Transcript File

Work, Energy & Power
IB Physics
There are many different TYPES of
Energy.



Energy is expressed
in JOULES (J)
4.19 J = 1 calorie
Energy can be
expressed more
specifically by using
the term WORK(W)
Work = Force x Displacement
if you apply a force on an object and it covers a displacement you
have supplied ENERGY or done WORK on that object.
Force must be parallel to displacement
 

W  F  x  Fx cos
F and x MUST be parallel. To ensure that
they are parallel we add the cosine on the
end.
FORCE
Displacement
 

W  F  x  Fx cos 
  0 ; cos 0  1

W  Fx
Work
 

W  F  x  Fx cos
FORCE
Displacement
 

W  F  x  Fx cos 
  180 ; cos180  1

 
W   Ff x
Work
 

W  F  x  Fx cos
FORCE
Displacement
 

W  F  x  Fx cos 
  90 ; cos 90  0

W  0J
Work
 

W  F  x  Fx cos
the woman is applying a force at an angle.
Only the HORIZONTAL COMPONENT actually causes the box to
move and thus imparts energy to the box. The vertical component
(FsinQ) does NO work on the box because it is NOT parallel to the
displacement.
The Work Energy Theorem
WORK-ENERGY THEOREM says
that if we do work on an object it
will undergo a CHANGE in speed
and thus a change in KINETIC
ENERGY.
Since both WORK and KINETIC
ENERGY are expressed in
JOULES, they are EQUIVALENT
TERMS!
" The net WORK done on an object is equal to the change in kinetic
energy of the object."
Work-Energy Theorem
Due to friction, energy is transferred both into the floor and
into the tire when the bicycle skids to a stop.
a. An infrared camera reveals the heated tire track on the
floor.
b. The warmth of the tire is also revealed.
Work-Energy Theorem
Typical stopping distances for cars equipped with
antilock brakes traveling at various speeds. The work
done to stop the car is friction force × distance of
slide.
Example
Suppose the woman in the figure above applies a 50 N force to a
25-kg box at an angle of 30 degrees above the horizontal. She
manages to pull the box 5 meters.
a) Calculate the WORK done by the woman on the box
b) The speed of the box after 5 meters if the box started from rest.

W  Fx cos 
W  (50)(5) cos 30 
216.5 J
W  KE  1 mv 2
2
W  1 (25)v 2
2
v  4.16 m/s
Force – displacement graphs
F
If the applied force on a body varies, the
total work done can still be found:
F
x
x
Total work done = area under a force-displacement graph.
E.g. Extending springs
We know that a spring obeys Hooke’s law, i.e. its
extension, x is proportional to the force applied, F:
As the spring extends the applied force
must increase to a maximum value, F:
F
 Average force applied = ½F
x
 Work done on spring = ½Fx
(This can also be seen from the area
under the graph)
 Energy stored in spring = ½Fx
Lifting mass at a constant speed
Suppose you lift a mass upward at a constant
speed, v = 0 & K=0. What does the work
equal now?
Since you are lifting at a constant
speed, your APPLIED FORCE
equals the WEIGHT of the object
you are lifting.
Since you are lifting you are raising
the object a certain “y”
displacement or height above the
ground.
When you lift an object above the ground it is said to have POTENTIAL ENERGY
Potential Energy

