friction theory e

8/12/2019 Friction Theory E

1/14

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"h`fdsbiuh`rpbysdms.df" 0

EZDM_DAF0. EZDM_DAF

Wblf twa jaodls `rl ilpt df maft`mt, lclmtrah`gfltdm earmls `mt jltwllf tbl mb rglo p`rtdmcls (haclmucls)

`t tbl sure`mls ae tbl jaodls. _bus, l`mb jaoy lxlrts ` maft`mt earml af tbl atblr. _bl h`gfdtuols ae tblmaft`mt earmls `mtdfg af tbl twa jaodls rl lqu c jut tbldr odrlmtdafs `rl appasdtl `fo tblrlearl tbl maft`mt

earmls ajly Flwtafs tbdro c`w.

_bl odrlmtdaf ae tbl maft`mt earml `mtdfg af ` p`rtdmuc r jaoy ds fat flmlss`rdcy plrplfodmuc r ta tbl maft`mt

sure`ml. Wl m`f rlsacvl tbds maft`mt earml dfta twa mahpaflfts, afl plrplfodmuc`r ta tbl maft`mt sure`ml

`fo tbl atblr p`r cclc ta dt (edgurl. _bl plrplfodmuc r mahpaflft ds m cclo tbl farh c maft mt earml ar farh c

earml ( glflr`ccy wrdttlf `s F) `fo tbl p`r`cclc mahpaflft ds m`cclo erdmtdaf (glflr`ccy wrdttlf `s e).

_blrlearl de Z ds maft`mt earml tblf

Z 8 :: Fe

:. ZL@]AF] EAZ EZDM_DAF

(d) ftlr-camidfg ae lxtlfolo p`rts ae afl ajklmt dfta tbl lxtlfolo p`rts ae tbl atblr ajklmt.

(dd) Jafodfg jltwllf tbl haclmucls ae tbl twa sure`mls ar ajklmts df maft`mt.

=. EZDM_DAF EAZML D] AE _WA _T^L].

`. Idfltdm j. ]t`tdm

(`) Idfltdm Erdmtdaf Earml

Idfltdm erdmtdaf lxdsts jltwllf twa maft`mt sure`mls afcy wblf tblrl dsrlc`tdvl hatdaf jltwllf

tbl twa maft`mt sure`mls. Dt staps `mtdfg wblf rlc`tdvl hatdaf jltwllf twa sure`mls ml`sls.

ODZLM_DAF AE IDFLM_DM EZDM_DAF AF @F AJKLM_

t ds appasdtl ta tbl rlc tdvl vlcamdty ae tbl ajklmt wdtb rlsplmt ta tbl atblr ajklmt df maft mt mafsdolrlo.

Fatl tb t dts odrlmtdaf ds fat appasdtl ta tbl earml `ppcdlo dt ds appasdtl ta tbl rlc`tdvl hatdaf ae tbl

jaoy mafsdolrlo wbdmb ds df maft`mt wdtb tbl atblr sure`ml.

H@GFD_\OL AE IDFL_DM EZDM_DAF

_bl h`gfdtuol ae tbl idfltdm erdmtdaf ds prapartdaf`c ta tbl farh`c earml `mtdfg jltwllf tbl twa jaodls. Wl

m`f wrdtl

ei

8i

F

wblrl F ds tbl farh`c earml. _bl prapartdaf`cdty mafst`ft i

ds m`cclo tbl maleedmdlft ae idfltdm erdmtdaf

`fo dts v`cul olplfos af tbl f`turl ae tbl twa sure`mls df maft`mt.

Lx`hpcl 0. Edfo tbl odrlmtdaf ae idfltdm erdmtdaf earml

(`) af tbl jcami, lxlrtlo jy tbl graufo.

(j) af tbl graufo, lxlrtlo jy tbl jcami.


2/14

^BT]DM]

"h`fdsbiuh`rpbysdms.df" :

]acutdaf ; ( )

(j)

wblrl e0 `fo e: `rl tbl erdmtdaf earmls af tbl jcami fo graufo rlsplmtdvlcy.

Lx`hpcl :. Df `javl lx`hpcl marrlmt rlc tdaf jltwllf h`gfdtuol ae e0

`fo e:

ds

(@) e06 e

: (J) e

:6 e

0

(M) e0

8 e:

(O) fat passdjcl ta olmdol oul ta dfsueedmdlft o`t`.

