Download Potential Energy

Objectives
• Recognize the difference between the scientific and
ordinary definitions of work.
• Define work by relating it to force and displacement.
• Identify where work is being performed in a variety of
situations.
• Calculate the net work done when many forces are
applied to an object.
Definition of Work
• Work is done on an object when a force causes a
displacement of the object.
• Work is done only when components of a force are
parallel to a displacement.
Work
• The result of force moving an object. Work is therefore
done on the object.
• Note: If the object does not move, than no work has
been done.
– You can try and push the wall for 2 hours, use all that
energy, and still not have done any work!
• Work is a transfer of energy.
Definition of Work
F
d
W = Fd
Definition of Work
W = Fd
Force x Distance =
Newton x meters =
Newton-meters = Joule
Definition of Work
Sign Conventions for Work
Example of Work
W = Fd
Example of Work
W = Fd
Homework
• Read and Outline Chapter 3 part 1
– pages 61-73
• Read and Outline Chapter 3 part 2
– Pages 74 - 82
• Vocabulary
– Define Key Terms within outline
– Underline clearly for future study
• Part 1 due Friday
• Part 2 due Monday
Review
W = Fd
Force in same Direction as
motion
Force opposes Direction of
motion
Force perpendicular to
Direction of motion
No Motion
Objectives
• Identify several forms of energy.
• Calculate kinetic energy for an object.
• Apply the work–kinetic energy theorem to solve
problems.
• Distinguish between kinetic and potential energy.
• Classify different types of potential energy.
• Calculate the potential energy associated with an
object’s position.
Energy
Energy is the Ability to do work. We cannot do anything
without energy. When something happens, energy is
transferred
Law of the Conservation of Energy
Energy can neither be created nor destroyed, it can only
be transformed from one form to another.
Within a closed isolated system energy can change
form, but the total amount must stay constant.
Kinetic Energy
• Kinetic Energy
The energy of an object that is due to the object’s
motion is called kinetic energy.
• Kinetic energy depends on speed and mass.
1
KE  mv 2
2
1
2
kinetic energy =  mass   speed
2
Kinetic Energy
• Moving objects have Kinetic Energy. Movement can be in
any direction, horizontal, vertical, etc.
• Forms of Kinetic Energy
– Vibrational – Due to vibrating
– Rotational – Due to rotation
– Translational – Motion from one place to another
Note: When using KE, we are referring to Trans. KE
Kinetic Energy
• The kinetic energy of an object is directly proportional to
the square of its velocity.
• That means it takes four times an objects kinetic energy
to double its velocity. Nine times for three times the
velocity.
• Scalar Quantity
– You can also use speed to solve for KE.
Kinetic Energy = ½ mass x velocity2
KE = ½ m v2
1 Joule = 1 kg x (m/s)2
KE is Measured in Joules
Kinetic Energy
Kinetic Energy, continued
• Work-Kinetic Energy Theorem
– The net work done by all the forces acting on an
object is equal to the change in the object’s kinetic
energy.
• The net work done on a body equals its change in
kinetic energy.
Wnet = ∆KE
net work = change in kinetic energy
Work-Kinetic Energy Theorem
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 kinetic friction is 25 N
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 kinetic friction is 25 N
Wnet = Change in KE
KE = ½ mv2
Review
KE = ½ mv2
W = Fd
Wnet = Change in KE
Potential Energy
• Three Forms
– Gravitational Energy
– Elastic Potential Energy
– Chemical Potential Energy
• Both have energy due to their position.
Potential Energy
• Potential Energy is the energy associated with an object
because of the position, shape, or condition of the object.
• Gravitational potential energy is the potential energy stored in
the gravitational fields of interacting bodies.
• Gravitational potential energy depends on height from a zero
level.
PEg = mgh
gravitational PE = mass  free-fall acceleration  height
Potential Energy
• The greater an object’s Mass, the greater its
Gravitational Potential Energy.
• The greater an object’s Height, the greater the
Gravitational Potential Energy.
• Doubling an object’s Height will result in a doubling of
the PE. Tripling the Height will increase PE by a
factor of 3.
Potential Energy
Sample Problem
Potential Energy
A 70.0 kg stuntman is about to jump off a bridge
spanning a river from a height of 50.0 m. What is his
gravitational potential energy?
Practice Exercise #1
What is the Potential Energy of each Ball?
A = 30 J
B = 30 J
C = 20 J
D = 10 J
E=0J
Practice Exercise #2
1. What is the PE of a 50 Kilogram object that
is 10 meters above the ground?
2. Calculate the PE of 75 Kilogram rock sitting
on the edge of a 235 meter high cliff.
3. What is the mass of an object that has a PE
of 400 Joules at a height of 70 meters?
4. How high is a 50 gram mass that has a PE
of 14,000 J?
