Download Work, Energy and Power

Work, Energy and Power
In text: Ch 5
Do you already know these
words?
• Work –
• Energy –
• Power –
Looking a little deeper at…
Work
• First a demo:
• One volunteer
• Hold a couple of books and walk across the room.
• How much work was done to the book?
• Any? A lot? A little? None?
Looking a little deeper at…
Work:
• Is the product of the magnitude of the
displacement and the component of the force
acting in the direction of the displacement
• Is the force applied over a distance
• When a force acts upon an object to cause a
displacement of the object
• two key ingredients:
• Force
• displacement
Looking a little deeper at…
Work:
• Everyday examples:
• a horse pulling a plow through the field
• a father pushing a grocery cart down the aisle of a
grocery store
• a weightlifter lifting a barbell above his head
• Olympian launching the shot-put
• Can you identify the three parts in each
example?
Looking a little deeper at…
Work:
• Are these examples of work?
1. A teacher applies a force to a wall and becomes
exhausted.
2. A book falls off a table and free falls to the ground.
3. A waiter carries a tray full of meals above his head by
one arm straight across the room at constant speed.
4. A rocket accelerates through space.
Looking a little deeper at…
Work:
• Or… W = F d cosΘ
• d is displacement or Δx
• F is force applied
• Θ is the angle between the force and the
displacement vector
Looking a little deeper at…
Work:
• Notice that the application of a force alone does
not constitute work.
• Work can only be done when looking at the
force applied parallel to the displacement.
• Most of the time F is in the direction of d so θ =
0° and cos 0° = 1 so… it all works out.
Looking a little deeper at…
Work:
• Consider theta:
• Three basic situations
Looking a little deeper at…
Work:
• Consider theta:
• Be careful!!
• Pay attention to the direction of the
displacement and the applied force.
• Ex. A car being pushed up a ramp
Looking a little deeper at…
Work:
• Consider “the sign”:
• If force and displacement are in the…
• Same directions, + W
• Opposite directions, - W
• Perpendicular directions, W = 0
See fig. 3 pg 162
Looking a little deeper at…
Work:
• Consider “the sign”:
• Ex. car skidding to a stop on a roadway surface
• Ex. a baseball runner sliding to a stop on the
infield dirt
Looking a little deeper at…
Work
• From all that we can say that the total work
done is dependant on the total force applied.
So….
• Wnet = Fnet d cosΘ
• So, what are the units?
•
•
•
•
If we break it down
W=F*d
?=N*m
J=N*m
• Basic question:
• What work is done to lift your Physics book
(m=12kg) up 1 m?
• What work is done to carry the book 1 m
across the room?
• Try this:
What is the work done on a vacuum
cleaner pulled 3m by a force of 50N at
an angle of 30° above the horizontal?
Working solution…
• The angle of the force means we have
to find the force acting in the direction
that the bag moves.
• It moves in the x-position, so we will use
the Fx component
• The upward component doesn’t do any
work as the y-position doesn’t change.
• Pg 162 Practice A
A few more:
• A 20kg suitcase is raised vertically 3m above a
platform by a conveyor belt. How much work is
done on the suitcase?
• A 100 N force is applied to move a 15kg object a
horizontal distance of 5m at constant speed.
• A 100N force is applied at an angle of 30° to the
horizontal to move a 15kg object at a constant
speed for a horizontal distance of 5m.
• An upward force is applied to lift a 15kg object to
a height of 5m at constant speed.
How ‘bout those angles:
• How far did a flying shark pull a box if it exerted a
force of 100N at an angle of 25°. It also did
1200J of work.
• You are at the beach and notice somebody in
trouble about 30m away from you. You throw a
rope to them and pull them in to the beach at an
angle of 15° above the horizontal. You did 7500J
of work. What is the force you used?
• You are pulling your little red wagon at an angle of
53.1° You pull it for a distance of 15m and do
90J of work.
Answers:
A.588J
B.500J
C.433J
D.735J
Energy – Flow Chart
Energy
Mechanical
Kinetic
Non-mechanical
Potential
Linear
Rotational
Gravitational
Elastic
Sound
Heat
Light
Chemical
Electric
Looking a little deeper at…
Energy
• In general Energy is the ability to do
work and create change.
• We will look at two basic types of
energy.
• Kinetic
• Potential
• We will also look at the conservation of
energy.