]acutdaf ; Jy Flwtafs tbdro c`w tbl `javl erdmtdaf earmls `rl `mtdaf-rl`mtdaf p`dr `fo lqu c jut appasdtl ta

l`mb atblr df odrlmtdaf. Blfml (M).

@csa fatl tb`t tbl odrlmtdaf ae idfltdm erdmtdaf b`s fatbdfg ta oa wdtb `ppcdlo earml E.

Lx`hpcl =. @cc sure`mls s sbawf df tbl edgurl rl raugb. Or`w tbl erdmtdaf earml af @ & J

J

@ 0>h/s

:>h/s

////////////////////////////////////////////////////////

]acutdaf ;

Idfltdm erdmtdaf `mts df sumb ` w`y sa `s ta rlouml rlc`tdvl hatdaf.

Lx`hpcl ?. Edfo aut tbl odst`fml tr`vlcclo jy tbl jcamis sbawf df tbl edgurl jlearl dt staps.

0> ig

0> h/s

///////////////////////////////////////// 8>.g

F

ei

F 0> g 8 >

F 8 0>> F

ex

8 iF

8 s8

iwblf fat hlftdaflo

ex8 >.< 0>> 8 F

Ex8 h`

8 0> ` ` 8 : 8 0>: + : ( h

Lx`hpcl h/s `fo maleedmdlft ae erdmtdaf jltwllf tbl jcami `fo dfmcdfl ds 8 >.

h/s

edxlo


3/14

^BT]DM]

"h`fdsbiuh`rpbysdms.df" =

]acutdaf ; F 8 hg mas=7

hg sdf =7 + F 8 h`

` 8 0> h/s: oawf tbl dfmcdfl

Faw v: 8 u: + :`s

> 8 0>: + :(0>) ]

] 8 < h

Lx`hpcl 5. Edfo tbl tdhl t`ilf df tbl `javl lx`hpcl jy tbl jcami ta rl`mb tbl dfdtd`c pasdtdaf.

]acutdaf ; ` 8 g sdf =7 g mas =7

h/s `fo ` earml ae 0>> F df `oodtdaf ta erdmtdaf earml ds `csa `mtdfg af

tbl jcami. Edfo tbl rlt`ro`tdaf ae tbl jcami1

]acutdaf ; @s tblrl ds rlc`tdvl hatdaf

idfltdm erdmtdaf wdcc `mt ta rlouml tbds rlc`tdvl hatdaf.

ei

8 F 8 >.0 0> 0> 8 0> F

0>> + 0> 8 0>`

` 80>

00>8 00 h/s:

(j) ]_@_DM EZDM_DAF

t lxdsts jltwllf tbl twa sure`mls wblf tblrl ds tlfolfmy ae rlc tdvl hatdaf jut fa rlc`tdvl hatdaf

`cafg tbl twa maft`mt sure`ml.

Ear lx`hpcl mafsdolr ` jlo dfsdol ` raah 9 wblf wl glftcy pusb tbl jlo wdtb ` edfglr, tbl jlo oals

fat havl. _bds hl`fs tb`t tbl jlo b`s ` tlfolfmy ta havl df tbl odrlmtdaf ae `ppcdlo earml jut oals

fat havl `s tblrl lxdsts st`tdm erdmtdaf earml `mtdfg df tbl appasdtl odrlmtdaf ae tbl `ppcdlo earml.

Lx`hpcl 2. Wb`t ds v`cul ae st`tdm erdmtdaf earml af tbl jcami1

]acutdaf ; Df bardzaft`c odrlmtdaf `s `mmlclr`tdaf ds zlra.

_blrlearlE 8 > . 8 >


4/14

^BT]DM]

"h`fdsbiuh`rpbysdms.df" ?

drlmt daf ae st`t dm e rdmtdaf earml_bl st`tdm erdmtdaf earml af `f ajklmt ds appasdtl ta dts dhplfodfg hatdaf rlc`tdvl ta tbl sure`ml.

Eaccawdfg stlps sbauco jl eaccawlo df oltlrhdfdfg tbl odrlmtdaf ae st`tdm erdmtdaf earml af f ajklmt.

(d) Or`w tbl erll jaoy od`gr`h wdtb rlsplmt ta tbl atblr ajklmt af wbdmb dt ds ilpt.

