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Unformatted text preview: Chapter 7 Lecture Essential University Physics Richard Welfeen
2nd Editien Conservation of Energy Conservative and Nonconseryatiye Forces  A oonaaryatiya foroa atoraa any work done against it, and
can “give back” the stored work as kinetic energy.  For a conaawatiya foroa, the work done in rnoying between
two points is inolapandant of the path:  Baoauaa the work done by a
oonaaryatiya force is path
independent, the work done in
going around any ofoaad path is
zero: if
i [BFwza  A nonoonaaryatiya foroa does not store work done against it, the work done may dapanal on path, and the work
done going around a closed path naaol not be zero. Potential Energy  The “atcred wcrk” aaacciated with a ccnaeryatiye fcrce is
called pctential energy. — Pctential energy ia atcred energy that can he released as
kinetic energy.  The change in pctential energy is deﬁned as the negative at the wcrk dcne by a ccneeryatiye fcrce acting cyer any path
between twc pcinta: 3..
ﬂUﬂz—AFdf — Pctential energy change is independent cf path.
— Only changes in pctential energy matter. — We’re free tc set the aerc cf pctential energy at any canyenient
pcint. Two Common Forms of Potential Energy  Gravitational potential energy stores
the work done against gravity: ﬁU: mg .ﬂy 5
— Gravitational potential energy increases
linearly with height y. — This reﬂects the constant gravitational force
near Earth's surface. Potential energy. if ' ii I Iciglu. _i'  Elastic potential energy stores the work done in stretching or compressing springs or t'
springlike systems:
U : 53mg — Elastic potential energy increases quadratically with
stretch or compression )6. — This reﬂects the lineany increasing spring force. "k. = [3" _ {.‘uiiiliruisinn Eiquiﬁhriuin leL'Iuli
spring’s equilibrium conﬁguration. Conservation of Mechanical Energy  By the workenergy theorem, the change in an object’s
kinetic energy equals the net work done on the object: AK = Wmat  When only conservative forces act, the net work is the negative of the potentialenergy change: Wm,1t = —AU  Therefore when only conservative forces act, any change in potential energy is compensated by an opposite change in
kinetic energy: AK + AU = 0
 Equivalently,
K + U = constant = Kﬂ + U.;}  Both these equations are statements of the law of
conservation of mechanical energy.  A spring—loaded dart gun  A spring and gravity — What’s the oert’s speed? — How high does the block go?
mon / Ir
' ﬂoor; j: _ L '
 5:: IL Eff;
‘ __ Es __ __ __ ' IJI' JVI *1 :45 4:: ' K+ U: Kn + Uﬂ becomes
émv2+020+éh2 ' SO vzqfk/mx wherexisthe initial spring  So 3:
compression.  K+ U: KtI + Uﬂ becomes
0+ring?!:0+%k:r2
hi
22mg Force and Potential Energy  Force is greatest where potential energy increases most
rapidly.  Mathematically, the component of force in a given direction is the negative derivative of the potential energy with
respect to position in that direction: At peaks and valleys.
there's no force. E
a; l‘orcc is grcatcr
F dU Li: Wi'lILtt'L? this. triii's't:
: — — = + I ' ' 'i. I. 'i. '
Is hiLJLpt. t.
I It:
dx E
H
E
C3
E‘— _ Position, .1:
its"hen the {Lii'vt is
rising In IilL‘ right.
l'an‘t' is 1H tho fi'fi. ...
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This note was uploaded on 02/12/2012 for the course PHYSICS 104 taught by Professor Staff during the Fall '10 term at Rutgers.
 Fall '10
 Staff
 Physics

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