
Objectives 
Essential Question:
Can energy be defined? 
The Nature of Work

Define mechanical energy.

Correctly use the SI unit of energy.
Joule = kg (m^{2} / s^{2})

Define work 3 ways.
 In words: mechanical energy transfer done by a
force (F) acting through a displacement (S) in its same dimension

Mathematically:
W
≡
∫ F_{(s) }
∙ ds,
 Graphically:
work is the area under a force
(F)
vs. displacement
(S)
curve.
Note: "S" is traditionally used to represent a
generic displacement that could occur in the x, y, or z dimensions.

State whether work and mechanical energy are vectors
or scalars.

State 2 requirements for work to be done by a force.
 Motion
 Nonzero force component in same dimension as motion

Explain what a dot product (scalar product) is and how the
concept relates to work.

Calculate the net work done by a constant force
acting through a displacement.

Calculate dot products for the i, j, k, form of
vectors.
 Multiply the i part of the force times
the i part of the displacement vector
 Repeat the above for the j & k parts
 Sum the 3 products from the above
steps.
 example:

force =

2i, 
3j,

 4k 
displacement = 
1i, 
3j, 
2k

work = 
2
+ 9  8 
=

3 
Note: work itself cannot be expressed in
i, j, k form because it is not a vector.
 Explain why work cannot be done by a centripetal force?
(The displacement is
perpendicular to the force.) Relevance:
This is why a satellite can remain in orbit for an indefinite period of time
with almost no energy input.
Metacognition Problem Solving Principle: While work
is a scalar, it does have a relationship to spatial dimensions. Note that the
components of forces and displacements in the same dimension do work. components
in a different dimensions do not. This relationship is most evident when
multiplying the i j k form of the vectors.
Homefun:
Questions 110 odd p 188; Problems 3, 5, 7 p. 189

Read:
Insultingly Stupid Movie Physics
 Chapter 3, Conservation of mass and Energy: Is
Anything Sacred?, pp 33  51
Relevance: Mechanical energy is
the most useful form. Its availability from a source other than muscle power
has profoundly influenced every aspect of human existence.


Activities 
Lesson 1
Key Concept: Work
is the mechanical energy transfer done by a force acting through a
displacement in its same dimension.
Purpose:
Use work as a powerful problem solving tool.
Interactive Discussion:
Objectives 18. Note that net positive work tends to increase
kinetic energy and net negative decrease it.
Demo
7.1: Student holding a book. Is work being done?
In Class Problem Solving:
How much work is done by the superman
force in each of the following:
 Superman pushing a trunk with and
without friction.
 Superman lifting a trunk.
 Superman swinging a trunk (assume
no air resistance).
Interactive Discussion:
Objectives 9. Total work is the sum of the dot products in all the
dimensions.
In Class Problem Solving:
 Superman pushing a trunk with a
variable force
 Superman lifting a trunk with a
variable force
Interactive Discussion:
Objectives 10, 11. Derive the spring potential energy equation.
Resources/Materials: 

Essential Question:
How are kinetic energy and work
related? 
The Nature of Kinetic Energy
 Define kinetic energy 2 ways
 In words: the work needed to accelerate an
object from rest to its current velocity. (The energy an object possesses
due to its motion)
 Mathematically:
K ≡
1/2 mv^{2}

Derive the equation for kinetic energy from the equation for work,
Newton's second law, and the kinematic equations assuming constant force and
acceleration.

Explain the difference between positive and
negative work.
 Negative work: reduces kinetic energy.
Done by a conservative force such as
gravity converts kinetic energy into potential energy. Done by sliding
friction converts kinetic energy into thermal energy (heat).
 Positive work:
increases kinetic energy
 Use the definition of kinetic energy and work in problem solving.
 Sliding Friction:
negative work = heat
 Gravity Force:
positive work = kinetic energy
Homefun: Read 7.5, Problems
17, 29, 31 p. 189190 Serway

Read:
Insultingly Stupid Movie Physics

Chapter 11, High Energy Films: Nuclear Firecrackers, Falling people,
and cars as weapons, pp 163 179

Lesson 2
Key Concept: Kinetic
energy and work are related
Purpose:
Understand that work is mechanical energy transfer and that
typically when work is done it either increases or decreases kinetic
energy.
Interactive
Discussion:
Objectives.
In Class Problem Solving :
 Derive the equation for kinetic energy
and the kinematic equations
 Work done by gravity with box sliding down
slope.
 Work done by friction with box sliding down a
slope.


