Transcript Energy - Images

Chapter 5
Work and Energy
Work and Energy
• Work
– describes something done to an
object or system.
– scientifically, is a net force applied
to or by an object through a
distance
– W = FdII
– is energy transfer.
– System: box in a warehouse
– Environment: you, gravitational
field, and anything external to the
box
• Work
Work and Energy
– is positive when energy is
transferred to the system.
– is negative when energy is
transferred out of the system
– occurs only when the
displacement is in the
direction parallel to the force
– is measured in joules (J)
– 1 J = 1 N.m = 1 kg.m2/s2
NO WORK!
Work and Energy
• Work
W = F cosq d or
W = Fd cosq
This is the definition of work. The magnitude of the force vector
times the magnitude of the displacement vector times the cosine
of the angle between the vectors.
Work and Energy
• Work
moving from A to B W = Fgd
moving from B to C W = - Fgd
Total work = 0
Fapp
Fapp
Fapp
d
A
B
C
Work and Energy
• Energy
– is a conserved quantity with
the capability to produce
change in itself and its
environment.
– is the property of a system
that describes its ability to
produce change.
– is measured in joules
– 1J = 1 kg.m2/s2
– Thermal
– Chemical
– Energy of motion
Work and Energy
• Kinetic Energy
– associated with motion
– KE = ½mv2
– the work an object can
do while changing
speed
– the amount of energy in
a moving object
Work and Energy
Suppose that an automobile of mass m is traveling with velocity vi when
the motor is shut off and the brakes are applied (locked). If the friction
force between the pavement and the squealing tires is Ff, how much
work does the car do against this force by the time it comes to rest?
W = Fd
vf2 = vi2 - 2ad
assuming constant acceleration
2ad = vf2 - vi2 and ad = 1/2 (vf2 - vi2 )
Using Newton’s 2nd law:
a=
F
m
F d = ad = 1/2 (v 2 - v 2 )
f
i
m
Fd = 1/2 m(vf2 - vi2 )
Work done = 1/2 m(vf2 - vi2 )
Work and Energy
• Energy
– Work done = 1/2 m(vf2 - vi2 ) = 1/2 mvf2 - 1/2 mvi2
– The ability of a moving object to do work because of its motion
forms the basis for the definition of the quantity kinetic energy
(KE).
– Work done is equal to the change in kinetic energy is true even
if the acceleration is not uniform.
– Work done is the same thing as net work or Wnet.
Work and Energy
• Work - Kinetic Energy Theorem
Wnet = DKE
F.d.cosq = ½mvf2 – ½ mvi2
The net work done by a net force acting on an object is
equal to the change in the kinetic energy of the
object.
+ Wnet then speed increases
Chapter 5
Section 2 Energy
Sample Problem
Work-Kinetic Energy Theorem
On a frozen pond, a person kicks a 10.0 kg sled,
giving it an initial speed of 2.2 m/s. How far does the
sled move if the coefficient of kinetic friction between
the sled and the ice is 0.10?
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Chapter 5
Section 2 Energy
Sample Problem, continued
Work-Kinetic Energy Theorem
1. Define
Given:
m = 10.0 kg
vi = 2.2 m/s
vf = 0 m/s
µk = 0.10
Unknown:
d=?
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Chapter 5
Section 2 Energy
Sample Problem, continued
Work-Kinetic Energy Theorem
2. Plan
Choose an equation or situation: This problem can be
solved using the definition of work and the work-kinetic
energy theorem.
Wnet = Fnetdcosq
The net work done on the sled is provided by the force
of kinetic friction.
Wnet = Fkdcosq = µkmgdcosq
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Chapter 5
Section 2 Energy
Sample Problem, continued
DKE = Wnet
3. Calculate
½mvf2 – ½ mvi2 = F.d.cosq
0 – ½ mvi2 = m . mg.d.cosq
(–2.2 m/s)2
d
2(0.10)(9.81 m/s2 )(cos180)
d  2.5 m
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Work and Energy
• Conservation of Energy
Conserved means remains constant.
