Transcript Work & Energy

WORK & ENERGY
Physics, Chapter 5
Energy & Work
• What is a definition of energy?
• Because of the association of energy with work, we begin
with a discussion of work.
• Work is intimately related to energy and how energy
moves from one system to another or changes form.
WORK
Section 5.1
Definition of Work
• In Physics, work means more than something
that requires physical or mental effort
• Work involves a transfer of energy
• Work is done on an object when a force causes
a displacement of the object
W  F cos  d
W  Fd cos 
• Where θ is the angle between F and d.
Caution!
• Work is done only when a force or a component
of a force is parallel to a displacement!
Net Work Done by a Constant Net Force
Wnet  Fnet d cos 
F
θ
F cos θ
d
Unit of Work
• From the formula for work, determine the unit of
work.
• The SI unit of work is the joule (J)
• The joule is the unit of energy, thus….
• Work is a type of energy transfer!!
Sample Problem A
• How much work is done on a sled pulled 4.00 m
to the right by a force of 75.0 N at an angle of
35.0° above the horizontal?
W  Fd cos 
W  75.0 N  4.00 m  cos35.0
W  246 J
How much work was done by Fg on the sled?
How much work was done by Fup on the sled?
If the force of kinetic friction was 20.0 N, how much work
was done by friction on the sled?
The Sign of Work
• Work is a scalar quantity and can be positive or negative
• Work is positive when the component force &
displacement have the same direction
• Work is negative when they have opposite directions
W  Fd cos 
W  75.0 N  4.00 m  cos35.0
W  246 J
If the force of kinetic friction was 20.0 N, how much
work was done by friction on the sled?
Wf = Fk∙d cos(180)= |-20.0 N|∙|4.00 m|∙(-1) = -80.0 J
Is work being done?
Why or why not?
Would it be positive or negative?
Is work being done?
Why or why not?
Would it be positive or negative?
Is work being done?
Why or why not?
Would it be positive or negative?
Graphical Representation of Work
• Work can be found by analyzing a plot of force and
displacement
• The product F∙d is the area underneath and Fd graph
Graphical Representation of Work
• This is particularly useful when force is not constant
(which it normally isn’t)
ENERGY
Section 5.2
Kinetic Energy
• Kinetic energy is energy associated with an
object in translational motion
• Motion in which an object moves from one point in space to
another (non-rotational)
• Ek (KE) is a scalar quantity
• Ek depends upon an objects mass and velocity
• SI unit is the joule
2
m
1 J  1 kg  2  1 N  m
s
1 2
Ek = mv
2
Relationship of Work and Energy
• Work is a transfer of energy
• Net work done on an object is equal to the
change in kinetic energy of the object
Work- Energy Theorem
Wnet = DEk
Proof of W-KE Theorem
Importance of W-KE Theorem
• Some problems that can be solved using Newton’s Laws
turn out to be very difficult in practice
• Very often they are solved more simply using a different
approach…
• An energy approach.
Sample Problem C
• A 10.0 kg sled is pushed across a frozen pond such that
its initial velocity is 2.2 m/s. If the coefficient of kinetic
friction between the sled and the ice is 0.10, how far does
the sled travel? (Only consider the sled as it is already in
motion.)
FN
vi
Fk
mg
d
Given : m  10.0 kg; μk  0.10; vi  2.2 m/s; v f  0
Wnet  Fk d cos   KE
1 2 1 2
mv f  mvi
KE
2
d
2
Fk cos 
μk mg cos 
 vi2
d
2 μk g cos(180)
FN
vi
Fk
 2.2m/s 
d
 2.5 m
2
20.19.81m/s  1
2
mg
d
Potential Energy
• PE is “stored” energy
• It has the “potential” to do work
• Energy associated with an object due to its
position
• Gravitational PEg
• Due to position relative to earth
• Elastic PEe
• Due to stretch or compression of a spring
Two Types of Potential Energy
Potential Energy
Gravitational
Elastic
PEg = mgh
PEe = ½ kx2
Gravitational Potential Energy
• Gravitational PE is
energy related to
position
PEg = mgh
• Gravitational PE is
relative to position
• Zero PE is defined by
the problem
• If PEc is zero, then PEA
> PEB > PEC
Hooke’s Law
a)
spring is unstretched
b) stretched by a force F a distance x
A restoring force generated by the
spring –F pulls the cart back toward
equilibrium
c) Block exerts force -F compressing
the spring a distance x
A restoring force F pushes spring
toward equilibrium
Hooke’s Law
•
Elastic PE & Hooke’s Law
• Hooke’s law is the foundation of Elastic PE
• When a spring is compressed or stretched from its resting
(equilibrium) position…
• The work done to the spring is now stored as elastic
potential energy.
