An Introduction to Work and
Energy
Unit 4 Presentation 1
What is Work?

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Work is defined as a force applied over a
distance
Work is a scalar
 
W  F  dll
Note that the distance must be parallel to
the applied force
kg  m 2
J
SI Unit: Joule
2
s
Work Examples
Calculate the work it takes to lift a 50N box 3 meters.
W ?
F  50N
d  3m
W  F  d  50N (3m)  150J
Calculate the work it takes to lift a 20 kg box 5 meters.
W ?
F  20kg (9.8m / s 2 )  196N
d  5m
W  F  d  196N (5m)  980J
Non-aligned forces
Remember, the applied force MUST be in the same direction
of the motion to calculate work. If not, consider the
following:
Consider the applied force vector:
Force applied,
through tension in
a rope

Fap
q

Fll

F


Fll  Fap cosq
Motion of the block
Therefore, work can also be
described as:


W  ( Fap cosq )  dll
What is Energy?
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
Energy is defined as the ability to
do work.
If an object has energy, it has an
ability to do work, which is a force
applied over a distance.
6 Main Types of Energy
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Heat
Sound
Light
Chemical
Electrical
Mechanical (Kinetic & Potential)
Mechanical Energy

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Mechanical Energy is divided into
Kinetic Energy and Potential Energy
Kinetic Energy: The Energy of
Motion
Potential Energy: Stored Energy
that can be converted into other
types of energy
Work – Kinetic Energy Theorem

Theorem: The net work done on an object is equal to the
change in the object’s kinetic energy.
W  KE f  KEo  KE

Kinetic energy is the energy of motion of an object:
1 2
KE  mv
2
SI Unit for Energy: Joule
Kinetic Energy Example
The driver of a 1000 kg car traveling on the interstate
at 35.0 m/s (nearly 80 mph) slams on his breaks to
avoid hitting a second vehicle in front of him, which
had come to rest because of congestion ahead.
After the breaks are applied, a constant friction force
of 8000 N acts on the car. Ignore air resistance.
(a) At what minimum distance should the breaks be
applied to avoid a collision with the other vehicle?
(b) If the distance between the vehicles is initially
only 30 m, at what speed would the collision occur?
Kinetic Energy Example
Lets apply the Work-Kinetic Energy theorem:
W
1 2 1 2
mv f  mv o
2
2
Now, consider that the only work being done is by kinetic
friction, and the force and direction of motion are opposite
of each other:
1
1
f k  8000N
d ?
m  1000kg
vo  35m / s
v f  0m / s
 fk  d 
mv 2f  mv o2
2
2
1 2 1 2
m vf  m vo
2
d 2
 fk
1
1
(1000)(02 )  (1000)(352 )
2
d2
 76.6m
 8000
Kinetic Energy Example
Now, find the speed at impact if the distance is only 30 m.
f k  8000N
d  30m
m  1000kg
vo  35m / s
vf  ?
1 2 1 2
 f k  d  mv f  mv o
2
2
1
 f k  d  m vo2
2
 vf
1
m
2
1
 8000 30  (1000)(352 )
2
 v f  27.3m / s
1
(1000)
2
Conservative and Nonconservative
Forces
Conservative Force: A force that allows a
user to recover their work, as kinetic
energy, completely and with very little
dissipation.
Nonconservative Force: A force that
does not allow a user to recover their
work, as kinetic energy, very well. In
fact, much of the work is dissipated as
various other forms of energy (heat,
sound, etc.)
Gravitational Potential Energy
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Work can be done on a system to
raise its level of energy without
giving it kinetic energy.
Ex: Lifting a brick from the floor to
a tabletop.
Work was done against the force of
gravity, and the brick is said to have
gravitational potential energy.
Gravitational Potential Energy
U  m gh
h  height
U = Potential Energy
SI Units: Joule
Gravitational Potential Energy Example
Calculate the change in gravitational potential energy when a
5 kg brick is lifted 20 meters above ground level.
m  5kg
g  9.8m / s
h  20m
U ?
2
U  mgh
U  5kg(9.8m / s 2 )(20m)  980J
Conservation of Energy
Energy can be neither created nor
destroyed in any type of reaction,
physical or chemical. Rather,
energy simply changes form.
Conservation of Mechanical Energy

In any isolated system of objects
interacting only through
conservative forces, the total
mechanical energy E = KE + GPE,
of the system, remains the same at
all times.
Conservation of Mechanical Energy
Mathematically
Eo  E f
KEo  GPEo  KE f  GPE f
1 2
1 2
m vo  m gho  m vf  m ghf
2
2