Download Mechanical Energy

Work, Energy and Power
Kinetic (work) potential
Energy - Types
Mechanical Energy: Energy due to
position in a field force or energy due to
movement
 Non-mechanical Energy: Energy that
does not fall into the above category

Energy – Flow Chart
Energy
Mechanical
Kinetic
Non-mechanical
Potential
Heat
Linear
Gravitational
Electromagnetic
Rotational
Elastic
Chemical
Sound
Electric
Nuclear
Magnetic
Kinetic Energy Equation
1
2
KE  mv
2
Potential Energy Equation
PEg  mgh
Work – Energy Principle or work
done by a net force or net work done
on an object
Wnet  Fnet d  KE
Energy Conservation

The total energy is neither increased nor
decreased in any process.

Energy can, however, be transformed from one
type to another AND transferred from one
body to another, BUT, the total amount of
energy in the process remains CONSTANT!
Conservative and Nonconservative
Forces


Conservative Force: A force such that the work
done on an object by the force does not depend on the
path taken, rather it depends only on the initial and
final positions (gravitational, elastic, electric)
Nonconservative Force: A force such that the work
done on the object by the force does depend on the
path taken (friction, air resistance, rocket propulsion).
A lot of times these forces generate heat or sound
which are non-mechanical energies.
Work – Energy Principle Redefined

So if energy is conserved we can
write it this way using mechanical
and non-mechanical energies
KE  PE  WNC
Work – Energy Principle &
Mechanical Energy Conservation

If we ignore nonconservative forces (friction
and the such), the implication is that no nonmechanical energies are present (heat, sound,
light, etc) therefore…
KE  PE  0
Mechanical Energy Conservation
E1  E2
Mechanical Energy Conservation with
energy lost
E1  E2  Elost
E1  E2  W friction
Kinetic and potential energy
convert to one another
Frictionless Coaster : Total = Mechanical Energy
Work and Power

Work – done when a force acts on an object in
the direction the object moves

Requires Motion and Force in one direction!
Man is not actually doing work when
holding barbell above his head
 Force is applied to barbell
 If no movement, no work done

He does work
They do no
work
Work and Power
Work Depends on Direction Continued…
A.
B.
C.
Force and Motion in the same direction
The horizontal component of the force does work.
The vertical force does no work on the suitcase.
Force
Direction of motion
This force
does work
This force
does no
work
Direction of motion
Force
Direction of motion
Work

Most of the time F is in the direction of d so θ =
0° and cos 0° = 1 so…
Wmax  Fd

Work is done by a force acting on a body!



Symbol: W
Unit : J, joule
1 J = 1 Nm
Work
The simplest definition for the amount of work a force does on an object
is magnitude of the force times the distance over which it’s applied:
W=Fx
This formula applies when:
• the force is constant
• the force is in the same direction as the displacement of the object
Symbol: W
Unit : J, joule
1 J = 1 Nm
F
x
When the force is at an angle
When a force acts in a direction that is not in line with the
displacement, only part of the force does work. The component of F
that is parallel to the displacement does work, but the perpendicular
component of F does zero work. So, a more general formula for
work is
W = F x cos
F sin
Tofu Almond
Crunch
F

F cos
x
This formula assumes
that F is constant.
Power
Power is defined as the rate at which work is done. It can also
refer to the rate at which energy is expended or absorbed.
Mathematically, power is given by:
W
P =
t
Since work is force in the direction of motion times distance, we can
write power as:
P = (F d cos  ) / t = (F cos) (d / t) = F v cos.
F
F sin

m
F cos
x
Power

Power is the rate at which work is done or the rate
at which energy is transformed.
Pave



W E Fd



 Fvave
t
t
t
Symbol: P
Unit: W, Watt
1W = 1J/s