Work & Power
Physics 2014
Work
• In Physics, Work is done when a
force moves a body through a
distance.
• WORK = Force x Displacement
Work Units
• Since, Force  Newton (N)
displacement  meter (m)
• DERIVED unit for work  Newton meter
(Nm).
• The FUNDAMENTAL unit for work is the
Joule.
1 JOULE = the
• Joule (J) = N • m
ability to exert a
force of 1 NEWTON
over a distance of 1
METER.
ConcepTest 7.1 To Work or Not to Work
Is it possible to do work on an
1) yes
object that remains at rest?
2) no
ConcepTest 7.1 To Work or Not to Work
Is it possible to do work on an
1) yes
object that remains at rest?
2) no
Work requires that a force acts over a distance.
If an object does not move at all, there is no
displacement, and therefore no work done.
Work
• Atlas bears the weight of the world on
his shoulders.
• How much work is done?
• NONE…… the world did not
move…The force must move the
object.
Work or No Work
No
work
occurs
when: work
Lifting
your
bookbag
Carrying your bookbag  no work
A waitress carrying a tray around?
No work because the supporting force is
perpendicular to the motion.
• Work is done on an object only if the
object moves and only if the force and
displacement are in the same direction.
• DIRECTION IS THE KEY TO WORK….
•
•
•
http://id.mind.net/~zona/mstm/physics/mecha
nics/energy/work/work2.gif
http://hyperphysics.phy-astr.gsu.edu/hbase/imgmec/wnot.gif
ConcepTest 7.4 Lifting a Book
You lift a book with your hand
1) mg  r
in such a way that it moves up
2) FHAND  r
at constant speed. While it is
3) (FHAND + mg)  r
moving, what is the total work
4) zero
done on the book?
5) none of the above
r
FHAND
v = const
a=0
mg
ConcepTest 7.4 Lifting a Book
You lift a book with your hand
1) mg  r
in such a way that it moves up
2) FHAND  r
at constant speed. While it is
3) (FHAND + mg)  r
moving, what is the total work
4) zero
done on the book?
5) none of the above
The total work is zero since the net
force acting on the book is zero. The
work done by the hand is positive,
r
FHAND
v = const
a=0
while the work done by gravity is
negative. The sum of the two is zero.
Note that the kinetic energy of the
book does not change either!
mg
Follow-up: What would happen if FHAND were greater than mg?
Work Problems
• A force of 825 N is required to push
a car across a lot. Two students
push the car 35 m. How much work
is done?
F= 825 N
d = 35 m
W = Fd
Cutnell & Johnson, Wiley Publishing, Physics 5th Ed.
Work
• Only force that is in the same
direction of the motion counts.
• If you pull a wagon at an angle, only
the horizontal part of motion counts –
only the horizontal part of the pull
does any work!
Cutnell & Johnson, Wiley Publishing, Physics 5th Ed.
Work Problems
An airplane passenger carries a 215N
suitcase up a flight of stairs a displacement
of 4.2m vertically and 4.6m horizontally.
How much work have they done?
Work
• If the angle between force and
displacement is θ then
Fx = F cos θ
• Then the work done is
W = Fx • d= F cos θ d
W=Fd (cos θ)
Cutnell & Johnson, Wiley Publishing, Physics 5th Ed.
Copywrited by Holt, Rinehart, &
W = Fd cos θ
• If θ = 90o W = Fd cos 90o
• So, W = 0
• Work is a scalar quantity.
• No direction is associated
with work even though it
depends on two vector
quantities.
http://www.physicsclassroom.com/Class/energy/U5L1a.html
Work
Work
To move a refrigerator into the
back of a moving van. Would you
prefer to lift it straight up or walk it
up a ramp?
• Calculate which method required
less work?
• Equal amounts of work are done.
• The ramp reduces the amount of
effort it takes to do work, but
DOES NOT CHANGE the
amount of work that is done.
Positive and Negative Work
• When positive work is done
on an object, its speed
increases; when negative
work is done, its speed
decreases.
Copywrited by Holt, Rinehart, & Winston
Cutnell & Johnson, Wiley Publishing, Physics 5th Ed.
Work Direction
ConcepTest 7.2a Friction and Work I
A box is being pulled
across a rough floor
1) friction does no work at all
at a constant speed.
2) friction does negative work
What can you say
3) friction does positive work
about the work done
by friction?
ConcepTest 7.2a Friction and Work I
A box is being pulled
across a rough floor
1) friction does no work at all
at a constant speed.
2) friction does negative work
What can you say
3) friction does positive work
about the work done
by friction?
Friction acts in the opposite
N displacement
direction to the displacement, so
the work is negative. Or using the
Pull
f
definition of work (W = F d cos q ),
since q = 180o, then W < 0.
mg
ConcepTest 7.2b Friction and Work II
Can friction ever
do positive work?
1) yes
2) no
ConcepTest 7.2b Friction and Work II
Can friction ever
do positive work?
1) yes
2) no
Consider the case of a box on the back of a pickup truck.
If the box moves along with the truck, then it is actually
the force of friction that is making the box move.
Work Problems
• A 10-N frictional force
slows a moving block to a
stop after a displacement
of 5.0 m to the right. What
is the net work done on
the block?
• A 10-N force is applied to
push a block across a
frictional surface at
constant speed for a
displacement of 5.0 m to
the right. What is the net
work done on the block?
http://www.physicsclassroom.com/Class/energy/U5L1a.html
http://www.physicsclassroom.com/Class/energy/U5L1a.html
http://www.physicsclassroom.com/Class/energy/U5L1a.html
Work Problems
A physics student pulls a box of books
as shown. The 455 N force is
applied along the rope itself. How
much work is done by the student on
the books if the box is dragged 24.5
m.
http://k12.albemarle.org/Instruction/Physics/energy2/test1c.htm
Questionable Work
Which ramp requires more work to
move the car up a set height?
a.
b.
c.
d.
30°
45 °
60 °
work is equal
http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html
http://www.physicsclassroom.com/mmedia/energy/au.html
ConcepTest 7.3 Force and Work
A box is being pulled up a rough
1) one force
incline by a rope connected to a
2) two forces
pulley. How many forces are
3) three forces
doing work on the box?
4) four forces
5) no forces are doing work
ConcepTest 7.3 Force and Work
A box is being pulled up a rough
1) one force
incline by a rope connected to a
2) two forces
pulley. How many forces are
3) three forces
doing work on the box?
4) four forces
5) no forces are doing work
Any force not perpendicular
to the motion will do work:
N does no work
N
T
T does positive work
f
f does negative work
mg does negative work
mg
Work Done by a Variable
Force
If the force changes with the displacement,
W=Fd is no longer valid
– Calculus is needed to calculate this directly
However, If force is plotted vs displacement the
work can be graphically found as the area
under the curve.
Constant Force
Changing Force
Work Done by a Variable
Force
Varying Force of a Spring
Recall the spring force is
Fs = kx
So, the work is
Calculate the work
Work Overview
http://hyperphysics.phy-astr.gsu.edu/hbase/wcon.html
ConcepTest 7.11a Time for Work I
Mike applied 10 N of force over 3 m
in 10 seconds. Joe applied the
same force over the same distance
in 1 minute. Who did more work?
1) Mike
2) Joe
3) both did the same work
ConcepTest 7.11a Time for Work I
Mike applied 10 N of force over 3 m
in 10 seconds. Joe applied the
same force over the same distance
in 1 minute. Who did more work?
1) Mike
2) Joe
3) both did the same work
Both exerted the same force over the same
displacement. Therefore, both did the same
amount of work. Time does not matter for
determining the work done.
Review
• Work is dependent on 
force and displacement.
The amount of work that is done in moving a
same
50N box a distance of 30 m is the ______
whether it takes 1 minute, 1 hour, or 1 day.
more power to
• Power is different. It takes ______
move that 50 N box 30 meters in 1 minute
than it takes to move it the same distance in
1 hour.
• When you’re talking about power…
TIME MATTERS!
Power
• Power is the rate at which work is done.
Work
Power 
Time
• Since work is equal to force x displacement: 
Force  Displaceme nt
Power 
Time
http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html
Power Units
• Derived Units:
Joule ( J )
J

