Transcript PHYSICS CHAPTERS 10

CHAPTERS 10 & 11
10.1 Energy and Work
ENERGY:
Energy =
The property/ability to produce a change in
an object or the environment
Forms of Energy:
Thermal, chemical, solar, nuclear, hydro,
fossil fuel, …
Kinetic Energy “K or KE” =
The energy an object has due to its motion
Equation:
K = ½ mv2
Units for KE, kgm2/s2 = Nm
Work “W” =
The process of changing the energy in a
system
W = Fdcos
If Force and displacement are in the same
direction then W = Fd
Units, Nm
Work Energy Theorem:
W = ΔK
W = K2 – K1
Joule “J” = unit of energy
1J = 1kgm2/s2 = 1Nm
WORK
ENERGY TRANSFER
If the environment does work on the
system, then work “W” is positive (+) and
the energy of the system increases.
If the system does work on the
environment, then W is negative (-) and
the energy of the system decreases.
System/Box example, put in/out
CALCULATING WORK
Example with stack of books & 2
volunteers
Who did more work and WHY?
When _______ picked up the book, she
applied a force in the same direction as
displacement,  work was done.
When ________ carried the books
throughout the room, his force on the
books was perpendicular (90o) to
his/books displacement,  NO work was
done, as far as physics is concerned.
Biologically, ______’s muscles did perform
work and required much more energy than
________ to simply pick up one book.
Earth & Sun Example
Mass of Earth = 5.97 x 1024kg
Speed of Earth = 20,000 m/s
Q: What is the KE of the Earth?
A: 1.194 x 1033J
Q: How much work does the sun do on the
Earth while keeping it in orbit?
A: zero
Q: Why?
A: two reasons
Explanation #1
W = ΔK
W = K2 – K1
W = 1/2mv22 – 1/2mv12
W = 1/2(5.97 x 1024kg)(20,000m/s)2 –
½(5.97 x 1024kg)(20,000m/s)2
W = 1.194 x 1033J – 1.194 x 1033J
W=0
Explanation #2
W = Fdcos
W = Fdcos90o
W = Fd(0)
W=0
 if force and displacement are
perpendicular to each other (90o), then NO
work is accomplished
Example Problem
A 150g hockey puck is at rest on ice. A
player exerts a constant 400N force over a
distance of 0.15m.
a) How much work does the player do to
the puck?
b) What is the Δ in the puck’s energy?
c) What is the velocity of the puck when it
leaves the stick?
Solution “a”
W = Fdcos
W = (400N)(0.15m)(cos 0o)
W = (400N)(0.15m)(1)
W = 60Nm
W = 60J
Solution “b”
ΔK = W
 ΔK = W = 60J
Solution “c”
ΔK = K2 – K1 = 60J
1/2mv22 – 1/2mv12 = 60J
½(.15kg)(v22) – 0 = 60J
0.075kg(v22) = 60kgm2/s2
v22 = 60kgm2/s2/0.075kg
v22 = 800m2/s2
v2 = √800m2/s2
v2 = 28.3m/s
Example Problem #1
A student lifts a box of books that weigh
185N. The box is lifted 0.8m. How much
work did the student do on the box?
A: W = FD = (185N)(.8m) = 148Nm/J
Example Problem #2
Two students together exert a force of
825N in pushing a car 35m.
a) How much work do they do on the car?
b) If the force were doubled, how much
work would they do pushing the car the
same distance?
A-a: W = Fd = (825N)(35m) = 28,875J
A-b: W = Fd = (1650N)(35m) = 57,750J
Example Problem #3
A 0.18kg ball falls 2.5m. How much work
does the force of gravity do on the ball?
A: W = Fd = ?????
What is the force?????
F = weight due to gravity = mg
W= mgd = (.18kg)(9.8m/s2)(2.5m) =4.41J
Example #4
A forklift raises a box 1.2m doing 7kJ of
work on it. What is the mass of the box?
A: W = Fd = mgd
m = W/gd
m = 7000kgm2s2/(9.8m/s2 x 1.2m)
m = 595kg
Example #5
You and a friend each carry identical
boxes to a room one floor above you and
down the hall. You choose to carry it first
up the stairs, then down the hall. Your
friend carries it down the hall, then back,
then down the hall again, then up the
stairwell. Who does more work?
Both do the same. The work done was
only carrying the box up the stairs.
Lawn Mower Example (pg227)
How much work is done by Hannah if she
pushes a lawn mower 10m with a force of
125N at an angle of 25o from horizontal?
Draw sketch, equation, steps,…
W = Fdcos
W = (125N)(10m)(cos25o)
W = 1132.8J
Finding Work Done When Forces
Change
Sketch 3 examples of Force vs
displacement graphs
a) rectangle
b) triangle
c) ½ circle
 Using a Force vs displacement graph,
the work done on an object is represented
by the area under the curve/line.
POWER
Power =
The rate of doing work.
Power “P” = W/t
W = work in joules
t = time in seconds
P = W/t (J/s)
1J/s = 1 W (watt)
A watt “W” is a small amount of power 
power is usually measured in kW
(kilowatts).
Power plant outputs are measured in MW
(MegaWatts)
Shippingport Nuclear plants  900MW (2)
Shippingport Bruce Mansfield, coal plants
 1200MW (3)
Light Bulb Example
How long can you leave a light on at home
before your parents yell at you?
Light bulb watts = _____
Time to get in trouble = _____
Cost of a kWhr  12 cents per kWhr,
National Average as of 4-4-11
Power Example
An electric motor lifts an elevator 9m in
15s by exerting an upward force of
12,000N. How much power did it take to
raise the elevator?