Kinetic
• Associated with objects in motion
• Depends on both an objects
speed and mass
• It is a scalar quantity
Kinetic
• Kinetic energy = 1/2 *mass*speed2
• KE=1/2 mv2
• The unit of KE is joule(J)
• If the speed is doubled the energy is
quadrupled.
Kinetic
• A bowling ball and a volleyball roll at the
same speed.
• Which has more kinetic energy?
Kinetic
• A 7kg bowling ball moves at 3 m/s.
How fast must a 2.45 g ping pong ball
move to have the same kinetic energy
as the bowling ball?
• KE=1/2 mv2
Practice:
• Determine the kinetic energy of a 625-kg roller coaster car
that is moving with a speed of 18.3 m/s.
• If the roller coaster car in the above problem were moving
with twice the speed, then what would be its new kinetic
energy?
• Missy Diwater, the former platform diver for the Ringling
Brother's Circus, had a kinetic energy of 12 000 J just prior
to hitting the bucket of water. If Missy's mass is 40 kg,
then what is her speed?
• A 900-kg compact car moving at 60 mi/hr has
approximately 320 000 Joules of kinetic energy. Estimate
its new kinetic energy if it is moving at 30 mi/hr. (HINT: use
the kinetic energy equation as a "guide to thinking.")
Answers:
A.105,000J
B.419,000J
C.24.5m/s
D.80,000J
Potential
• Associated with an object that has the
potential to move because of its position
• Depends on the interaction with its
environment
• store energy as the
result of its position
Potential
• Gravitational potential energy
• Potential energy due to gravity
• the energy stored in an object as the
result of its vertical position or height.
• PEg = mass*free-fall acceleration*height
• PEg = mgh
Potential
• PEg = mgh
• Notice that PEg is dependant on free-fall
acceleration being constant.
• Also notice that g and h aren’t properties of
the actual object.
Potential
• PEg = mgh
• The higher that an object is elevated, the
greater the gravitational potential energy
• a doubling of the height will result in a
doubling of the gravitational potential energy
Potential
• Is it possible to have a negative
potential energy?
• Can an object have both a positive
potential energy and a negative
potential energy?
Potential
• How is h defined?
• Relative to a “zero”
• What can be a “zero”?
• Anything can be defined as “zero”
• Discussion: A ball that falls from one
building rooftop to another buildings
rooftop. Where is zero?
Potential
Springs!!!
Potential
Springs:
• a device which can store elastic potential energy
due to either compression or stretching
• force is required to compress a spring
• the amount of force is directly proportional to the
amount of stretch or compression
• Equilibrium position – when a spring isn’t being
stretched or compressed
Potential
• Springs:
• Fspring = k * x
• k is the spring constant
• x is the amount stretched or compressed
Potential
• Relaxed length
• Length of spring when no external forces
are acting on it.
• Nothing is pulling or pushing it.
• Spring Constant
• Small for flexible springs
• Large for stiff springs
• Units of (N/m)
• PEtotal = PEg + PEspring
Potential
• Elastic Potential energy
• Stored in any compressed or stretched object
• PEelastic = ½*spring constant*(distance
compressed or stretched)2
• PEelastic = ½kx2
Practice:
• Pg 166 practice B # 1-5
• Pg 172 practice D # 1-3
Practice:
• A 70kg stuntman is attached to a bungee cord with an unstretched length of 15m. He jumps off a bridge spanning a
river from a height of 50m. When he finally stops, the cord
has a stretched length of 44m. Treat the stuntman as a
point mass, and disregard the weight of the bungee cord.
Assuming the spring constant of the bungee cord is
71.8N/m, what is the total potential energy relative to the
water when the man stops falling?
Practice:
1. Mr. B got a new fish tank. As he moves it he
uses 200J of work. He pushes it with a force
of 50N at an angle of 30°. How far did he
push the tank?
2. The mass of the fish tank is 50kg. How fast
did Mr. B push the tank?
3. Once the tank is set up the water has a
height of 1.8m and a mass of 150kg. How
much potential energy does the water have?
4. A mass is hung from a slinky it stretchs the
slinky .4m. The slinky has a spring constant
of .3N/m. How much potential energy does
the spring have?
Answers:
A.13.2J
B.13.2J
C.34,300J
Energy – Flow Chart
Energy
Mechanical
Kinetic
Non-mechanical
Potential
Linear
Rotational
Gravitational
Elastic
Sound
Heat
Light
Chemical
Electric
HEAT AND TEMPERATURE
Temperature
• Temperature: A measure of how hot (or cold)
something is
• Specifically, a measure of the average kinetic
energy of the particles in an object.
Concept Check
• What is the relationship
between the temperature of a
substance and the speed of its
molecules?
• High temperature = _____ KE
(high or low)?
Thermometers
a.
• Thermometer: an instrument that measures
and indicates temperature
b.
c.
Bimetallic
strip
Temperature Scales
• Kelvin
• International System (SI) of measurement
• Fahrenheit
• Celsius
Kelvin and Absolute Zero
• The Kelvin scale is based on absolute zero
• Absolute Zero: the temp at which molecular
movement stops
• 0 K on the Kelvin scale = -273.16ºC
What is heat?
• Heat: the transfer of energy
between objects that are at
different temperatures.
• All matter has heat.
• Measured in JOULES
Heating and Cooling
• If an object has become hotter,
it means that it has gained heat energy.
• If an object cools down, it means it has
lost energy
Endothermic and Exothermic
Processes
• Endothermic Process – heat is
absorbed from the surroundings
• Endo = Into
HEAT
Endothermic and Exothermic
Processes
• Exothermic process – heat is
released into the surroundings
• Exo = Exit
HEAT
Heating and Cooling cont…
• Heat energy always moves from:
HOT object
COOLER object
ex1. Cup of water at 20 °C in a room at 30°C gains heat energy and heats up – its temperature
rises
ex2. Cup of water at 20 °C in a room at 10°C
loses heat energy and cools down – its temperature
will fall.
ARE HEAT AND TEMP THE
SAME THING?
• NO….although the two quantities are
related.
Example: a beaker of water at 60 °C is
hotter than a bath of water at 40 °C BUT
the bath contains more joules of heat energy
Review
What is the difference between heat and
temperature?
• HEAT is energy that transfers from one
object/substance to another
• TEMPERATURE is a measure of the
amount of energy an object/substance has
(how quickly the molecules are moving
around)
Measuring Heat Flow
Two Common Units
• Joule
• calorie
4.184 J = 1 cal
1Calorie = 1 kilocal = 1000 cal
Concept Check
• What causes heat to flow?
Energy Transfer
• The transfer of heat is normally from a
high temperature object to a lower
temperature object.
1) Conduction
• Thermal Conduction: the transfer of heat
within a substance, molecule by
molecule.
2) Convection
• Convection: the movement of matter due to
the differences in density that are caused by
temp. variations applet
3) Radiation
• Radiation: the energy that is transferred as
electromagnetic waves, Doesn’t need matter
• Most radiation comes from the sun
Conductor vs. Insulator
• Conductor: any material through which
energy can be transferred as heat
• Insulator: poor conductors
Energy
Definition of Energy
• The ability to do work
• Potential energy is the energy of position
• Kinetic energy is the energy of motion
(depends on speed and mass)
• Mechanical energy= Potential + Kinetic
energy
The Law of Conservation of
Energy
• States that energy can be neither created nor
destroyed, it is conserved
• Energy can transform from one form to
another, but it always adds up to the same
amount.
Energy conversion
• Mechanical energy is converted into thermal energy
whenever you bounce a ball. Each time the ball hits the
ground, some of the energy of the ball's motion is
converted into heating up the ball, causing it to slow down
at each bounce
Forms of energy
• Energy can neither be created nor
destroyed, but it can be changed into
different forms of energy…
• This is energy transformation.
• The forms include: thermal (heat),
chemical, electrical, sound, light, nuclear
Conservation of Energy
• What does it mean to conserve
something?
• Think about:
• Recycling
• Money
• H2O
Lingo to Know
• Mechanical Energy is:
• the energy which is possessed by an object
due to its motion or due to its position.
• the total kinetic energy and potential energy
associated with an object
• ME = KE + PEtotal
• Mechanical energy is just a classification,
not another type of energy.
Lingo to Know
• Nonmechanical energy:
• Other forms of energy
• Ex. light, sound, heat
Conservation of Energy
With that said:
• Mechanical energy is conserved (in the
absence of friction)
• So => initial mechanical energy = final
mechanical energy
So => MEi = MEf
So => KEi + Ptotal,i = KEf + Petotal,f
Conservation of Energy
This is famed snowboarder Mr. Williams!
Notice his ME is constant the entire
time.
Conservation of Energy
• The question is if a 75g egg falls off a 1m
counter top what is it’s total ME half way
down?