Second ( s) s
• Fundamental Units:
Joule( J ) J
Watt (W ) 

Second ( s) s
• 1 kilowatt = 1 kW = 1000 watts
• 1 kWh (kilowatt hour) = 3.60 x 106 J
• 1 horsepower (hp) = 745.7 W
Power Derivation
W
P
t
d
 v
t
Fd

t
 P  Fv
P=Fv
ConcepTest 7.11b Time for Work II
Mike performed 5 J of work in
1) Mike produced more power
10 secs. Joe did 3 J of work
2) Joe produced more power
in 5 secs. Who produced the
3) both produced the same
greater power?
amount of power
ConcepTest 7.11b Time for Work II
Mike performed 5 J of work in
1) Mike produced more power
10 secs. Joe did 3 J of work
2) Joe produced more power
in 5 secs. Who produced the
3) both produced the same
greater power?
amount of power
Since power = work / time, we see that Mike produced 0.5 W
and Joe produced 0.6 W of power. Thus, even though Mike
did more work, he required twice the time to do the work, and
therefore his power output was lower.
Power Problems
A small motor does 4000J of work in
20 seconds. What is the power of
the motor in watts?
W = 4000 J
T = 20 s
P=?
Power Problems
An electric motor lifts an elevator that
weighs 1.2 x 104N a distance of
9.00 meters in 15.0 s. What is the
power of the motor in kilowatts?
F = 1.2 x 104 N
d = 9.00 m
t = 15.0 s
P = ? (kW)
ConcepTest 7.11c Power
Engine #1 produces twice the
power of engine #2. Can we
conclude that engine #1 does
twice as much work as engine #2?
1) yes
2) no
ConcepTest 7.11c Power
Engine #1 produces twice the
power of engine #2. Can we
1) yes
2) no
conclude that engine #1 does
twice as much work as engine #2?
No!! We cannot conclude anything about how much
work each engine does. Given the power output, the
work will depend upon how much time is used. For
example, engine #1 may do the same amount of work
as engine #2, but in half the time.
Efficiency (η)
η greek letter ‘eta’
In an ideal world, work out equals work in.
However, in the real world work is lost to
friction, heat and other inefficiencies (bureaucracy).
Efficiency (η) measures how much work
is produced for the work inputted
• the ratio of useful work
actual work
Wout

 100%
Win
Fout d out

 100%
Fin d in