• The potential energy can then do work.
• Example: a toy dart gun
Elastic Potential Energy
• PE resulting from the
compression or
stretching of an elastic
material or spring.
• PEe = ½ kx2 where…
• x = distance
compressed or
stretched
• k = spring constant
Spring constant
indicates resistance to
stretch.
5.3 Conservation of Energy
Objectives
At the end of this section you should be able to
1.
2.
3.
Identify situations in which conservation of mechanical
energy is valid
Recognize the forms that conserved energy can take
Solve problems using conservation of mechanical
energy
Conserved Quantities
• For conserved quantities, the total remains constant, but
the form may change
• Example: one dollar may be changed, but its quantity
remains the same.
• Example: a crystal of salt might be ground to a powder,
but the mass remains the same. Mass in conserved
Conservation of Energy
• First law of thermodynamics
• Energy cannot be created or destroyed
• Energy gained/lost by the system must be lost/gained by
the surroundings
• Conservation of energy in the World Series
• https://www.youtube.com/watch?feature=player_embedded&v=a4c
cDBsf6OE
Mechanical Energy
• Is conserved in the absence of friction
i.e. initial ME equals final ME
• MEi = MEf
• If ME = KE + PE
• Then KEi + PEi = KEf + PEf
• ½ mvi2 + mghi = ½ mvf2 + mghf
Conservation of Mechanical Energy
( A Falling Egg)
0.00
0.10
Hght
(m)
1.00
0.95
Spd
(m/s)
0.00
0.98
PE
(J)
KE
(J)
ME
(J)
0.74
0.00
0.74
0.70
0.04
0.74
0.20
0.80
2.00
0.59
0.15
0.74
0.30
0.56
2.90
0.41
0.33
0.74
0.40
0.22
3.90
0.16
0.58
0.74
0.45
0.00
4.43
0.00
0.74
0.74
Conservation of Mechanical Energy
0.80
0.70
Energy (J)
Time
(s)
0.60
PE
0.50
KE
0.40
ME
0.30
Poly. (PE)
0.20
Poly. (KE)
0.10
Linear (ME)
0.00
-0.100.00
0.10
0.20
0.30
0.40
0.50
Time (s)
• As a body falls, potential energy is converted to kinetic energy
• Since ME is conserved (constant)…. ΣPE + KE = ME
•In the absence of friction & air resistance, this is true for mechanical
devices also
Mechanical Energy
• Is the sum of KE and all forms of PE in the system
• ME = ΣKE + ΣPE
• sigma (Σ ) indicates “the sum of”
Sample Problem 5E
• Starting from rest, a child of 25.0 kg slides from a height
of 3.0 m down a frictionless slide. What is her velocity at
the bottom of the slide?
• Could solve using kinematic equations, but it is simpler to
solve as energy conservation problem.
• MEi = MEf
ME may not be conserved
• In the presence of
friction, mechanical
energy is not
conserved
• Friction converts some
ME into heat energy
• Total energy is
conserved
MEi = MEf + heat
Work-Kinetic Energy Theorem
• The net work done on an object is equal to the change in
kinetic energy of the object
• Wnet = ∆KE
• The work done by friction is equal to the change in
mechanical energy
• Wfriction = ∆ME
Power
• Is the rate of work, the rate at which energy is transferred
• P = W/∆t
• Since W = Fd, P = Fd /∆t or
• P = Fvavg
• Unit of power = the watt (W)
1 W = 1 J/s
1 hp = 746W
horsepower