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Work, Energy, and Power - Coggle Diagram
Work, Energy, and Power
Lesson 2 - The Work-Energy Relationship
Analysis of Situations in Which Mechanical Energy is Conserved
Equations
KEi + PEi + Wext = KEf + PEf
KEi + PEi = KEf + PEf
Examples
Analysis of Situations Involving External Forces
Equations
KEi + PEi + Wext = KEf + PEf
TMEi + Wext = TMEf
Examples
Bar Chart Illustrations
Equations
KEi + PEi + Wext = KEf + PEf
KEi + PEi-grav + PEi-spring + Wext = KEf + PEf-grav + PEf-spring
Procedure for Constructing Bar Charts
Analyze the initial and final states of the object in order to make decisions about the presence or absence of the different forms of energy.
Analyze the forces acting upon the object during the motion to determine if external forces are doing work and whether the work (if present) is positive or negative.
Construct bars on the chart to illustrate the presence and absence of the various forms of energy for the initial and final state of the object; the exact height of the individual bars is not important; what is important is that the sum of the heights on the left of the chart is balanced by the sum of the heights on the right of the chart
An Energy Bar Chart
There is no kinetic and elastic potential energy in the initial state.
There is no gravitational and elastic potential energy in the final state.
There is no work done by external forces.
The sum of the heights on the right (5 units) equals the sum of the heights on the left (5 units).
Examples
Internal vs. External Forces
Internal Forces
Include the gravity forces, magnetic force, electrical force, and spring force.
Fgrav
Fspring
External Forces
Include the applied force, normal force, tension force, friction force, and air resistance force.
Fapp
Ffrict
Fair
Ftens
Fnorm
Lesson 1 - Basic Terminology and Concepts
Potential Energy
The stored energy of position possessed by an object.
Types of Potential Energy
Elastic potential energy
The energy stored in elastic materials as the result of their stretching or compressing.
Spring: PEspring = 0.5 • k • x2
Gravitational potential energy
The energy stored in an object as the result of its vertical position or height.
Mass: PEgrav = mass • g • height
Height: PEgrav = m *• g • h
Kinetic Energy
The energy of motion.
Types of Kinetic Energy
Vibrational
The energy due to vibrational motion
Rotational
The energy due to rotational motion.
Translational
The energy due to motion from one location to another.
KE = 0.5 • m • v2
1 Joule = 1 kg • m2/s2
Kinetic energy is a
scalar quantity
; it does not have a direction. Unlike velocity, acceleration, force, and momentum, the kinetic energy of an object is completely described by
magnitude
alone.
Calculating the Amount of Work Done by Forces
What is a free-body-diagram?
A diagram that depicts the type and the direction of all the forces acting upon an object.
Mechanical Energy
The energy acquired by the objects upon which work is done. It can either be kinetic or potential.
TME = PE + KE
TME = PEgrav + PEspring + KE
Definition and Mathematics of Work
When a force acts upon an object to cause a displacement of the object, it is said that
work
was done upon the object.
In order for a force to qualify as having done
work
on an object, there must be a displacement and the force must
cause
the displacement.
Examples of Work
A horse pulling a plow through the field
A father pushing a grocery cart down the aisle of a grocery store
A freshman lifting a backpack full of books upon her shoulder
Work Equation
W = F • d • cos Θ
F = Force
D = Displacement
The angle (theta) = Θ
Theta
The angle between the force and the displacement vector.
Force and Displacement
A
force
is applied to a cart to
displace
it up the incline at constant speed
Negative Work
A force acts upon a moving object to hinder a displacement.
Units of Work
The
Joule
(J) is the unit of work.
1 Joule = 1 Newton * 1 meter
Non-standard Units of Work
foot•pound
kg•(m/s2)•m
kg•(m2/s2)
Power
The quantity work has to do with a force causing a displacement.
Equations for Power
Power = Work / time
The standard metric unit of power is the
Watt
.
