Raised eyebrows
ways that energy
can be transferred
7/5/15 Page 3
 
efinition of Work • Work re!"ires a force be app#ied to an object "ndergoing
a disp#acement.
• Work is not done "n#ess the object mo$es in the
direction of the app#ied force.
• %he app#ication of force a#one does not make work.
 
•  
are $ectors.
the force that acts in the
direction of the
 – -f θ = 0 then the cos 0 1 and therefore
 – if θ = 90 then cos 0 and therefore .
 
•  
 
efinition of work • -f yo" are p"shing down on a bo and the bo
is mo$ing sideways )not down* then yo" are
not doing work.
• %his imp#ies that no work is done if the force
app#ied is perpendic"#ar to the direction of
motion of the object
Work
• Work can be positi$e or negati$e.  – Work is positi$e when the component of
force is in the same direction as
disp#acement
Positive Work 
the direction opposite to the
disp#acement
 egative Work 
amp#e 18 Work on a point object.
•  9 r"bber band app#ies a force of :. & to an 9ngry
;ird o$er a distance of .3 m. 4ow m"ch work is
done on the bird by the r"bber band
• G: 
• U: 
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•  
 
•  9n 9ngry bird is dragged 1. m across a friction#ess
tab#e. %he app#ied force is :. & at an ang#e of 3
degrees from hori<onta#. 4ow m"ch work does the
app#ied force do
   !
 
for a distance of :. m at a constant speed.
4ow m"ch work was done by the teacher on
the bird
   !
 
Work
• -f more than one force acts on an object then we ca#c"#ate net work two ways8  – +ind the work done by each force and add
the works.
Work
) "
Hooke’s Law
0 1 2 3 4 5 6 7 8 9 0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
Force vs. displacement
 The force exerted on a sprn! s drect"# proportona" to the dstance
the sprn! s stretched.
 The force exerted $# the sprn! s opposte the drecton of
dsp"ace%ent.
*raphca" +nterpretaton of ,ork
-onsder a !raph of the co%ponent of the force n the drecton of the dsp"ace%ent s. poston.
,ork s ca"c/"ated as the area /nder the !raph
(
(nd the work done $# the force !raphed $e"ow.
(
xa%p"e 5 ,ork on a prn!
sprn! that o$e#s Hooke’s Law s attached to a statonar# $racket. Hooke’s Law !es the force of a sprn! as (
kx
(nd the work done on the sprn! when t s
 
 
 
   n 
    t       o   n  
       n    #   o    /   r
   3 
 
 
=ractce pro$"e%s sprn! stretches .020 % when a force of
0.60 ) s app"ed. ,hat s the sprn! constant of the sprn!> How %/ch work wo/"d $e done on the sprn! to stretch t to a "en!th of 0.040 %>
 
?/eston 1 so"/ton
 
 
G:  U: E:  S:  S: 
 
 
 
?/eston 2 so"/ton
 
 
G:  U: E:  S:  S: 
 
 
 
ways energy can be
transferred to or from
of energy transfer.
    R    a   d
   n
C   o n d  u c t  i  o n  
C   o n v  e c t  i  o n 
Work 
Energy
of
Object
What happens when we do work?
When we do positive work on the obe!t" we in!rease its energy#
When negative work is done" we de!rease its energy#
 
 
Work trans$ers energy to or $rom an obe!t or system#
The net work done on an obe!t or system e%&a's the !hange in energy o$ the obe!t or system#
 E W  NET    =
 
Work and )ineti! Energy
The net work done on a point obe!t is the work done by the net $or!e#
*y +ewton,s e!ond .aw" F  NET =ma,
sing an e%&ation $rom kinemati!s"
*y s&bstit&tion" we get
 xavv
 xavv
 f  
 f  
 xmaW  NET    =
m has a kinetic energy gi$en by8
"
%he work done on a point object is e!"a#
to the change in its kinetic energy.
  "
#" $"
 
E(amp'e 1: 0pp'ying the Work- Energy Theorem to a oint be!t#  0 $or!e o$ 123# + p&shes a bo( a'ong a smooth
board a distan!e o$ 3#433 m# The board e(erts a $or!e o$ 5#33 + opposite the motion# ow $ast wi'' the bo( be moving a$ter this p&sh? The mass o$ the bo( is 3#3 kg#
G: 
U:
E:
S:   
S: 
 
E(amp'e 2: 0pp'ying the Work- Energy Theorem to a oint be!t  9 6.'kg bo is raised
from rest a distance of 3.
meters by a $ertica# force
of 2. &. +ind the work
done by the force the
work done by gra$ity and
the fina# speed of the bo.
)9ss"me g 0 1. m/s:.*
 9nswer8 ?:= ( '12 (
=.5 m/s
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E(amp'e 2: 0pp'ying the Work- Energy Theorem to a oint be!t
 3 forceW  3 gravityW  4=v
 x F W   NET  NET    =
"
#" $"
01 "
 J $2#0&01$#-1   −=−×=
Work !an be done on systems o$ obe!ts#
When net work is done on a sing'e parti!'e" the kineti! energy !hanges#
When work is done on a system" the energy !an be !hanged in other ways#
10 kg
9onsider the mass to be a separate obe!t#
9a'!&'ate the net work done on the mass#
4 kg
 +2#%m0 01"5#1   =−= g W 
 #+2#%+2# == NET W 
E(amp'e 5: Work on a system
+ow treat the Earth and the mass as part o$ the same system#
9a'!&'ate the net work done on the system#
4 kg " m
 +2#==  APP  NET    W W 
 
if the tota# work it does
on a partic#e is <ero
when the partic#e
mo$es a#ong any
c#osed path ret"rning
to its initia# position.
%hese forces are part
 
=ri!tion: 0 +on!onservative =or!e  9 bo s#iding "p a ramp is acted on by a force
of gra$ity of magnit"de 5. & and a frictiona#
force of magnit"de 1. &.
%he bo s#ides "p a distance of 3 meters and
back down a distance of 3 meters.
When the bo ret"rns to the starting point
what is the net work done by gra$ity What
is the net work done by friction
%he work done by a nonconser$ati$e force
#ike friction depends on the path taken.
 
