Physics 101Chapter 02
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Transcript of Physics 101Chapter 02
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Chapter 2
Motion in One Dimension
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Kinematics Describes motion while ignoring
the agents that caused the motion For now, will consider motion in
one dimension Along a straight line
Will use the particle model A particle is a point-like obect, has
mass but in!nitesimal si"e
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#osition De!ned in terms o$
a frame ofreference One dimensional, so
generall% the &- or%-a&is
'he obect(s
position is itslocation withrespect to the$rame o$ re$erence
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#osition-'ime )raph 'he position-time
graph shows the
motion o$ theparticle *car+
'he smooth cureis a guess as to
what happenedbetween the datapoints
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Displacement De!ned as the change in position
during some time interal epresented as x
x .xf-xi /0 units are meters *m+ xcan be
positie or negatie Di1erent than distance the length
o$ a path $ollowed b% a particle
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Aerage /peed /peed is a scalar 4uantit%
same units as elocit%
total distance 6 total time
'he aerage speed is not*necessaril%+ the magnitude o$ the
aerage elocit%
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0nstantaneous 3elocit%'he limit o$ the aerage elocit% as
the time interal becomes
in!nitesimall% short, or as the timeinteral approaches "ero
'he instantaneous elocit%
indicates what is happening ateer% point o$ time
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0nstantaneous 3elocit%,
e4uations'he general e4uation $or
instantaneous elocit% is
'he instantaneous elocit% can bepositie, negatie, or "ero
0limx
t
x dxv
t dt
= =
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0nstantaneous 3elocit%,
graph 'he instantaneous
elocit% is the slopeo$ the line tangentto thexs: tcure
'his would be thegreen line
'he blue lines showthat as tgetssmaller, the%approach the greenline
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0nstantaneous /peed'he instantaneous speed is the
magnitude o$ the instantaneous
elocit% emember that the aerage speed
is not the magnitude o$ the
aerage elocit%
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Aerage Acceleration Acceleration is the rate o$ change
o$ the elocit%
Dimensions are 86'2
/0 units are m6s;
xf xixx
v vva
t t
= =
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0nstantaneous
Acceleration'he instantaneous acceleration is
the limit o$ the aerage
acceleration as tapproaches
3elocit% and acceleration are in the same direction
Acceleration is uni$orm *blue arrows maintain thesame length+ 3elocit% is increasing *red arrows are getting longer+ 'his shows positie acceleration and positie elocit%
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Acceleration and 3elocit%,
?
Acceleration and elocit% are in opposite directions
Acceleration is uni$orm *blue arrows maintain thesame length+ 3elocit% is decreasing *red arrows are getting shorter+ #ositie elocit% and negatie acceleration
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Kinematic @4uations,
speci!c For constant acceleration,
'his gies %ou the position o$ the
particle in terms o$ time andelocities
Doesn(t gie %ou the acceleration
() 12
fiixifx xxvtxvvt =+=++
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Kinematic @4uations,
speci!c For constant acceleration,
)ies !nal position in terms o$elocit% and acceleration
Doesn(t tell %ou about !nal elocit%
212
f i xi xx x v t a t= + +
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Kinematic @4uations,
speci!c For constant a,
)ies !nal elocit% in terms o$
acceleration and displacement
Does not gie an% in$ormationabout the time
() 222xfxixfi
vvaxx =+
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)raphical 8ook at Motion
displacement time cure 'he slope o$ the
cure is the
elocit% 'he cured line
indicates theelocit% is
changing 'here$ore, there is
an acceleration
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Acceleration o$ Freel%
Falling Obect 'he acceleration o$ an obect in $ree $all
is directed downward, regardless o$ the
initial motion 'he magnitude o$ $ree $all acceleration
is g. :< m6s2
gdecreases with increasing altitude
garies with latitude
:< m6s2is the aerage at the @arth(ssur$ace
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Acceleration o$ Free Fall,
cont: We will neglect air resistance
Free $all motion is constantl%
accelerated motion in onedimension
8et upward be positie
Ese the kinematic e4uations withay. g. -:< m6s2
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Free Fall @&le 0nitial elocit% at A is upward *5+
and acceleration is g*-: m6s2+
At , the elocit% is < and theacceleration is g*-: m6s2+
At C, the elocit% has the samemagnitude as at A, but is in theopposite direction
'he displacement is G
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Motion @4uations $rom
Calculus Displacement
e4uals the area
under the elocit% time cure
'he limit o$ thesum is a de!niteintegral
0
lim ( )f
in
t
xn n xtt
n
v t v t dt
=
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Kinematic @4uations Calculus Form with
Constant Acceleration
'he integration $orm o$ vf vigies
'he integration $orm o$xfxigies
xf xi xv v a t =
21
2f i xi xx x v t a t = +
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)eneral #roblem /oling
/trateg% Conceptuali"e
Categori"e
Anal%"e
Finali"e
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#roblem /oling
Categori"e /impli$% the problem
Can %ou ignore air resistanceH
Model obects as particles
Classi$% the t%pe o$ problem
'r% to identi$% similar problems %ou
hae alread% soled
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#roblem /oling Anal%"e /elect the releant e4uation*s+ to
appl%
/ole $or the unknown ariable /ubstitute appropriate numbers
Calculate the results
0nclude units ound the result to the appropriate
number o$ signi!cant !gures
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#roblem /oling Finali"e Check %our result
Does it hae the correct unitsH
Does it agree with %ourconceptuali"ed ideasH
8ook at limiting situations to besure the results are reasonable
Compare the result with those o$similar problems
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