Vectors and Projectile Motion
vectors magnitude
direction his
same magnitude
n.iq is v
to comatethemasritude
T no fifteen idle
an
atmaximumheight vis o
no
iq sohu.ua
o usino at
finn ran
milk in usinoft 9 and 0 isin o aan
Thetimeofflightisthesameforboth a ydirection range Ittucoso
sousuallytimewillbefoundbyapplying acceleration tisthetimetomaximumheight
formulasto ydirection subtto finda direction
Lusigns
a direction y direction
un ucoso my using s Using
cos0 2 g
ay 9.8ms
tosolve we canuse vy uy at
4
hastobepos t
aug
to findmaximumvertical displacement
sy 0.592 uyt
usethetimetakentoreachvy 0
If theflightis symmetrical i.elaunchingandlanding
atthesameheight unisconstant
timeby2
multiplythis
similarlyin a symmetricalflightthespeeds are
symmetricaltoo speedsatstart endarethesame
v u
findingtherange horizontaldisplacementbetween
startingandwindingpoint use
Un un
Fisactingdownward 9.8ms2 onlyonverticalspeed
he isconstant i an o
, Friction and Inclined Planes
py
T man
fairlysimpletoreaconisehowevertheycansometimesbe
a p m
confusedwithbankedtrack questionsinthecircular
Fac Img
motiontopic circularmotionalwayshas aforcedirected
towardsthecentreoracircle netforceisparallelto
the aroma
Inclinedplanequestionsrelyon understandinghow
weight i.eforceduetogravity andthenormalforce
it it Ei i
Fn Fa Fe
ae
interacttoformaresultantforce
aban the
with and
direction magnitudeor
relative each
force
normal
weight
I pm to the
combined form
forcev
net
resultant
resultant
weightforceis spited macoso
intocomponents parallel and perpendicular Imahl
sincethenormalforceisperpendiculartothesurfacethe
objectison theanglethat theplanemakewthegroundis frictionless Fnet Fp
important steepclose higheracceleration trig
use
P
Fe α Fn directlyrelatedtoFn 1,1in
µ constantorproportionality
usually
µ coefficientorfriction Fpisthecomponentorthegravitationalforce1
Fse usfor theincline plane
Fice man Fnetjust dueto gravitationalforce
Dependson materials typeorsurface
ex If the coefficientorfirebetween35kg a theflooris
0 so withfriction
whathorizontalforceis requiredtomovethecratetotherightat Metforce isdependson gravitationalforce
a constantspeedacrossthefloor Fret
Ff Fa Fa meFN micemg hqtgf.tt Ytngcoso
Fa 0.30 35 19.8 Fnet masino unacoso
102.9N
gag
T mg ma
met ᵗ
nm
Ft
Fnet unacoso
masino
casel F Fp accelerate uptheincline
case2 F C
Fp accelerate down_
yeI.fi
fp fer
o ifg cases F Fp remainstatormoveatconstantspeed siIFe
vectors magnitude
direction his
same magnitude
n.iq is v
to comatethemasritude
T no fifteen idle
an
atmaximumheight vis o
no
iq sohu.ua
o usino at
finn ran
milk in usinoft 9 and 0 isin o aan
Thetimeofflightisthesameforboth a ydirection range Ittucoso
sousuallytimewillbefoundbyapplying acceleration tisthetimetomaximumheight
formulasto ydirection subtto finda direction
Lusigns
a direction y direction
un ucoso my using s Using
cos0 2 g
ay 9.8ms
tosolve we canuse vy uy at
4
hastobepos t
aug
to findmaximumvertical displacement
sy 0.592 uyt
usethetimetakentoreachvy 0
If theflightis symmetrical i.elaunchingandlanding
atthesameheight unisconstant
timeby2
multiplythis
similarlyin a symmetricalflightthespeeds are
symmetricaltoo speedsatstart endarethesame
v u
findingtherange horizontaldisplacementbetween
startingandwindingpoint use
Un un
Fisactingdownward 9.8ms2 onlyonverticalspeed
he isconstant i an o
, Friction and Inclined Planes
py
T man
fairlysimpletoreaconisehowevertheycansometimesbe
a p m
confusedwithbankedtrack questionsinthecircular
Fac Img
motiontopic circularmotionalwayshas aforcedirected
towardsthecentreoracircle netforceisparallelto
the aroma
Inclinedplanequestionsrelyon understandinghow
weight i.eforceduetogravity andthenormalforce
it it Ei i
Fn Fa Fe
ae
interacttoformaresultantforce
aban the
with and
direction magnitudeor
relative each
force
normal
weight
I pm to the
combined form
forcev
net
resultant
resultant
weightforceis spited macoso
intocomponents parallel and perpendicular Imahl
sincethenormalforceisperpendiculartothesurfacethe
objectison theanglethat theplanemakewthegroundis frictionless Fnet Fp
important steepclose higheracceleration trig
use
P
Fe α Fn directlyrelatedtoFn 1,1in
µ constantorproportionality
usually
µ coefficientorfriction Fpisthecomponentorthegravitationalforce1
Fse usfor theincline plane
Fice man Fnetjust dueto gravitationalforce
Dependson materials typeorsurface
ex If the coefficientorfirebetween35kg a theflooris
0 so withfriction
whathorizontalforceis requiredtomovethecratetotherightat Metforce isdependson gravitationalforce
a constantspeedacrossthefloor Fret
Ff Fa Fa meFN micemg hqtgf.tt Ytngcoso
Fa 0.30 35 19.8 Fnet masino unacoso
102.9N
gag
T mg ma
met ᵗ
nm
Ft
Fnet unacoso
masino
casel F Fp accelerate uptheincline
case2 F C
Fp accelerate down_
yeI.fi
fp fer
o ifg cases F Fp remainstatormoveatconstantspeed siIFe
