Download Work & Energy - Christos N. Hadjichristidis

Work & Energy
By Christos
Work

Work is defined as a force acting upon an
object to cause a displacement.
Be aware: Work  Force Distance is not always true
 If the acting force has no component in the direction of
the movement (or if the force is acting perpendicular at the
direction of the movement) then the force does not cause
the movement and therefore it produces 0 work.
 No matter how big force one exerts to an object, if there is
no resulting displacement the work produced will be zero.
 In the special case, however, in which a force is acting in
the direction of the displacement, then and only then, one
can claim that:
Work  Force  Distance
Work done by a Force




Work done by a force=F x distance moved in the direction of force
Be Extra Careful: Work is not always Force x Distance:
If the acting force has no component in the direction of the movement
(or if the force is acting perpendicular at the direction of the
movement) then the force does not cause the movement and therefore
it produces 0 work.
No matter how big is the force acting upon an object if there is no
displacement there is no work.
However, in the case that an force is acting in the same direction of the
displacement, then and only then, one can claim that: Work=Force x
displacement.
Lets see if we got it right!
The direction of
the force is in the
same direction
that the object
moves
The direction of
the force is in the
opposite
direction that the
object moves
The direction of
the force is
perpendicular to
the direction that
the object moves
The object
doesn't move
The force pushing a car
along a road
The force the brakes exert
to stop a car.
Force x distance
-Force x distance
The gravitational force the
Earth exerts on the Moon
0
The force you exert when
pushing on a wall
0
The truth of the matter
Work  Force  Distance  cos
a force will do work only if the force has a component in
the direction that the object moves
Special cases we’ve seen so
far
Work = Force x Distance
(cos00=1)
Work = - Force x Distance
(cos1800=-1)
Work = 0 since cos900=0
If displacement is equal to zero then the
work done is zero no matter the
direction and magnitude of the Force .
NO DISPLACEMENT = NO WORK
Kinetic Energy

Kinetic energy is the energy of
motion. Kinetic Energy  1 2  m  v 2
Where :
m  mass of the object
v  speed of the object
To derive this equation one should
use advance maths!(so forget it)
 However, you should understand
what this equation means …..>

… Kinetic Energy Continued
Kinetic Energy  1 2  m  v




2
The kinetic Energy of an object is directly proportional to
its mass.
The Kinetic Energy of an object is directly proportional to
the square of its speed. That means that for a twofold
increase in speed, the kinetic energy will increase by a
factor of four; for a threefold increase in speed, the kinetic
energy will increase by a factor of nine
Kinetic Energy is a Scalar quantity.
Units of Kinetic Energy Kg m2/s2 = 1 Joule
Lets check our understanding
Suppose that you were
captured by an evil
physicist who gave you
the following choice:
You must either:
 Stand in front of a
1000 kg. truck moving
at 1 m/s, or
 Stand in front of a 1
kg. meatball moving at
1000 m/s.
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
– Elastic potential
energy is the energy
stored in elastic
materials as the result
of their stretching or
compressing
… Potential Energy Continued
PE grav  Weight  Height  mass  acceleration due to gravity  Height
 PEgrav  m  g  h Units: Kg  m s 2  m  Kg  m 2 / s 2  Joule
Mechanical Energy

Mechanical energy is the total energy which is possessed
by an object due to its motion and/or its stored energy of
position.
… Mechanical Energy
Continued

The total amount of mechanical energy is merely
the sum of the potential energy and the kinetic
energy. This sum is simply referred to as the total
mechanical energy :
TME=Kinetic Energy+Potential Energy
(units make a wild guess!)
 an object with mechanical energy is able to do
work on another object.
Work Energy Theorem

Plethora of ways to categorize forces.
– contact forces or as action-at-a-
distance forces
– External-Internal Forces:


External forces can change the total mechanical
energy while doing work on a system
Internal forces can not change the total mechanical
energy of a system while performing work upon it.
External Forces
applied forces,
normal forces,
tensional forces,
friction forces,
and air resistance
forces.
Work=change of
mechanical energy
TME Before  Work  TME After 

KE i  PEi  W  KE f  PE f
Internal Forces
Internal forces include gravitational
forces, magnetic forces, electrical
forces, and spring forces.
 When work is done upon an object by
an internal force the total mechanical
energy (KE + PE) of that object remains
constant. In such cases, the object's
energy changes form.

The roller coaster +Book
http://www.physicsclassroom.com/mmedia/qt/energy/coaster.mov
http://www.batesville.k12.in.us/Physics/PhyNet/Mechanics/Energy/lifting_a_book
.htm
http://www.batesville.k12.in.us/Physics/PhyNet/Mechanics/Energy/pushing_a_bo
ok.htm
http://www.batesville.k12.in.us/Physics/PhyNet/Mechanics/Energy/Work_as_Area
.html
Check our Understanding
Description of Motion
1 A ball falls from a height of 2
meters in the absence of air
resistance.
2 A skier glides from location A to
location B across the friction free
ice.
3 A baseball is travelling upward
towards a man in the bleachers.
A bungee chord begins to exert
an upward force upon a falling
bungee jumper.
KE to PE or PE to KE?
Explain.