Total energy is conserved.
Energy can be converted from one
form to another but the total
amount of energy remains
constant!
What is another quantity that is conserved?
Work and Energy
ENERGY
Mechanical
Kinetic
Nonmechanical
Potential
Gravitational
Elastic
Work and Energy
• Potential Energy
– the amount of work an object is
capable of doing because of its
position
• Gravitational potential energy is the
potential energy stored in the gravitational
fields of interacting bodies.
• Gravitational potential energy depends
on height from a designated zero or
reference level.
PEg = mgh
gravitational PE = mass  free-fall
acceleration  height
Work and Energy
•
Elastic potential energy is the energy available for
use when a deformed elastic object returns to its
original configuration.
PEelastic
elastic PE =
1
1 2
 kx
2
 spring constant  (distance compressed or stretched)
2
•
The symbol k is called the spring constant, a
parameter that measures the spring’s resistance to
being compressed or stretched.
2
Chapter 5
Section 2 Energy
Elastic Potential Energy
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Chapter 5
Section 2 Energy
Sample Problem
Potential Energy
A 70.0 kg stuntman is attached to a bungee cord with
an unstretched length of 15.0 m. He jumps off a
bridge spanning a river from a height of 50.0 m.
When he finally stops, the cord has a stretched
length of 44.0 m. Treat the stuntman as a point mass,
and disregard the weight of the bungee cord.
Assuming the spring constant of the bungee cord is
71.8 N/m, what is the total potential energy relative to
the water when the man stops falling?
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Chapter 5
Section 2 Energy
Sample Problem, continued
Potential Energy
1. Define
Given:m = 70.0 kg
k = 71.8 N/m
g = 9.81 m/s2
h = 50.0 m – 44.0 m = 6.0 m
x = 44.0 m – 15.0 m = 29.0 m
PE = 0 J at river level
Unknown: PEtot = ?
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Chapter 5
Section 2 Energy
Sample Problem, continued
Potential Energy
2. Plan
Choose an equation or situation: The zero level for
gravitational potential energy is chosen to be at the
surface of the water. The total potential energy is the
sum of the gravitational and elastic potential energy.
PEtot  PEg  PEelastic
PEg  mgh
PEelastic 
1 2
kx
2
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Chapter 5
Section 2 Energy
Sample Problem, continued
Potential Energy
3. Calculate
Substitute the values into the equations and solve:
PEg  (70.0 kg)(9.81 m/s2 )(6.0 m) = 4.1 10 3 J
1
PEelastic  (71.8 N/m)(29.0 m)2  3.02  10 4 J
2
PEtot  4.1 103 J + 3.02  10 4 J
PEtot  3.43  10 4 J
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Chapter 5
Section 2 Energy
Sample Problem, continued
Potential Energy
4. Evaluate
One way to evaluate the answer is to make an
order-of-magnitude estimate. The gravitational
potential energy is on the order of 102 kg  10
m/s2  10 m = 104 J. The elastic potential energy
is on the order of 1  102 N/m  102 m2 = 104 J.
Thus, the total potential energy should be on the
order of 2  104 J. This number is close to the
actual answer.
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Work and Energy
• Mechanical Energy: the sum of kinetic energy
and all forms of potential energy
ME = KE + SPE
• Conservation of Mechanical Energy
– In the absence of friction mechanical energy is
conserved.
• MEi = MEf
• KEi + PEi = KEf + PEf
• Energy conservation occurs even when
acceleration varies and the kinematic equations
are not valid.
Work and Energy
• Mechanical Energy: is the ability to do work
• Conservation of Mechanical Energy
ME = KE + SPE
– In the absence of friction mechanical energy is conserved.
• MEi = MEf
• KEi + PEi = KEf + PEf
• Why is mechanical energy not conserved in the presence of friction?
Work and Energy
• Power
– is the rate at which work is done.
– is the rate of energy transfer.
P = W/t = work / time
P = Fd/t
P = Fv
– J/s = Watt (W)
– Horsepower (hp) = 746 W