(dd) Dfmcuol psluoa earml `csa de maft`mt sure`ml ds mmlclr`tdfg.

(ddd) Olmdol tbl rlsuct`ft earml `fo tbl mahpaflft p`r`cclc ta tbl sure`ml ae tbds rlsuct`ft earml.

(dv) _bl odrlmtdaf ae st`tdm erdmtdaf ds appasdtl ta tbl `javl mahpaflft ae rlsuct`ft earml.

Fatl ; Blrl afml `g df tbl st tdm erdmtdaf ds dfvacvlo wblf tblrl ds fa rlc`tdvl hatdaf jltwllf twa

sure`mls.

Lx`hpcl 4. Df tbl eaccawdfg edgurl `f ajklmt ae h`ss H ds ilpt af ` raugb t`jcl `s sllf

erah `javl. Earmls `rl `ppcdlo af dt `s sbawf. Edfo tbl odrlmtdaf ae st`tdm

erdmtdaf de tbl ajklmt oals fat havl.

]acutdaf ; Df tbl `javl prajclh wl edrst or`w tbl erll jaoy od gr`h ae edfo tbl rlsuct`ft earml.

@s tbl ajklmt oal fat havl tbds ds fat ` m`sl ae cdhdtdfg erdmtdaf. _bl odrlmtdaf ae st`tdm erdmtdaf ds appasdtl ta

tbl odrlmtdaf ae tbl rlsuct`ft earml EZ

`s sbawf df edgurl jy es

. Dts h`gfdtuol ds lqu`c ta :< F.

H@GFD_\OL AE IDFL_DM @FO ]_@_DM EZDM_DAFIdfltdm erdmtdaf ;

_bl h`gfdtuol ae tbl idfltdm erdmtdaf ds prapartdaf`c ta tbl farh`c earml `mtdfg jltwllf tbl twa jaodls. Wl

m`f wrdtl

ei

8i

F

wblrl F ds tbl farh`c earml. _bl prapartdaf`cdty mafst`ft i

ds m`cclo tbl maleedmdlft ae idfltdm erdmtdaf

`fo dts v`cul olplfos af tbl f turl ae tbl twa sure`mls df maft`mt. De tbl sure`mls `rl shaatb i

wdcc jl

sh cc, de tbl sure`mls `rl raugb i

wdcc jl c rgl. Dt `csa olplfos af tbl h`tlrd cs ae tbl twa jaodls df maft`mt.

]t`tdm erdmtdaf ;_bl h`gfdtuol ae st`tdm erdmtdaf ds lqu`c `fo appasdtl ta tbl lxtlrf`c earml lxlrtlo, tdcc tbl ajklmt `t wbdmb

earml ds lxlrtlo ds `t rlst. _bds hl`fs dt ds ` v`rd`jcl `fo slce `okustdfg earml. Bawlvlr dt b`s `

h`xdhuh v`cul m`cclo cdhdtdfg erdmtdaf.

eh`x

8 sF

_bl `mtu`c earml ae st tdm erdmtdaf h`y jl sh`cclr tb`f sF `fo dts v cul olplfos af atblr earmls `mtdfg af tbl

jaoy. _bl h`gfdtuol ae erdmtdaf`c earml ds lqu`c ta tb`t rlqudrlo ta illp tbl jaoy `t rlc`tdvl rlst.

> es esh`x

Blrl s

`fo i

`rl prapartdaf`cdty mafst`fts. s

ds m`cclo maleedmdlft ae st tdm erdmtdaf `fo i

ds m`cclo maleedmdlft

ae idfltdm erdmtdaf. _bly `rl odhlfsdafclss qu`ftdtdls dfolplfolft ae sb`pl `fo `rl` ae maft`mt . Dt ds `

praplrty ae tbl twa maft`mt

sure`mls.s6iear ` gdvlf p`dr ae sure`mls. De fat hlftdaflo tblfs8i m`f jl

t`ilf. U`cul aem`f jl erah > ta.


5/14

^BT]DM]

"h`fdsbiuh`rpbysdms.df" .

]tllc fo jr`ss >.=< _lecaf fo tlecaf >.>?

Gc`ss fo gc`ss 0.>>

Waao fo waao >.=

Waao fo hlt`c >.?> Zujjlr tyrl af wlt

mafmrltl ra`o >.7

Lx`hpcl 0>. Edfo `mmlclr`tdaf ae jcami. Dfdtd`ccy tbl jcami ds `t rlst.

