Download WORK – ENERGY – POWER

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WORK – ENERGY – POWER
The WORK done by constant force acting on a body is defined
as the scalar product of the displacement and the
force.
   
 
W  F  s  F  s cos  Fs  s

F


Fs

s

Fs : is the component of F in the
direction of the displacement

s : is the displacement 

 : is the angle between F and s
In the SI, the unit for work is Nm but the unit of the work has a
special name Joule (J ) : 1J  1Nm
1 J is the work done by a force of one Newton through one
meter along the line of the force.
Work is a scalar quantity
Work can be 0 if the angle between the force and displacement
is   0 or   90 as for these angles: cos  0
If   90 , the work done by the applied force is positive
If   90 , work is negative (e.g.: when an object is lifted, the
work done by the gravitational force on the object is negative)
Important consideration that: work is an energy transfer.
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WORK DONE BY A FORCE
Work done by a force is represented and calculated as the area
under the curve of Fs versus displacement s , where Fs is that
component of the force, which is parallel to s .
Fs
Work
sA
Efficiency:  
sB
s
useful  work
total  work
POWER is the rate at which work is done: P 
W
t
The SI the unit for power is called Watt (W) which is equivalent
J
with the Joule per second:
1Watt  1  1Js1
s
Note:
1) For motors and engines power is often named in
horsepower, where
1horsepower  746Watt
2) Commonly used the kilowatt: 1kW  1000Watt
and the megawatt: 1MW  1000kW  106W
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3) A conveniently large energy unit in common usage is the
kilowatt-hour (Not unit of power!):
J
1kWh  1kW  1h  1000  3600s  3.6  106 J
s
4) If many forces are acting on an object, you can calculate
the work done by each force individually. The net work will
be the sum of these. Or we can find the net force and
calculate the work done by it.
ENERGY
is a property of objects, the measure of the ability of the object
to perform work, which can be transferred to other objects or
converted into different forms, but cannot be created or
destroyed.
KINETIC ENERGY: the energy possessed by a body as a result
of its motion (translational or rotational KE )
The translational KINETIC ENERGY of an object of mass m
moving with a speed v is:
1
KE  mv 2
2
1
1
2
2
Change in KE= Work done by Fnet  KE  mv2  mv1
2
2

Work-energy theorem for net force



1
1
1 2
2
2
2
2
Note: KE  m  v2  v1  mv2  v1   v2  2v2v1  v1
2
2
2

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POTENTIAL ENERGY: the energy possessed by a body as a
result of its position or configuration
GRAVITATIONAL POTENTIAL E:
The object has a potential energy
as a result of its position in the
gravitational field of the Earth
ELASTIC POTENTIAL E:
The object has a potential
energy as a result of
change its elastic body
Example: waterfall
Example: the clock spring
when the clock
is wound
The change in gravitational or elastic potential energy when
a body changes from one position or configuration to
another is the work done against the gravitational or elastic
forces during the change
GRAVITATIONAL POTENTIAL ENERGY
When we are lifting up a distance h an object, which has the
mass m with constant speed, then we need to exert a force
against the gravitational force.
LIFTING WORK DONE = Force  distance  mgh
The work the object can do by its position in the gravitational
field is its potential energy: PE  m  g  h .
Note:
Gravitational potential energy depends on the height or
vertical position of the object’s center of mass relative to
some specified reference level.