Potential Energy, continued
•
Elastic potential energy is the energy available for
use when a deformed elastic object returns to its
original configuration.
1 2
PEelastic  kx
2
elastic PE =
1
 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
Potential Energy, continued
•
Elastic potential energy is the energy available for use
when a deformed elastic object returns to its original
configuration.
•
It is based on two things:
– The spring constant
• (i.e. how strong the spring is)
– The displacement of the spring
• (i.e. how far you push it or stretch it from a relaxed
position)
Elastic Potential Energy
Spring Constant
Objectives
• 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
• When we say that something is conserved, we mean
that it remains constant.
Mechanical Energy
• Mechanical energy is the sum of kinetic energy and
all forms of potential energy associated with an object
or group of objects.
ME = KE + ∑PE
• Mechanical energy is often conserved.
MEi = MEf
initial mechanical energy = final mechanical energy
(in the absence of friction)
Conservation of Mechanical Energy
Sample Problem
Conservation of Mechanical Energy
Starting from rest, a child zooms down a frictionless
slide from an initial height of 3.00 m. What is her
speed at the bottom of the slide? Assume she has a
mass of 25.0 kg.
Sample Problem, continued
Conservation of Mechanical Energy
1. Define
Given:
h = hi = 3.00 m
m = 25.0 kg
vi = 0.0 m/s
hf = 0 m
Unknown:
vf = ?
Sample Problem, continued
Conservation of Mechanical Energy
2. Plan
Choose an equation or situation: The slide is
frictionless, so mechanical energy is conserved.
Kinetic energy and gravitational potential energy are
the only forms of energy present.
1
2
KE 
mv
2
PE  mgh
Sample Problem, continued
Conservation of Mechanical Energy
2. Plan, continued
The zero level chosen for gravitational potential
energy is the bottom of the slide. Because the child
ends at the zero level, the final gravitational potential
energy is zero.
PEg,f = 0
Sample Problem, continued
Conservation of Mechanical Energy
2. Plan, continued
The initial gravitational potential energy at the top of
the slide is
PEg,i = mghi = mgh
Because the child starts at rest, the initial kinetic
energy at the top is zero.
KEi = 0
Therefore, the final kinetic energy is as follows:
1
KEf  mv f2
2
Sample Problem, continued
Conservation of Mechanical Energy
3. Calculate
Substitute values into the equations:
PEg,i = (25.0 kg)(9.81 m/s2)(3.00 m) = 736 J
KEf = (1/2)(25.0 kg)vf2
Now use the calculated quantities to evaluate the
final velocity.
MEi = MEf
PEi + KEi = PEf + KEf
736 J + 0 J = 0 J + (0.500)(25.0 kg)vf2
vf = 7.67 m/s
Sample Problem, continued
Conservation of Mechanical Energy
4. Evaluate
The expression for the square of the final speed can
be written as follows:
2mgh
v 
 2gh
m
2
f
Notice that the masses cancel, so the final speed
does not depend on the mass of the child. This
result makes sense because the acceleration of an
object due to gravity does not depend on the mass
of the object.
Mechanical Energy, continued
•
Mechanical Energy is
not conserved in the
presence of friction.
•
As a sanding block
slides on a piece of
wood, energy (in the
form of heat) is
dissipated into the
block and surface.
Objectives
• Review ideas connecting work and energy
• Relate the concepts of energy, time, and
power.
• Calculate power in two different ways.
• Explain the connection between power, work
and energy
HW Problem
Power
• Power is the rate of doing work.
• A more powerful system is one which is
producing/transferring a larger amount of
energy.
• or one that transfers the same amount, just in
a shorter period of time.
• Units for Power are Watts.
Rate of Energy Transfer
• Power is a quantity that measures
the rate at which work is done or
energy is transformed.
P=W
∆t
power = work ÷ time interval
Power
Power
Work (= F x D)
Power =
Time (in seconds)
Watts =
Joules
s
Practice
• How much power is required to do 100 J of work on an object
in a time of 0.5 s?
• How much power is required if the same work is done in 1s?
Rate of Energy Transfer
• How much work is required to pull a sled if you use 60J of
work in 5 seconds?
• How much work does an elephant do while moving a
circus wagon 20meters with a pulling force of 200N?
• If it takes 5 seconds for you to do 1000J of work, what is
your power output?
Rate of Energy Transfer
• An alternate equation for power in
terms of force and speed is
P = Fv
power = force  speed
Practice
• How much power is required to lift a 500 N block of ice with a
velocity of 4 m/s?
Practice
• If the power is 2000 Watts, over 5 seconds, how much Work is
done?
Practice
• By the way, if the velocity is 4 m/s and it takes 5 seconds, what
is the height? What is the Potential Energy of the 500 N block?