0> Ig

F

8>.> 8 > ear vlrtdm`c odrlmtdaf

F 8 75 F

Faw > es

sF

> es 75 >.es=2 F

=: 3 =2 Blfml e 8 =:

`mmlclr`tdaf ae jcami ds zlra.


6/14


7/14

^BT]DM]


Lx`hpcl 0e]

F

hg sdf6 esh`x

hg sdf6 F

hg sdf 6 hg mas

t`f 6 8 t`f0

ear t`f fa scdodfg af dfmcdflo pc`fl.

_bds hltbao ds uslo ear edfodfg aut tbl v`cul ae pr`mtdm ccy.

Lx`hpcl 05. Edfo aut tbl `mmlclr tdaf ae tbl jcami. De tbl jcami ds dfdtd`ccy `t rlst.

]acutdaf ; (EJO ae tbl jcami lxmcuodfg erdmtdaf)

Hgmas

=7

0>ig

7 g mas =7 8 2> F

Faw >esF

>es>.< 2>

es?> F

2>

7

F

Wl wdcc put v cul ae e df tbl c`st d.l. df tbl odrlmtdaf appasdtl ta rlsuct`ft ae atblr earmls. e `mts oawf

tbl dfmcdfl `fo dts v`cul ds ae 8 7< 5> 8 0< F

]a `mmlclr`tdaf ds zlra


8/14

^BT]DM]


Lx`hpcl 07. Df tbl `javl prajclh baw humb earml sbauco jl `oolo ta 7< F earml sa tb t jcami st rts ta havl

up tbl dfmcdfl.

]acutdaf ; 5> + ?> 8 7< + elxtr`

es8 :< F

Lx`hpcl 02. Df tbl `javl prajclh wb t ds tbl hdfdhuh earml jy wbdmb 7< F earml sbauco jl rlpc mlo wdtb sa tb`t

tbl jcami oals fat havl.

]acutdaf ; Df tbds m`sl tbl jcami b`s ` tlfolfmy ta havl oawfw`ros.

Blfml erdmtdaf `mts upw`ros.

E

?>

5>

E + ?> 8 5>

E 8 :> F

Lx`hpcl 04. _ap vdlw ae ` jcami af ` t`jcl ds sbawf (g 8 0> h/s:) .

Edfo aut tbl `mmlclr`tdaf ae tbl jcami.

]acutdaf ;

?> g

?>F

E 8 ?>Z

:?> 8 . Edfo hdfdhuh sa tb`t tbl jcamis rlh`df st`tdaf`ry.

]acutdaf ; _ 8 0>> g 8 0>>> F 0>>>

ee 8 0>>> ta illp tbl jcami st`tdaf`ry

Faw eh`x

8 0>>>

F8 0>>>

8 :

M`f jl grl`tlr tb`f 0 1

Tls > 3


9/14

^BT]DM]


Lx`hpcl :0. Edfo aut hdfdhuh `mmlclr tdaf ae jcami @ sa tb t tbl 0> ig jcami oalsft e`cc.

]acutdaf ;

0> g

0>F`

F@ppcydfg FC df bardzaft`c odrlmtdaf

F 8 0> ` ......... (0)

@ppcydfg FC df vlrtdm`c odrlmtdaf

0> g 8 F .......(:)

0> g 8 0> ` erah (0) & (:)

` 8

g8 :> h/s:

Lx`hpcl ::. Edfo tbl tlfsdaf df tbl strdfg df sdtu tdaf `s sbawf df tbl edgurl jlcaw. Earmls 0:> F `fo 0>> F st rt

`mtdfg wblf tbl systlh ds `t rlst `fo tbl h`xdhuh v cul ae st tdm erdmtdaf af 0> ig ds 4> F `fo tb`t af

:> ig ds 5>F1

]acutdaf ; (d) Clt us `ssuhl tb t systlh havls taw`ros clet tblf `s dt ds mcl`r erah EJO, flt earml df bardzaft`c

odrlmtdaf ds taw`ros rdgbt. _blrlearl tbl `ssuhptdaf ds fat v`cdo.

@javl `ssuhptdaf ds fat passdjcl `s flt earml af systlh mahls taw`ros rdgbt. Blfml systlh ds

fat havdfg taw`ros clet.(dd) ]dhdc`rcy clt us `ssuhl tb`t systlh havls taw`ros rdgbt.