Potentia# energy is defined as stored energy.
Potentia# energy is present in an object that has the potentia# to mo$e beca"se of its position re#ati$e to some other #ocation.
@n#ike Ainetic energy potentia# energy depends not on#y on the properties of an object b"t a#so on the objects interaction  with the en$ironment
7/5/15

 
>ra$itationa# Potentia# energy is the energy d"e to the position of the object re#ati$e to the arth or some other gra$itationa# so"rce.  
@nits are jo"#es )(*
E'asti! otentia' Energy
#astic potentia# energy is stored in any compressed or stretched object s"ch as a spring or the stretched strings of a tennis racket or g"itar.
 
 
spring is to being compressed or
stretched.
+irm Bpring 0 #arge k
Bpring constant "nits 0 &/m
0 distance compressed or stretched
7/5/15 8
inc#"de8 echanica# energy8
object
Chemica# energy
#ectrica# energy
ra!ti!e prob'em A 1
 9 =. kg chi#d is in a swing that is attached
to ropes :. m #ong. +ind the gra$itationa#
potentia# energy associated with the chi#d at
the bottom of the arc. 9s she swings.
7/5/15 5
ra!ti!e prob'em A2
 9 7 kg man is attached to a b"ngee cord with an "nstretched #ength of 15m. 4e j"mps off a bridge that is 5 m high. When j"mping his cord stretches to ==m. %he spring constant of the cord is 71.2 &/m. What is his change in tota# potentia# energy re#ati$e to the water when the man stops fa##ing
7/5/15 55
 
E(amp'e 1: 0 tossed ba''#  9 physics st"dent tosses a ba## with a mass of
1 grams straight "p. Whi#e she is throwing
the ba## she eerts a constant force of 3 & on
the ba## o$er a $ertica# distance of 1 m. g0 1
m/s:
4ow m"ch work did gra$ity do
;y how m"ch did the systems potentia# energy
change
 
 9 .6 kg basketba## is dropped o"t of a window
that is 6.1 m abo$e the gro"nd. %he ba## is
ca"ght by a person whose hands are 1.5 m
abo$e the gro"nd.
4ow m"ch work is done on the ba## by gra$ity
What is the gra$itationa# P when it is
re#eased
What is the gra$itation P when it is ca"ght
4ow is the change in P re#ated to the work
done on the ba##
 
otentia' Energy o$ a pring %he work done in stretching a spring can be
fo"nd "sing the area "nderneath a force $s.
distance graph.
TO ANOTHER 
7/5/15 62
 
Be!hani!a' Energy %he description of motion of objects in$o#$es the
combination of kinetic energy and potentia# energy.
Consider the motion of the different parts of a pend"#"m
c#ock.
 9t the highest point of the swing there is on#y
gra$itationa# potentia# energy associated with its
position
 9t the other points in the swing when the pend"#"m is
in motion it has both kinetic and potentia# energy.
#astic potentia# energy is a#so present in many
springs that are part of the inner workings of the c#ock
7/5/15 6
energy and a## the forms of potentia#
energy associated with an object or gro"p
of objects.
 
9onservation o$ Be!hani!a' Energy &et work done on objects is the tota# work done which
changes the kinetic and potentia# of the objects
;"t the forces doing this work are conser$ati$e. %hat
means when they do work potentia# energy decreases.
%h"s if the A of the objects increases the P m"st
decrease.
 
interna#
conser$ati$e
energy
conser$ation of mechanica# energy does not
ho#d beca"se kinetic energy is not a## con$erted
potentia# energy b"t some is #ost to heat and
so"nd.
ra!ti!e prob'em A1
 9 6 m #ong ramp is "sed to bring carts "p 3m
from the gro"nd to a #oading dock. 9
care#ess worker #ets go of a : kg cart at the
top of the ramp and it ro##s to the bottom.
4ow fast is the cart mo$ing when it reaches
the bottom
bottom f  topi   ME  ME  0101   =
## "
" $
 
 0ssignment C&estion A 1  9 bird is f#ying with a speed of 12 m/s o$er water
and drops a : kg fish. -f the bird is 5.= m high
what is the speed of the fish when it hits the water
G
c#ass tomorrow
-f other forms of
 
The =irst .aw o$ Thermodynami!s: The .aw o$ 9onservation o$ Energy
nergy can neither be created or destroyed
b"t can on#y be con$erted from one form to
another.
 
 
 
ower Power is the rate at which work is done.
ore genera##y power is the rate of energy
transfer by any method.
an a#ternati$e form by s"bstit"ting the definition
of work into the definition of power 
  t 
"se an a#ternati$e power
form"#a.
Watt 0 1 (o"#e / second
4orsepower is another "nit of
power.
 
do the same work in different times.
%he higher the rating the more work
done in a set amo"nt of time.
%he important difference is that the
more powerf"# motors wi## do the
work in a shorter amo"nt of time
 
ra!ti!e rob'em A1
 9 motor is "sed to #ift a #oad of #"mber weighing
= & to a height of 5 m in 1 s. What is the
minim"m power the motor m"st prod"ce
G: 
U: 
E: 
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ra!ti!e prob'em A2
 9 rain c#o"d contains :.66 17 kg of water $apor. 4ow #ong
wo"#d it take a :. kW p"mp to raise the same amo"nt of
water to the c#o"ds a#tit"de :.km
G: 
U: 
E:
S: