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King Fahd University ofPetroleum & Minerals
Mechanical EngineeringDynamics ME 201
B
Dr! Meyassar "! #l$%addadecture ' 1(
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Chapter 14
Kinetics of a Particle ; Work & Energy
Objectives To develop the principle of work and energy and
apply it solve problems that involve force, velocity,and displacement.
To study problems that involve power and
efficiency.
To introduce the concept of a conservative forceand apply the theorem of conservation of energy
to solve kinetic problems.
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Work of a Force
F
S
U = F . S
F
U = (F cos ) . S
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Work of a Weight
)(21 yWU =
nt.displacemeverticalits
timesweightsparticle'theofmagnitude
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Work of a Spring Force
)2
1
2
1(
21
2221 ksksU =
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Work and Energy relation
=+ 2211 TUT
Initial .! " #ork $one % &inal .!
)2
1(])(
2
1[)
2
1(
2
2
22
1 mvmv NsyWksFs k =+
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Power and Efficiency
'ower is defined as the amount of work performed per unit time.
(rate of downing work)
*echanical !fficiency +
vFr
FrF
==
==dt
d
dt
d
dt
dUP
W
slbfthpsJsmNW
746
!!"1
=
===
inputenerg#outputenerg#
inputpoweroutputpower)(%fficienc# == 1
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14. Conser!ati!e Forces and Potential Energy
1onservative &orce+independent of the path
!ample weight 2 spring force
The work done by the frictional and applied force
/3 depends on the path /3 non/conservative/3 the work is dissipated 4heat5
'otential !nergy+(capacity for doing work)
!nergy comes from the motion /3 inetic energy
!nergy comes from the position/3 'otential energy
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6ravitational potential !nergy:
WyVg =
2
2
1
ksV +=
!lastic potential energy:
do!ny
upy
+
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2
2
1ksWsVVV g +=+=
'otential &unction+particle subjective to both gravitational and elastic force
)(2
1
)(
)2
1()
2
1(
*+or,
2
1
2
212
2
22
2
112121
2121
ksksssW
ksWsksWsVVU
VVU
=
++==
=
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Conser!ation of "echanical Energy
+=+ 2211 VTVT
2.21211 -)()( TUVVT non"ons =++
2211 VTVT +=+2
2
1mvT=
2
2
1skyWV +=
&or a system of 'articles
=+ 2211 TUT
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1
2
'
[ ] Whghg
WWv
g
WVT# =
=+=+=
22
22
1"
2
1
!ample
WhWhVT# =+=+= "111
WhWhghg
W#
ghh
gv$y%yavv
hWv
g
WVT#
C
=+=
==+=
+=+=
2
1
2
1
222
22
1
2
"
2
"
2
2
2222
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NmgT
mgT
maF nn
14!.14""1!cos
2"
!.1&"""1!cos
2
2
=+=
=
=
1!
"
6"
&"""
2
21
1
=
=
==
=
=
T
vv
&stat
kgm
o
o
!ample -/7
2211 VTVT +=+
smv
g
gv
gvg
!.1
&.1&246!."4"
)6"cos1!(cos2"&"""4"""
1
1!cos2"&"""&"""2
1
6"cos2"&""""
2
2
2
2
2
=
==
=
=
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8eview
!ample -/9
!ample -/-:
!ample -/--
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