P = W/t
P = Fd/t
P = (12,000kgm/s2)(9m) ÷ 15s
P = 7200kgm2/s2
P = 7200W
11.1 THE MANY FORMS OF
ENERGY
A Model of The Work-Energy Theorem
Your own notes
Kinetic Energy
KE = energy due to an object’s motion
KE = ½ mv2
A 1000kg car is traveling at 20m/s, how
much KE would it have if its velocity
doubled?
KE = ½ mv2
KE = ½ (1000kg)(20m/s)2
KE = ½ (1000kg)(400m2/s2)
KE = 200,000J
KE = ½ (1000kg)(40m/s)2
KE = ½ (1000kg)(1600m2/s2)
KE = 800,000J
Example
A 555kg car is traveling at 15m/s, a force
is applied increasing its velocity to 40m/s.
a) What is the initial and final KE?
b) How much work was done to the car?
STORED ENERGY
Example with chair, book, meter stick &
eraser/…..????
Stored Energy = Potential Energy = …
The energy stored in an object that has
the “potential” to do work.
Examples:
Stretched springs, chemical, batteries, …
GRAVITATIONAL POTENTIAL
ENERGY
Gravitational potential energy “Ug” =
The stored energy in an object by virtue of
its position above some reference level
and the force of gravity acting on it.
Ug = mgh
W = Fdcos → when  = 0 → W = Fd
 W = mad
W = ΔUg = Δmgh
Example Tossing Ball
How does gravity affect
the work done on the
ball?
When is the work positive,
Negative, zero?
When is the acceleration
Positive, negative, zero?
Sketch diagrams of Force & d
How does gravity affect work?
On the way up, the work done by gravity is
negative.
Why?
Because F & d are in opposite directions,
the force (force of gravity) is in the
negative direction (pulling down), but the
displacement is positive (upward).
W = ∆Ug = Δmgh = m(-g)(h)
At the top.
Work is zero
Why?
B/c ball is not moving. W = m(-g)(0) = 0
On the way down.
Work is positive.
Why?
Because W = ∆mgh = m(-g)(-h)
W = Fd
Using W = ∆K = K2 - K1
On the way up the ball looses KE,
therefore K2 is less than K1 making W = a
negative value.
On the way down the ball increases its KE,
therefore K2 is greater than K1 making W
= a positive value.
Refer to book on a stool
example again
Does the book have any PE (Ug) when its
on the stool?
Does the book have any Ug (PE) when its
laying on the desk?
Does the book have any Ug when its
laying on the floor?
Answer ???????????????????????
We cannot say.
WHY?
ANSWER
Because a “REFERENCE LEVEL” was not
established, therefore a determination if
the book has Ug cannot be made.
REFERENCE LEVEL =
Some arbitrary point where the
gravitational potential energy (Ug) is = 0
The reference level must established
before an object’s Ug can be determined.
Return to Book-Chair-Eraser
Example
Does the book have any PE (Ug) when its
laying on the desk?
No/Yes??
Does the book have any PE when its
laying on the floor?
No/Yes??
Answer =
We cannot say for sure.
WHY???????
Because we did not establish a
REFERENCE LEVEL.
Reference Level = some arbitrary point
where the gravitational potential energy
(Ug-PE) is equal to ZERO
the reference level would have to be
established before we could determine if
the book has any PE or not.
Elastic Potential Energy
Elastic Potential Energy =
The potential energy stored in an object
that is released as KE when the object
undergoes Δ form or shape.
Examples:
Rubber band, trampoline, springs, bow &
arrow, pole vault pole
11.2
CONSERVATION OF
ENERGY
CHOOSING A SYSTEM
Drop a ball, roll a ball, slide a book, …etc
Q: Why do they stop?
Newton’s First Law, AKA Law of Inertia,
says “An object at rest remains at rest and
an object in motion remains at a constant
velocity unless an outside net force acts
on it”
The Law of Conservation of Energy is a
description of nature. As long as the
“system” under investigation is closed so
that the objects do not move in and out,
and as long as the system is isolated from
external forces, then the energy can only
change form. The total amount of energy
remains constant. In other words, energy
can neither be created nor destroyed, in a
closed, isolated system, energy can only
change form, ENERGY IS CONSERVED.
Mechanical Energy
E = KE + Ug
for this chapter, there are other forms of
mechanical energy
Conservation of mechanical energy
E1 = E2
KEbefore + Ugbefore = KEafter + Ugafter
K = 1/2mv2
Ug = mgh
Ball thrown off cliff example
Draw on board.
Q: Where does the ball have the greatest
amount of energy? Point A,B,C,D,E…???
A: Same amount everywhere
If the ball has a mass of 0.5kg, what is the
velocity of the ball a) just before it hits the
ground and b) when it leaves the hand???
Choosing A system Continued
Q: What weighs more
a) Cold potato or hot potato
b) Straight or bent pole vault pole
Answers:
a) Hot potato
b) Bent pole vault pole
Q: WHY?????
Energy is transferred to the hot potato and
bent pole, this energy has mass, however
the added mass is in the form of energy, in
this case the mass is insignificant but the
added energy does add small amounts of
weight to objects. This can be compared
to adding a bucket of water to the oceans
or dropping a ball and having the Earth
accelerate upwards during free fall.
Albert Einstein
What was Albert Einstein’s most famous
equation?
E = mc2
E = energy
m = mass
c = speed of light in a vacuum
if E is added and the speed of light is a
constant, then the mass must increase
When forces holding atoms together in the
nucleus are considered, huge amounts of
energy can be released when mass
changes/decreases. This happens when
atoms are split (fission), enourmous
amounts of energy is released due to
nuclear fission. Hence; nuclear power and
nuclear weapons.
ANALYZING COLLISIONS
Examples of Elastic, Inelastic and
Super-elastic collisions on board.