MiniLab
Physics Investigation (Requires only Purpose,
data, and conclusion) 
Title 
Pendulum /energy Lab (groups of three) 
Purpose 
Determine if a pendulum can be considered
frictionless. 
Overview 
The law of conservation of energy (1st law of
Thermodynamics) is as close to absolute truth as anything in all
of science. If a pendulum can be considered frictionless then
the potential energy at the top of the swing will exactly match
the kinetic energy at the bottom.
 Set up a photogate to measure velocity at the bottom of a
pendulum's swing
 Release the pendulum from a variety of different heights
and measure its velocity at the bottom of its swing.

Data,
Calculations 
 Make a plot a kinetic energy at the
bottom verses potential energy at the top.
 Show a theoretical line on the plot.

Questions,
Conclusions 
 Should the theoretical line be above or below the line of
best fit for the above plot?
 Why does the photogate not measure instantaneous velocity
and how does this error impact the above plot.

Resources/Materials: 
photogate, pendulum 

Essential Question:
Throughout history, how have
springs enabled war? How have springs enable peaceful development? 
 The Nature of
Spring Potential Energy
 (The Linear Spring as an Energy
Storage Device)

Calculate the net work done by a variable
force.

Explain why the net work done in compressing an ideal spring is always zero.

Derive the equation for the potential energy of a linear spring.

Plot the spring potential energy vs. displacement for a linear spring and
compare it to the force vs. displacement curve.

 General
Case: F =  dU/dx

(spring force @ x) = (slope @ a point)
 Linear spring: F = kx



 General
Case: U =
 ∫F_{(x) }
∙ dx
 (U @ x) = (area under curve
from 0 to x)
 or
 (U at x) = (work to compress spring)

Linear spring: U = 1/2 kx^{2}


 Find the spring constant with springs in parallel or series.
Homefun
(formative/summative assessment): Read 7.4, Problems 47, 57 p. 192193 Serway Relevance:
Springs are a ubiquitous mechanical component found in numerous
applications including the suspension systems in vehicles and all kinds of
mechanical devices. The bow and arrow is an example of a spring system in
which energy is slowly input then quickly released. 
Lesson 3 Key Concept:
The equations for springs can be used to model many common
situations involving the storage and release of energy.
Purpose:
Use spring equations in problem solving.
 Interactive Discussion:
Objectives.
In Class Problem Solving:
14  17
 Horizontal spring launcher
 Catapult
 Spring bumper
 springs in parallel or series


Essential Question:
What would driving a car be like
if it had no suspension system? 
Spring and Mass Systems
 Define simple harmonic motion.
 periodic
 restoring force magnitude
linear with respect to displacement
 restoring force direction
always toward the equilibrium position
Notes:
 If
friction = 0, the displacement is symmetrical about the equilibrium
position.
 equilibrium position is location where
total force = 0.
 restoring force is actually the sum of
all forces

Give an example of motion that is periodic but not simple harmonic.
The orbit of planets

Draw the energy diagram for a spring in
simple harmonic motion (p. 232), define the equilibrium position and
describe location along the masses path of:
 max velocityat
equilibrium position
 max accelerationat
extremes
 max restoring forceat
extremes
 max kinetic energyat
equilibrium position
 max spring potential energyat
extremes
Note: the above does not change with the
orientation of the spring. In other words, it does not matter if the spring is
vertical, horizontal, or on a slope. If the spring is vertical, it does not
matter if the mass is hung from the spring or placed on top of it.

Explain why the mechanical energy in a ideal spring/mass system is
constant. There's no friction

Solve problems involving a spring mass
system when the mass is not attached. (Assume the spring itself is massless.)
Homefun (formative/summative
assessment):
Relevance:
Modeling mechanisms as springs/mass systems is the first step in the
analysis done by engineers to minimize vibration.

Lesson 4 Key Concept:
Harmonic motion.
Purpose:
Introduce and define harmonic motion.
Demo
7.2: The Mr. Rogers YoYo object: give an example of
simple harmonic motion and how it relates to resonance.
 Interactive Discussion:
Explain simple harmonic motion vs
periodic motion.
In Class Problem Solving:
 Find the maximum deflection a vertical spring
can have without losing the mass, if the mass is not attached.


