Chapter 8

Potential Energy and
Conservation of Energy
8-1 Potential Energy
Potential Energy U: energy
associated with
the configuration of a system of objects that
exerts force on one another.
Gravitational Potential Energy Ug: energy
associated with the separation between two
objects that attracts each other by gravitational
Elastic Potential Energy Us: energy associated
with the compression or extension of an elastic
Ch 8-2 Work and Potential Energy
 Kinetic (K) and Gravitational
Potential energy (Ug) of tomatoearth system
 Negative work Wg done by
gravitational force in the rise of
tomato in transferring K
(decreasing) into Ug (increasing)
of tomato
 Positive work Wg done by
gravitational force in the fall of
tomato in transferring Ug
(decreasing) into K (increasing)
of tomato.
  Ug =- Wg or - Ug = Wg
Ch 8-2 Work and Potential Energy
 Kinetic (K) and Elastic Potential
energy (Us ) of block-spring
 Negative work Ws done by spring
force in the rightward motion
transferring K (decreasing) of
block into Us (increasing) of
 Positive work Ws done by spring
force in the leftward motion
transferring Us (decreasing) of
spring into K (increasing) of
  Us =- Ws or - Us = Ws
Ch 8-2 Conservative and Nonconservative
 System contains two or more
objects including a point-like objects
(tomato or block)
 A force acts between point-like
object and rest of the system
 When the configuration change
force does work W1, changing
kinetic energy K of the object and
other type of energy of the system
 When the configuration change
reversed, force reverse the energy
transfer and does work W2
 Conservative Force: W1=-W2
 Nonconservative Force: W1-W2
Ch 8-3 Path Independence of Conservative
 The net work done by a
conservative force on a
particle moving around any
closed path is zero.
Ui=Uf (cylic process)
 The work done by a
conservative force on a
paticle moving between two
points does not depends on
the path
Ch 8 Check Point 1
The figure below show three
paths connecting points a and
b. A single force F does the
indicated work on a particle
moving along each path in the
he indicated direction. On the
basis of this information is the
force conservative?
• Non-conservative
Ch 8-4: Determining Potential Energy
 Work
done by a conservative force F
W=xi F (x) dx but U =-xfW , then
U =- W =- xi F (x) dx
 Gravitational Potential Energy Ug:
Ug=-yi -mg dy= mg(yf-yi); Ug(y)= mgy
 Elastic Potential Energy Us:
US=-yi -kx dx= k(xf2-xi2)/2; Us(y)=(kx2)/2
Ch 8 Check Point 2
•A particle to move along an xaxis from x=0 to x=x1., while
a conservative force , directed
along the x-axis, acts on the
particle. The figure shows
three situations , in which the
x component of that force
varies with x. The force has
same maximum magnitude F1 in
all three situations. Rank the
the situation according to the
potential energy during the
particle motion , most positive
U= -Fxdx
Calculate area under the
1) U=-(Fi X1)/2
2) U=-(Fi X1)
3) U=-[-(Fi X1)/2]= FiX1/2
Ans: 3, 1, 2
Ch 8-5: Conservation of Mechanical
 Mechanical energy Emec:
 In an isolated system where
only conservatives forces
cause energy change Emec is
K=W; U =-W then K=-U
Kf-Ki=-(Uf-Ui)=Ui –Uf
Kf+Uf =Ki+Ui
 Emec-f = Emec-i
Ch 8-7: Work Done on a System by an
External force
Work Wa is energy
transfer to or from
a system by means
of an external
force acting on
that system
Work done on a
system , no friction
involved (Ball –Earth
Wa=K+U= Emec
Ch 8-7: Work done on a system by an
external force
Work done on a system ,
friction involved (Block–floor
v2=v02+2ad; a=(v2-v02)/2d
F=fk+ma= fk+m(v2-v02)/2d
Wa =Fd=fkd+m(v2-v02)/2
Wa =fkd +K= Eth + Emec
Wa=K+U= Emec
Ch 8-8 Conservation of Energy
 Total energy E= Emec+Eth+Eint
The total energy E of a system can change only by amounts of
energy W that are transferred to or from the system
W=E=  Emec+  Eth+  Eint , W is work done on the system.
 Isolated System: The total energy E of an isolated system
cannot be changed then
E=  Emec+  Eth+  Eint=0
Emec-f-Emec-i + Eth+  Eint=0
 Emec-f= Emec-i - Eth-  Eint

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