@javl `ssuhptdaf ds `csa fat passdjcl `s flt earml af tbl systlh ds taw`ros clet df tbds sdtu`tdaf.

Blfml `ssuhptdaf ds `g`df fat v`cdo.

_blrlearl dt m`f jl mafmcuolo tb`t tbl systlh ds st`tdaf`ry.

@ssuhdfg tb`t tbl 0> ig jcami rl`mbls cdhdtdfg erdmtdaf edrst tblf usdfg EJOs.

0:> 8 _ + 4> _ 8 => F

@csa _ + e 8 0>>

=> + e 8 0>>

e 8 7> F wbdmb ds fat passdjcl `s tbl cdhdtdfg v`cul ds 5> F ear tbds sure`ml ae jcami.

Aur `ssuhptdaf ds wrafg `fo faw t`idfg tbl :> ig sure`ml ta jl cdhdtdfg wl b`vl


10/14

^BT]DM]

"h`fdsbiuh`rpbysdms.df" 0>

_ + 5> 8 0>> F _ 8 ?> F

@csa e + _ 8 0:> F e 8 2> F

_bds ds `mmlpt`jcl `s st`tdm erdmtdaf `t tbds sure`ml sbauco jl clss tb`f 4> F.

Blfml tbl tlfsdaf df tbl strdfg ds

_ 8 ?> F.

Lx`hpcl :=. Df tbl eaccawdfg edgurl earml E ds gròu ccy dfmrl`slo erah zlra. Or`w

tbl gr`pb jltwllf `ppcdlo earml E `fo tlfsdaf _ df tbl strdfg. _bl

maleedmdlft ae st`tdm erdmtdaf jltwllf tbl jcami `fo tbl graufo ds s

.

]acutdaf ; @s tbl lxtlrf`c earml E ds gròu`ccy dfmrl`slo erah zlra dt ds

mahplfs`tlo jy tbl erdmtdaf `fo tbl strdfg jl`rs fa tlfsdaf. Wblf

cdhdtdfg erdmtdaf ds `mbdlvlo jy dfmrl sdfg earml E ta ` v cul tdcc shg,

tbl eurtblr dfmrl`sl df E ds tr`fselrrlo ta tbl strdfg.

Lx`hpcl :?. Earml E ds gròu`ccy dfmrl`slo erah zlra. Oltlrhdfl wbltblr tbl jcami wdcc edrst scdol ar cdet up1

]acutdaf ; _blrl `rl hdfdhuh h`gfdtuol ae earmls rlqudrlo jatb df bardzaft`c `fo vlrtdm`c odrlmtdaf ldtblr ta

scdol af cdet up tbl jcami. _bl jcami wdcc edrst scdol af cdet up wdcc olplfo upaf wbdmb hdfdhuh h`gfd-

tuol ae earml ds clsslr.

Ear vlrtdm`c odrlmtdaf ta st`rt cdetdfg up

E sdf =7 + F Hg >.

F jlmahls zlra kust cdetdfg mafodtdaf.

Ecdet

Ecdet

=

>F

Ear bardzaft`c odrlmtdaf ta st`rt scdodfg

E mas =7 sF

E mas =7 6 >.< Y 0>g E sdf =7X ( F 8 0> g E sdf =7)

Blfml Escdol

6=7sdf=7mas

Escdol

600

>F

Ecdet

6=

>F.

Escdol

3 Ecdet

_blrlearl tbl jcami wdcc jlgdf ta scdol jlearl cdetdfg.

_WA JCAMI ^ZAJCLH]

LR@H^CL : J

]haatb

8>.< 0> @ E 8 F

//////////////////////////////////////////////////


11/14

^BT]DM]


]acutdaf ; Hltbao ae sacvdfg

]tlp 0 ; H`il earml od`gr`h.

]tlp : ; ]baw st`tdm erdmtdaf earml jy e jlm`usl v`cul ae erdmtdaf ds fat ifawf.

]tlp = ; M`cmuc`tl slp`r`tlcy ear twa m`sls.

M`sl 0 ; Havl tagltblr

]tlp ? ; M`cmuc`tl `mmlclr`tdaf.

]tlp < ; Mblmi v`cul ae erdmtdaf ear `javl m`sl.]tlp 5 ; De rlqudrlo erdmtdaf ds clss tb`f `v`dc`jcl dt

hl`fs tbly wdcc havl tagltblr lcsl

havl slp`r`tlcy.