Formal Lab Investigation 
Title 
Simple Harmonic Motion of a Spring and
Mass System 
Category 
Energy 
Purpose 
Determine if the
natural frequency of a spring and mass system can be predicted. 
Models 
Linear spring force equation: F = k (x)
natural frequency of a mass & spring system: f =
1/(2p)(k / m)^{2}

Overview 
Using a spring scale, measure the force
required to deflect a spring various distances and plot force vs.
displacement. From the above, determine the spring constant.
Attach the spring to a ring stand so that it hangs vertically and
attach a known weight to the end of the spring.
Lift the eight up and release it so that the system vibrates.
Measure the system's frequency.
Calculate the system's frequency from the natural frequency
equation
using the mass and spring constant. 
Safety
Issues 
Do not start the harmonic motion by
pulling the mass downward and releasing it. This can launch the
weight. 
Resources/Materials: 
spring, known weights, stop watch, spring
scale 

Essential Question:
For an athlete, is power the same
thing as strength? 
Power Basics
 Correctly use the SI unit of power. Watt is the unit of power.
 Define power.
In words:
power is the rate of doing work or the rate of using
energy.
Mathematically:
 Calculate the power requirements of a car
driving up an incline at constant velocity.

P = F (Δx/Δt)
P = Fv 
Remember: W =
F (Δx) 
Homefun
(formative/summative assessment): Read 7.8, Problems 29, 33, 35 p.221
Relevance:
The Watt is a ubiquitous unit. Every electrical appliance has a power
rating in watts listed on its side. Power is a greatly misused term but it
is important to understand it for many reasons including to understand
household energy usage.

Lesson 5
Key Concept: Power is work per unit of time.
Purpose:
Use power equations in problem solving.
 Interactive Discussion:
Objectives
In Class Problem Solving
(two person teams): Calculate the power required to drive up various
slopes at 65 mph and 35 mph. Assume no friction or air resistance.


Essential Question:
How dangerous are falls? 
 The Nature of Gravitational Potential
Energy
 And Conservative Forces Sec. 8.6

Define gravitational potential energy 2 ways:
 In words:
the minimum work needed to
move a mass from one position to another
assuming gravity is the only possible resistance force.
Note this depends only on the starting and
ending positions. it is path independent.

Mathematically: U_{g} = mgh (for a constant gravity field)

Solve problems in which mechanical energy is
conserved. In other words:
(U_{s0} + U_{g0} + K_{0}) = (U_{s1}
+ U_{g1} + K_{1})
Homefun
(formative/summative assessment): Read 81 & 8.2,
Problems 11, 15, 21 pp. 219220 Serway 

Lesson 6
Key Concept:
Gravitational potential energy and conservative forces
Purpose: Solve
problems in which mechanical energy is conserved.
Interactive Discussion:
Objectives
In Class Problem Solving (assume
no friction)
:
 Bob slides down a slope
 Robin hood shoots an arrow straight up. (His
bow is a spring.)
 Robin hood shoots an arrow at an angle.
(His bow is a spring.)
 Robin hood shoots an arrow over a cliff as he
gallops on a horse. (His bow is a spring.)


Essential Question:
We have a law: conservation of
energy. Do we have any similar law for force? 
Conservative Forces and Potential
Energy Diagrams

Identify conservative forces (p. 218).
 work done is path independent
 work done moving thru a closed path = 0
 Name two types of conservative
forces. Note that the equations in objective 17 (p. 232) can be
applied to both types of forces even if the forces are not
linear with displacement:
 ideal spring force (no friction)
 gravity force

Be
aware that potential energy can only be associated with
conservative forces.

