Chapter 7
Work and Energy
Conservation Laws



Mass
Electric Charge
Conservation of Energy
Sum of all forms of energy is conserved
Energy: ability to do work
Forms of Energy

Mechanical
• Focus for now
• May be kinetic (associated with motion)
or potential (associated with position)


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Chemical
Electromagnetic
Nuclear
Some Energy Considerations

Energy can be transformed from one
form to another
• Essential to the study of physics,
chemistry, biology, geology, astronomy


From one body to another – Work!
Can be used in place of Newton’s
laws to solve certain problems more
simply
Work


Provides a link between force and
energy
The work, W, done by a constant
force on an object is the product of
the force times the distance through
which the force acts.
W  Fs
Units of Work

SI
• Newton • meter = Joule



N•m=J
J = kg • m2 / s2
US Customary
• foot • pound

ft • lb
• no special name
Work, cont.
In general
W  ( F cos ) s
• F is the magnitude of the force
• s is the distance of the object moved
•  is the angle between force and direction of
motion
Work, cont.

This gives no information about
• the time it took for the motion to occur
• the velocity or acceleration of the object

Work is a scalar quantity
More About Work

The work done by a force is zero when the
force is perpendicular to the displacement
• F=0
• s=0
• cos 90° = 0

If there are multiple forces acting on an
object, the total work done is the
algebraic sum of the amount of work done
by each force
More About Work, cont.

Work can be positive or negative
• Positive if s is in the same direction as F
• Negative if s is in opposite direction to F
• Zero if s is perpendicular to F
Work Can Be Positive or
Negative


Work is positive
when lifting the
box
Work would be
negative if
lowering the box
• The force would
still be upward,
but the
displacement
would be
downward
Example
50N force pulls a 20 kg object at 30°
above horizontal and moves it 2m,
friction f=15N. Acceleration along the
ground? Work done? Work done by
friction?
Kinetic Energy

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

Energy associated with the motion of
an object
1
KE  mv 2
2
Scalar quantity with the same units
as work
Work is related to kinetic energy
Work-Kinetic Energy Theorem


When work is done by the resultant
external force on an object and the
only change in the object is its
speed, the work done is equal to the
change in the object’s kinetic energy
Wnet  KEf  KEi  KE
• Speed will increase if work is positive
• Speed will decrease if work is negative
Work and Kinetic Energy

An object’s kinetic
energy can also be
thought of as the
amount of work
the moving object
could do in coming
to rest
• The moving
hammer has kinetic
energy and can do
work on the nail
Example
50N force pulls a 20 kg object at 30°
above horizontal and moves it 2m,
friction f=15N. Find vf if vi=4m/s.
Power


Often also interested in the rate at which
the energy transfer takes place
Power is defined as this rate of energy
transfer
•

W
P
t
SI units are Watts (W)
•
J kg  m 2
W 
3
s
s
Power, cont.

US Customary units are generally hp
• Need a conversion factor
ft lb
1 hp  550
 746 W
s
• Can define units of work or energy in terms of
units of power:


kilowatt hours (kWh) are often used in electric bills
1kWh=3.6x10^6 J
This is a unit of energy, not power
Example
An 80hp outboard motor, operating at
full speed, can drive at speed boat at
11 m/s. What is the forward
thrust(force) of the motor?
W Fs
P 
 Fv
t
t
Potential Energy

Potential energy is associated with
the shape or position of the object
• Potential energy is a property of the
system, not the object
• A system is a collection of objects
interacting via forces or processes that
are internal to the system
Elastic Potential Energy


Compression of a spring
Restoring force
F  kx
(k : spring constant)

Elastic potential energy
1 2
PE  kx
2

Energy is available to do work:
Gravitational Potential Energy

Lift object vertically, work is done
against the force of gravity of Earth
and energy is stored in the object in
the form of Gravitational Potential
Energy (PE)
• Falling object: PE is changed to KE
• PE of water in reservoir is used to
generate electricity
PE  mgh
Example
A 1500kg pile driver lifted 20 m in the
air have PE …
Energy Conservation
Energy is never created or destroyed.
Energy can be transformed from one
kind into another, but the total
amount of energy remains constant.
Example: Pendulum
Conservation of Mechanical
Energy

Conservation in general
• To say a physical quantity is conserved
is to say that the numerical value of the
quantity remains constant throughout
any physical process

In Conservation of Energy, the total
mechanical energy remains constant
E  PE  KE  constant
Conservation of Energy, cont.

Total mechanical energy is the sum
of the kinetic and potential energies
in the system
Ei  E f
KEi  PEi  KEf  PEf
• Other types of potential energy
functions can be added to modify this
equation
Work and Energy


If a force (other than gravity) acts on
the system and does work
Need Work-Energy relation
PEi  KEi  W  PEf  KEf

or
1 2
1 2
mghi  mvi  W  mghf  mv f
2
2
Example
Cart on a roller-coaster…
Example
Two cars each with mass 2000kg and
speed 80km/h collide.
Example
Child on a slide
If a child of 25kg slides down and
reaches only 3m/s. What work was
done by the frictional force acting on
the child?