]tlp 7; (`) `javl `mmlclr tdaf wdcc jl mahhaf

`mmlclr`tdaf ear jatb

M`sl : ; Havl slp`r`tlcy

]tlp 7(j) De tbly havl slp`r tlcy tblf idfltdm erdmtdaf ds dfvacvlo. wbasl v`cul ds F.

]tlp 2 ; M cmuc tl `mmlclr`tdaf ear `javl m`sl.

e

@ eJ

eh`x

8 F

e F (`v`dc`jcl erdmtdaf)

Havl tagltblr Havl slp`r`tlcy

(d) ` 80>0>

8 :.< h/s: Fa fllo ta m`cmuc`tl

(dd) Mblmi erdmtdaf ear J ;

e 8 0> :.< 8 : J

8>. @ 0>0 F

//////////////////////////////////////////////////

]acutdaf ; eh`x 8 < > Fe F

0>0

e

@

e

J

(d) De tbly h avl tagltblr ` 8:>

0>08 < h/s:

(dd) Mblmi erdmtdaf af J

e

0> e 8 0> < 8 .< (rlqudrlo)

.< 6 (tblrlearl rlqudrlo 6 `v`dc jcl)

Blfmltbly wdcc fat havl tagltblr.


12/14

^BT]DM]

"h`fdsbiuh`rpbysdms.df" 0:

(ddd) Blfml tbly havl slp`r`tlcy sa idfltdm erdmtdaf ds dfvacvlo.

0>0

e 8i

@

e 8 F8i

J

ear @

80>

0>08

8 < h/s:

@csa @

6 `J

`s earml ds `ppcdlo af @.

Lx`hpcl :7. Edfo tbl `mmlclr`tdaf ae tbl twa jcamis. _bl systlh ds dfdtd`ccy `t

rlst `fo tbl erdmtdaf maleedmdlft `rl `s sbawf df tbl edgurl1 :>]haatb

8>.

E 8 5> F

///////////////////////////////////////////

]acutdaf ; Havl _agltblr Havl ]lp`r`tlcy

` 8=>

5>8 : h/s: Fa fllo ta m`cmuc`tl.

Mblmi erdmtdaf af :> ig.

e 8 :> x :

e 8 ?> (wbdmb ds rlqudrlo)

?> 3 (tblrlearl rlqudrlo 3 `v`dc`jcl)

wdcc havl tagltblr.

Lx`hpcl :2. Df `javl lx`hpcl edfo h`xdhuh E ear wbdmb twa jcamis wdcc havl tagltblr.

]acutdaf ; Ajslrvdfg tbl mrdtdm c sdtu`tdaf wblrl erdmtdaf jlmahls cdhdtdfg.

E

e 8 h`x0>

e 8 h`x:>

E eh`x

8 0> ` ......... (0)

eh`x 8 :> ` .......... (:)

E 8 7< F

Lx`hpcl :4. Dfdtd`ccy tbl systlh ds `t rlst. edfo aut hdfdhuh v`cul ae E ear wbdmb

scdodfg st`rts jltwllf tbl twa jcamis.:>

]haatb

8>.

E

////////////////////////////////////]acutdaf ; @t kust scdodfg mafodtdaf cdhdtdfg erdmtdaf ds `mtdfg.

e 8 0> E

e 8

:>

E 8 :> ` ........... (0)

e 8 0> ` .................. (:)

8 0> `

` 8 < h/s:

blfml E 8 + :> < 8 0 F

Ehdf

8 0 F

Lx`hpcl =>. Df tbl edgurl gdvlf jlcaw earml E `ppcdlo bardzaft`ccy af cawlr

jcami, ds gr`ou`ccy dfmrl`slo erah zlra. Odsmuss tbl odrlmtdaf

`fo f`turl ae erdmtdaf earml `fo tbl `mmlclr`tdafs ae tbl jcami

ear odeelrlft v culs ae E (_ il g 8 0> h/s:).

]acutdaf ; Df tbl `javl sdtu`tdaf wl sll tb`t tbl h`xdhuh passdjcl v`cul ae erdmtdaf jltwllf tbl jcamis ds

sh

@g 8 >.= 0> 0> 8 => F.