Correctly use the following equation (p. 219):
Wc = Ui  Uf
Where Wc = work done by a conservative force.
 Solve problems using
energy diagrams and the concept of stable and unstable
equilibrium.
 stable equilibrium:
If an object is disturbed from its
equilibrium position (B) by displacing it, it will return to
the same position once it's released.
Displaced to any position with a
potential energy below AC, the system will be in stable
equilibrium.
 unstable equilibrium:
If an object is disturbed from its
equilibrium position (B) by displacing it, it will go to a
new position once it's released.
Displaced to any position with a potential energy above AC,
the system will be in unstable equilibrium.
Homefun
(formative/summative assessment): Read chap 8.3
 8.6, 
Lesson 4 Key Concept:
Conservative forces and potential energy diagrams.
Purpose: Solve
problems with potential energy diagrams.
In Class Problem Solving:
 Potential energy vs. displacement problems
 rope over cliff problem
 Jurassic park bus problem


Essential Question:
Efficiencies aside, how could an electric car
require less energy to operate than a gasoline fueled car? 
Using Kinetic, Gravitational Potential
Energy, Spring Potential Energy, and Work All Together With the
First Law of Thermodynamics

State the first law of thermodynamics.

Solve problems with all the forms of mechanical energy including
mechanical energy transfer.

Be aware that sliding friction is not a conservative force and that
when it does negative work it converts mechanical energy into heat.

Solve energy problems in which mechanical energy is converted into
heat. Relevance: This is
what the brakes on your car do when you slow down.
Metacognition Problem Solving Principle:
Energy problems are straightforward as long as you remember that all the
energy in a system at the beginning of a problem has to still be there at
the end, except for energy transferred into or out of the system using
work. In equation form:
(energy at start) + (sum of work done by
nonconservative
forces acting on the system) = (energy at end)
or
(U_{s0} + U_{g0} + K_{0})
+ (W_{ncf})
= (U_{s1} + U_{g1} + K_{1})
W_{ncf}
= DK + DU_{s}
+ DU_{g}
Note that work can be either positive or negative. Remember negative
work decreases kinetic energy and positive work increases it.

Homefun
(formative/summative assessment): Problems 
Lesson 7
Key Concept:
Conservation of energy.
Purpose: Use all
the energy equations to solve problems.
Interactive
Discussion: Objectives
In Class Problem Solving
(friction present)
:
 Bob slides down a slope
 Robin hood shoots an arrow straight up. (His
bow is a spring.)
 Robin hood shoots an arrow at an angle.
(His bow is a spring.)
 Robin hood shoots an arrow over a cliff as he
gallops on a horse. (His bow is a spring.)


MiniLab
Physics Investigation (Requires only Purpose,
data, and conclusion) 
Title 
Measurement of Friction on an Air Track 
Purpose 
Estimate the friction force on an air track 
Overview 
Although air tracks come about as close to creating a zero
friction environment as possible, they still have some. The
results of any air track experiment could be improved by
including friction in the mathematical models, but if the
friction force is indeed very small, including it would have
little effect on an air track experiment.
To estimate the friction force we will assume that it is
constant and that there are no energy losses in the spring when
a slider rebounds.
 Set up an air track at a known angle and place a slider at
the top.
 Release the slider and let it rebound off the bottom.
 Record the height the slider rebounds to and calculate the
change in height from the original position. Repeat the
process several times and record your data.

Data,
Calculations 
Given the above assumptions and data, estimate the friction
force acting continuously on the slider. (Hint: the friction
force does work and in the process converts mechanical energy to
heat. Write an energy balance equation) Construct a 95%
confidence interval for your estimate of the friction force. 
Questions,
Conclusions 
 Devise an experiment to measure the mechanical energy loss
in the slider's spring.
 Devise an experiment to determine if the friction force on
the track is indeed constant.

Resources/Materials: 
air track 

Essential Question:
Are we energy beings? 
The Nature of the World's Most Famous Equation
 Explain all the variables in the equation E = mc^{2}
E = energy
m = mass converted into energy
c = speed of light, approx 3.0 (10^{8})
 Calculate the energy released if a quantity of mass is
converted to energy. (one megaton of TNT = 4.184 X 10^{15} Joules
of energy)
Relevance: E =
mc^{2 }
is arguably the most famous
mathematical equation not just in physics but simply the single most
famous equation. it explains why nuclear bombs are so incredibly
destructive.
Summative Assessment
: Unit Exam objectives 1 38 
Lesson 9 Key Concept:
Matter is condensed energy
Purpose: Use
E = mc^{2}.
Interactive Discussion:
Objectives
In Class Problem Solving:
 Calculate the energy released by reacting 8 grams of
antimatter with matter.

