyed. It may
be transformed from one form into another;
however, the total amount of energy in the
universe remains constant. (Transformers)
LAW OF CONSERVATION OF ENERGY
Energy conversions occur without a gain or loss
in energy
Energy into a system = energy out of a system
Due to friction, energy might seem to be lost,
but it has changed into thermal energy.
.
ENERGY ANALOGY
When energy is transferred, it can transform
(change form) but it still remains energy.
Analogy:
How is energy like money?
When money is transferred from one person or place
to another it can change form (transform) but it still
remains money.
ENERGY TRANSFORMATIONS (BALL)
Demonstrate: how bounce height of ball becomes lower and
lower each time it bounces. Have students infer why this
happens.
Each time the ball bounces, part of its energy is
transformed into other forms of energy, such as
thermal (heat) energy, sound energy and
vibrations in the ground. In addition, some
energy is absorbed by the ball. Therefore, it will
never bounce as high as the initial drop height.
ENERGY TRANSFORMATIONS
Ex: A light bulb is a device that transforms
electrical energy into electromagnetic (light)
energy and thermal energy
Chemical energy (coal)
heat energy (burn
to create steam)
mechanical energy
(steam is used to turn turbines)
Electromagnetic energy (generates
electricity)
heat energy (blow drier,
oven)
ROLLER COASTER
PE: 354kJ
KE: 0kJ
V: 0m/s
h=70m
PE: 0kJ
KE: 354kJ
V: 37.1m/S
PE: 0kJ
KE: 354kJ
V:
37.1m/S
Potential energy
becomes Kinetic
energy.
Kinetic
energy can
become
Potential
177kJ
energy. PE:
KE: 177kJ
h=35
V: 26.2m/S
m
Conservation of Energy
A roller coaster is at the top of a track that is 80 m high. How fast will it be going at the
bottom of the hill?
Eo + W = Ef
Eo = Ef
W=0
GPE = KE
E0 = GPE, Ef = KE
mgh = 0.5mv2
Substitute GPE and KE equations
v2 = 2gh
Solving for v yields
v2 = 2 (9.8) 80
v =39.6 m/s
answer
A spring gun with a spring constant of 250 N/m is compressed 5 cm. How fast will a
0.025 kg dart go when it leaves the gun?
answer
A student uses a spring (with a spring constant of 180 N/m) to launch a marble
vertically into the air. The mass of the marble is 0.004 kg and the spring is compressed
0.03 m. How high will the marble go?
A student uses a spring gun (with a spring constant of 120 N/m) to launch a marble
vertically into the air. The mass of the marble is 0.002 kg and the spring is compressed
0.04 m.
a)How high will the marble go?
answer
b)How fast will it be going when it leaves the gun?
answer
A roller coaster has a velocity of 25 m/s at the bottom of the first hill.
How high was the hill?
answer
A student uses the lab apparatus shown above. A 5 kg block compresses a spring 6 cm.
The spring constant is 300 N/m. What will the block's velocity be when released?
answer
A 5 kg rock is dropped a distance of 1 m onto a spring. It compresses the spring 2 cm.
What is the spring constant?
answer
How much work is done in stopping a 5 kg bowling ball rolling with velocity of 10 m/s?
answer
How much work is done compressing a spring with a 450 N/m spring constant 2 cm?