W  Fx cos  F  mg; x  h
  0, cos 0  1
W  mgh  PE
h
mg
Since this man is lifting the package
upward at a CONSTANT SPEED, the
kinetic energy is NOT CHANGING.
Therefore the work that he does goes
into what is called the ENERGY OF
POSITION or POTENTIAL ENERGY.
All potential energy is considering to be
energy that is STORED!
Potential Energy
The man shown lifts a 10 kg package
2 meters above the ground. What is
the potential energy given to the
package by the man?
PE  mgh
h
PE  (10)(9.8)( 2) 
196 J
Suppose you throw a ball upward
W  KE  PE
What does work while it is
flying through the air?
GRAVITY
Is the CHANGE in kinetic
energy POSITIVE or
NEGATIVE?
NEGATIVE
 KE  PE
 ( KE  KEo )  PE  PEo
 KE  KEo  PE  PEo
KEo  PEo  KE  PE
Is the CHANGE in potential
energy POSITIVE or
NEGATIVE?
POSITIVE
 Energy
Before
  Energy After
Potential Energy
The potential energy of the 100-N boulder with respect to the ground below
is 200 J in each case.
a. The boulder is lifted with 100 N of force.
Potential Energy
The potential energy of the 100-N boulder with respect to the ground below
is 200 J in each case.
a. The boulder is lifted with 100 N of force.
b. The boulder is pushed up the 4-m incline with 50 N of force.
Potential Energy
The potential energy of the 100-N boulder with respect to the ground below
is 200 J in each case.
a. The boulder is lifted with 100 N of force.
b. The boulder is pushed up the 4-m incline with 50 N of force.
c. The boulder is lifted with 100 N of force up each 0.5-m stair.
ENERGY IS CONSERVED
The law of conservation of mechanical energy
states: Energy cannot be created or
destroyed, only transformed!
Energy Before
Energy After
Am I moving? If yes,
Ko
Am I moving? If yes,
K
Am I above the
ground? If yes, Uo
Am I above the
ground? If yes, U
Conservation of Energy
A
B
C
D
In Figure A, a pendulum
In Figure B,
is a pendulum
In Figure C,
is astill
pendulum
In Figure D,
is the
at the
pendulum has
released from above
rest at the
some
ground
height
ground
position,
position
yet
reached
and
it is moving
the same
with a
height above
above the ground
alsoposition.
moving. maximum velocity.
the ground position as A.
It has only potential
It has energy.
BOTH potential
It has only
energy
kinetic
Itand
has
energy.
only potential energy.
kinetic energy.
Conservation of Energy
Part of the PE of the wound spring changes into KE. The
remaining PE goes into heating the machinery and the
surroundings due to friction. No energy is lost.
Conservation of Energy
When the woman leaps from the
burning building, the sum of her PE
and KE remains constant at each
successive position all the way down
to the ground.
Energy consistently changes forms
ME = PE + KE
Energy consistently changes forms
Am I above the ground? NO, h = 0, U = 0 J
Am I moving? Yes, v = 8 m/s, m = 60 kg
K  1 mv 2  1 (60)(8)2
2
2
K  1920 J
Position
m
v
U
K
ME
(= U+K)
1
60 kg
8 m/s
0J
1920 J
1920 J
Energy consistently changes forms
Energy Before
= Energy After
KO
=U+K
1920= (60)(9.8)(1) + (.5)(60)v2
1920= 588 + 30v2
1332 = 30v2
44.4 = v2
v
= 6.66 m/s
Position m
v
U
1
60 kg
2
60 kg
8 m/s
0J
6.66 m/s 588 J
K
ME
1920 J
1332 J
1920 J
1920 J
Energy consistently changes forms
Am I moving at the top?
EB =
Using
Ko
1920
1920
h
No, v = 0 m/s
EA
position 1
= U
= mgh
=(60)(9.8)h
= 3.27 m
Position
m
v
U
K
ME
1
60 kg
8 m/s
0J
1920 J
1920 J
2
60 kg
6.66 m/s
588 J
1332 J
1920 J
3
60 kg
0 m/s
1920 J
0J
1920 J
Power
One useful application of Energy
is to determine the RATE at
which we store or use it. We
call this application POWER!
As we use this new application,
we have to keep in mind all
the different kinds of
substitutions we can make.
Unit = WATT or Horsepower
Important formulas and units
Quantity
Force
Work
Energy
Power
Definition
mass x accel.
force x distance
power x time
work / time
Units
newtons
joules
joules
watts
Assessment Questions
1.
Raising an auto in a service station requires work. Raising it twice
as high requires
a. half as much work.
b. the same work.
c. twice the work.
d. four times the work.
Assessment Questions
1.
Raising an auto in a service station requires work. Raising it twice
as high requires
a. half as much work.
b. the same work.
c. twice the work.
d. four times the work.
Answer: C
Assessment Questions
2.
Raising an auto in a service station requires work. Raising it in half the