• To better understand lets remember a few
things.
• First Vf = Vi + aΔt
• Second Δx = ½ (Vi + Vf)Δt
Conservation of Energy
• Lets make a chart:75g egg/1m
Time
0s
.1s
.2s
.3s
.4s
Vf
KE
Δx
Height
PE
ME
Law of Conservation of
Energy
• Energy can neither be created nor
destroyed
• Energy is always changing from one
kind to another.
• The total energy of an object never
changes.
Conservation of Energy
• Mechanical energy is not conserved in
the presence of Kinetic friction.
So what happens to the energy?
• Ex rubbing your hands together
• Total energy is always conserved, but
mechanical energy is lost.
• Mechanical energy is converted in to…
Conservation of Energy
• Now can you answer this basic
question: If an object (m=10kg) falls
from a height of 10 m, what is it’s:
• Potential and kinetic energy at the top
• Potential and kinetic energy just before
hitting the ground.
Practice:
• Starting from rest, a child zooms down a
frictionless slide from an initial height of 3m.
What is her speed at the bottom of the
slide? Assume she has a mass of 25kg
Practice:
• A frog is sitting on a rock. It sees a cat that is
trying to eat it. The frog jumps directly up with an
initial velocity of .85m/s. What is the total height
the frog jumps?
• The cat then jumps directly upward 1.2m. What
was the initial velocity of the cat’s jump?
POWER!!!
• What is power!!
• Tim “the tool man” Taylor knows what
power is, right???
• Not quite
POWER!!!
• Lets look at:
• a rock climber takes 30min. to elevate his
body up a few meters along the side of a
cliff.
POWER!!!
• Lets look at:
• a trail hiker, who selects the easier path
up the mountain, might elevate his body a
few meters in 10min.
POWER!!!
• They both do the same amount of work.
• Which one had more power?
POWER!!!
• is the rate at which work is done
• or the rate at which energy is consumed
• P = W/t
So….
• The more power you have the more
work you can do in the same time.
• The more power you have you can do
the same amount of work in a shorter
time.
• There is an inverse relationship
between work and power
How did we get there?
Remember: P = W/t
Quick review: what is work?
• W = Fd
Quick review: what is velocity?
• v = Δx/Δt or v = d/t
• So P = F (d/t)
• Or P = F v
POWER!!!
• P=Fv
• This equation shows us that a powerful
machine is both strong (big force) and
fast (big velocity).
• Ex. A powerful car engine is strong and
fast.
That was a lot to take in
• Equations for power are:
•
•
•
•
P = W/t
P = F (d/t)
P=Fv
P = ΔE/t
W

E
Fd
P


F
av
e
a
t t t
What units??
The SI unit of power is the watt.
• 1 watt is = 1 joule / second
• W=J/s
What units??
Horsepower is also a unit.
• 1 horsepower = 746 watts
• Hp = 746W
Examples of power
•
•
•
•
A dim light bulb 40 W
A really bright bulb 500 W
Indoor Christmas light .7 W
Outdoor Christmas light 7 W
Examples situation
• A 193kg curtain needs to be raised
7.5m, in 5s. You have 3 motors with
power ratings 1.0kW, 3.5kW and 5.5kW.
Which motor is best for the job?
• How much time would it take for
each motor to do the same amount of
work?
Examples situation
• Two horses pull a cart. Each exerts a
force of 250.0 N at a speed of 2.0 m/s
for 10.0 min.
• 1) What is the power delivered by the
horses?
• 2) How much work is done by the two
horses?
Practice:
• Two physics students, Will N. Andable and Ben Pumpiniron,
are in the weightlifting room. Will lifts the 100-pound barbell
over his head 10 times in one minute; Ben lifts the 100-pound
barbell over his head 10 times in 10 seconds. Which student
does the most work? Which student delivers the most power?
• During a physics lab, Jack and Jill ran up a hill. Jack is twice as
massive as Jill; yet Jill ascends the same distance in half the
time. Who did the most work? Who delivered the most power?
(plug in fake numbers)
• When doing a chin-up, a physics student lifts her 42.0-kg body
a distance of 0.25 meters in 2 seconds. What is the power
delivered by the student's biceps?
• Mr. B gets bored after school one day and decides to play in
the hall. He sits in his rolling chair and pushes off the wall with
12N of force producing 30W of power. What was his resulting
speed he traveled down the hallway?
Answers:
A.1