13/14

^BT]DM]

"h`fdsbiuh`rpbysdms.df" 0=

M`sl (d) Wblf E 8 A.

Mafsdolrdfg tb`t tblrl ds fa scdppdfg jltwllf tbl jcamis tbl `mmlclr`tdaf ae systlh wdcc jl

` 80>:>

0:>

8 ? h/s:

Jut tbl h`xdhuh `mmlclr`tdaf ae J m`f jl ajt`dflo jy

tbl eaccawdfg earml od`gr`h.

`J

8:>

=>8 0.< h/s: ( afcy erdmtdaf earml jy jcami @ ds rlspafsdjcl ear praoumdfg `mmlclr`tdaf df

jcami J)

Jlm`usl ? 6 0.< h/s: wl m`f mafmcuol tb`t tbl jcamis oa fat havl tagltblr.

Faw or`wdfg tbl E.J.O. ae l`mb jcami, ear edfodfg aut dfodvdou`c `mmlclr`tdafs.

@8

0>

=>0:>8 4 h/s: taw`ros rdgbt

`J

8:>

=>8 0.< h/s: taw`ros rdgbt.

M`sl (dd)E ds dfmrl`slo erah zlra tdcc tbl twa jcamis kust st`rt havdfg tagltblr.

@s tbl twa jcamis havl tagltblr tbl erdmtdaf ds st`tdm df f`turl `fo dts v`cul ds cdhdtdfg. EJO df tbds m`sl

wdcc jl

`@

80>

=>0:>8 4 h/s: `

J

8:>

=>E 8`

@

:>

=>E 8 4

E 8 0 F

Blfml wblf > 3 E 3 0 F tbl jcamis oa fat havl tagltblr `fo tbl erdmtdaf ds idfltdm. @s E

dfmrl`sls `mmlclr`tdaf ae jcami J dfmrl`sls erah 0.< h/s:.

@t E 8 0 F cdhdtdfg st`tdm erdmtdaf st`rt `mtdfg `fo tbl twa jcamis st`rt havdfg tagltblr.

M`sl (ddd)Wblf E ds dfmrl`slo `javl 0 F.

Df tbds smlf rda tbl st`tdm erdmtdaf `okusts dtslce sa `s ta illp tbl jcamis havdfg tagltblr. _bl v`cul

ae st`tdm erdmtdaf st`rts rloumdfg jut tbl odrlmtdaf stdcc rlh`dfs s`hl. _bds b`pplfs maftdfuauscy tdcc

tbl v`cul ae erdmtdaf jlmahls zlra. Df tbds m`sl tbl EJO ds `s eaccaws

@8 `

J8

0>

e0:>8

:>

eE

wblf erdmtdaf earml e glts rloumlo ta zlra tbl `javl `mmlclr`tdafs jlmahl

@8

0>

0:>8 0: h/s: `

J8

:>

E8

@8 0: h/s:

E 8 :?> F

Blfml wblf 0 E :?> F tbl st tdm erdmtdaf earml maftdfuauscy olmrl`sls erah h`xdhuh ta zlra

`t E 8 :?> F. _bl `mmlclr`tdafs ae tbl jcamis dfmrl`sl erah 4 h/s: ta 0: h/s: ourdfg tbl mb`fgl ae

earml E.

M`sl (dv) Wblf E ds dfmrl`slo `g`df erah :?> F tbl odrlmtdaf ae erdmtdaf earml af tbl jcami rlvlrsls jut dt ds

stdcc st`tdm. E m`f jl dfmrl`slo tdcc tbds rlvlrslo st`tdm erdmtdaf rl`mbls dts cdhdtdfg v`cul. EJO `t tbds

kufmturl wdcc jl


14/14

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"h`fdsbiuh`rpbysdms.df" 0?

_bl jcamis havl tagltblr tblrlearl.

@8

0>

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J8

:>

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@8 0< h/s:

:>

=>E 8 0< h/s:

Blfml E 8 ==> F.

M`sl (v) Wblf E ds dfmrl`slo jlyafo ==> F. Df tbds m`sl tbl cdhdtdfg erdmtdaf ds mbdlvlo `fo scdppdfg t`ils

pc`ml jltwllf tbl jcamis (idfltdm erdmtdaf ds dfvacvlo).

@

8 0< h/s: wbdmb ds mafst`ft

`J8 :>

=>E

h/s: wblrl E 6 ==> F.

friction theory e

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