time requires
a. half the power.
b. the same power.
c. twice the power.
d. four times the power.
Assessment Questions
2.
Raising an auto in a service station requires work. Raising it in half the
time requires
a. half the power.
b. the same power.
c. twice the power.
d. four times the power.
Answer: C
Assessment Questions
3.
The energy due to the position of something or the energy due to
motion is called
a. potential energy.
b. kinetic energy.
c. mechanical energy.
d. conservation of energy.
Assessment Questions
3.
The energy due to the position of something or the energy due to
motion is called
a. potential energy.
b. kinetic energy.
c. mechanical energy.
d. conservation of energy.
Answer: C
Assessment Questions
4.
After you place a book on a high shelf, we say the book has
increased
a. elastic potential energy.
b. chemical energy.
c. kinetic energy.
d. gravitational potential energy.
Assessment Questions
4.
After you place a book on a high shelf, we say the book has
increased
a. elastic potential energy.
b. chemical energy.
c. kinetic energy.
d. gravitational potential energy.
Answer: D
Assessment Questions
5.
An empty truck traveling at 10 km/h has kinetic energy. How much
kinetic energy does it have when it is loaded so its mass is twice, and
its speed is increased to twice?
a. the same KE
b. twice the KE
c. four times the KE
d. more than four times the KE
Assessment Questions
5.
An empty truck traveling at 10 km/h has kinetic energy. How much
kinetic energy does it have when it is loaded so its mass is twice, and
its speed is increased to twice?
a. the same KE
b. twice the KE
c. four times the KE
d. more than four times the KE
Answer: D
Assessment Questions
6.
Which of the following equations is most useful for solving a problem
that asks for the distance a fast-moving crate slides across a factory
floor in coming to a stop?
a. F = ma
b. Ft = ∆mv
c. KE = 1/2mv2
d. Fd = ∆1/2mv2
Assessment Questions
6.
Which of the following equations is most useful for solving a problem
that asks for the distance a fast-moving crate slides across a factory
floor in coming to a stop?
a. F = ma
b. Ft = ∆mv
c. KE = 1/2mv2
d. Fd = ∆1/2mv2
Answer: D
Assessment Questions
7.
A boulder at the top of a vertical cliff has a potential
energy of 100 MJ relative to the ground below. It rolls off
the cliff. When it is halfway to the ground its kinetic
energy is
a. the same as its potential energy at that point.
b. negligible.
c. about 60 MJ.
d. more than 60 MJ.
Assessment Questions
7.
A boulder at the top of a vertical cliff has a potential
energy of 100 MJ relative to the ground below. It rolls off
the cliff. When it is halfway to the ground its kinetic
energy is
a. the same as its potential energy at that point.
b. negligible.
c. about 60 MJ.
d. more than 60 MJ.
Answer: A
Assessment Questions
8.
In an ideal pulley system, a woman lifts a 100-N crate by pulling a
rope downward with a force of 25 N. For every 1-meter length of rope
she pulls downward, the crate rises
a. 25 centimeters.
b. 45 centimeters.
c. 50 centimeters.
d. 100 centimeters.
Assessment Questions
8.
In an ideal pulley system, a woman lifts a 100-N crate by pulling a
rope downward with a force of 25 N. For every 1-meter length of rope
she pulls downward, the crate rises
a. 25 centimeters.
b. 45 centimeters.
c. 50 centimeters.
d. 100 centimeters.
Answer: A
Assessment Questions
9.
When 100 J are put into a device that puts out 40 J, the efficiency of
the device is
a. 40%.
b. 50%.
c. 60%.
d. 140%.
Assessment Questions
9.
When 100 J are put into a device that puts out 40 J, the efficiency of
the device is
a. 40%.
b. 50%.
c. 60%.
d. 140%.
Answer: A
Assessment Questions
10. An energy supply is needed for the operation of a(n)
a. automobile.
b. living cell.
c. machine.
d. all of these
Assessment Questions
10. An energy supply is needed for the operation of a(n)
a. automobile.
b. living cell.
c. machine.
d. all of these
Answer: D
Assessment Questions
11. The main sources of energy on Earth are
a. solar and nuclear.
b. gasoline and fuel cells.
c. wind and tidal.
d. potential energy and kinetic energy.
Assessment Questions
11. The main sources of energy on Earth are
a. solar and nuclear.
b. gasoline and fuel cells.
c. wind and tidal.
d. potential energy and kinetic energy.
Answer: A