Please enable JavaScript.
Coggle requires JavaScript to display documents.
Work, Energy and Power - Lessons 1 and 2 - Coggle Diagram
Work, Energy and Power - Lessons 1 and 2
Lesson 1: Basic Terminology and Concepts
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.
Mathematically, work can be expressed by the following equation.
W = F • d • cos Θ
where
F
is the force,
d
is the displacement, and the angle (
theta
) is defined as the angle between the force and the displacement vector.
the standard metric unit is the
Joule
(abbreviated J).
Calculating the Amount of Work Done by Forces
A
free-body diagram
is a diagram that depicts the type and the direction of all the forces acting upon an object.
Potential Energy
Potential energy
is the stored energy of position possessed by an object.
Gravitational potential energy
is the energy stored in an object as the result of its vertical position or height.
PEgrav = mass • g • height
PEgrav = m *• g • h
Elastic potential energy
is the energy stored in elastic materials as the result of their stretching or compressing.
Fspring = k • x
PEspring = 0.5 • k • x2
where k = spring constant
x = amount of compression (relative to equilibrium position)
Kenetic Energy
Kinetic energy
is the energy of motion.
KE = 0.5 • m • v2
where m = mass of object
v = speed of object
Kinetic energy is a
scalar quantity
; it does not have a direction.
Mechanical Energy
The energy acquired by the objects upon which work is done is known as
mechanical energy
.
The
total amount of mechanical energy
is merely the sum of the potential energy and the kinetic energy.
TME = PEgrav + PEspring + KE
Power
Power
is the rate at which work is done. It is the work/time ratio.
Power = Work / time
The standard metric unit of power is the
Watt
.
Lesson 2 - The Work-Energy Relationship
Internal vs. External Forces
External forces
include the applied force, normal force, tension force, friction force, and air resistance force.
Internal forces
include the gravity forces, magnetic force, electrical force, and spring force.
Because internal forces are capable of changing the form of energy without changing the total amount of mechanical energy, they are sometimes referred to as
conservative forces.
If the force and the displacement are in the same direction, then
positive work
is done on the object. If positive work is done on an object by an external force, then the object gains mechanical energy. If the force and the displacement are in the opposite direction, then
negative work
is done on the object; the object subsequently loses mechanical energy.
Analysis of Situations Involving External Forces
The quantitative relationship between work and mechanical energy is expressed by the following equation:
TMEi + Wext = TMEf
or
KEi + PEi + Wext = KEf + PEf
Analysis of Situations in Which Mechanical Energy is Conserved
Whenever work is done upon an object by an external force (or nonconservative force), there will be a
change in the total mechanical energy
of the object. If only internal forces are doing work (no work done by external forces), then there is
no change in the total amount of mechanical energy
.