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Chapter 5
Work, Power and
Provides a link between force and
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
• Newton • meter = Joule
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 (or d) is the distance of the object moved
•  is the angle between force and direction of
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
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
Work is positive
when lifting the
Work would be
negative if
lowering the box
• The force would
still be upward,
but the
would be
50N force pulls a 20 kg object and
moves it 2m, friction f=15N.
Acceleration along the ground? Work
done? Work done by friction? Total
What about pulling at 30?
Power is defined as this rate of work
SI units are Watts (W)
J kg  m 2
W 
Power, cont.
US Customary units are generally hp
• Need a conversion factor
ft lb
1 hp  550
 746 W
• 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
A crane lifts a 5000 kg object 800 m in
10 min. How much power must the
engine produce?
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
Conservation Laws
Electric Charge
Conservation of Energy
Sum of all forms of energy is conserved
Energy: ability to do work
Forms of Energy
• Focus for now
• May be kinetic (associated with motion)
or potential (associated with position)
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
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
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 (Ep)
• PE of water in reservoir is used to
generate electricity
E p  mgh
Reference Levels for Gravitational
Potential Energy
A location where the gravitational
potential energy is zero must be chosen
for each problem
• The choice is arbitrary since the change in
the potential energy is the important
• Choose a convenient location for the zero
reference height
often the Earth’s surface
may be some other point suggested by the
• Once the position is chosen, it must remain
fixed for the entire problem
A 1500kg pile driver lifted 20 m in the
air have EP …
Kinetic Energy
Energy associated with the motion of
an object
1 2
Ek  mv
Scalar quantity with the same units
as work
Work is related to kinetic energy
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
Consider energy of a falling ball of
mass m from height of h.
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
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  E p  Ek  constant
Conservation of Energy, cont.
Total mechanical energy is the sum
of the kinetic and potential energies
in the system
Ei  E f
E pi  Eki  E pf  Ekf
• Other types of potential energy
functions can be added to modify this
Conservation of (mechanical) Energy
True if only conservative forces are
• Conservative forces: gravity, springs
• Non-conservative forces: push, pull, friction,
Apply the conservation of energy equation
to the system
• Immediately substitute zero values, then do
the algebra before substituting the other
Solve for the unknown(s)
Work and Energy
If a force (other than gravity) acts on
the system and does work
Need Work-Energy relation
E pi  Eki  Wnc  E pf  Ekf
Wnc work done by non-cons. forces
1 2
1 2
mghi  mvi  W  mghf  mv f
Cart on a roller-coaster with no
friction. Start from rest at h=30m.
What is the speed at the end
Two cars each with mass 2000kg and
speed 80km/h collide and come to
Child on a 3 m high slide (no friction),
what is the speed at the end?
If a child of 25kg slides down from rest
and reaches only 3m/s. What work
was done by the frictional force
acting on the child?
If the slide is 10 m long, how large
was the average friction force?
Same child is on a swing with 6m rope
and starts at 60° with respect to
vertical direction. Maximum speed?
If the child starts with speed of 1 m/s
with a push, what is the max speed?