132519199 Newton s Laws Force Friction 291

By N.K.C. SIR NEWTONS

LAW

FORCE

&

FRICTION

KEY KEY CONCE CONCEPT PT ............................................................. ............................................................. Page –2 OBJECTIVE QUESTION BANK...................................... BANK.......................... ............ Page –4 SUBJEC SUBJECTI TIVE VE LEVE LEVEL L - I .. ........ .......... ...... .... .............................. .............................. Page –11 –11

SUBJEC SUBJECTIV TIVE E LEVE LEVEL L - II . ........ .......... ...... .... .............................. .............................. Page –16 ANSWER ANSWER KEY.................................... KEY ............................................................... ........................... Page –19

KEY CONCEPT CONCEP T FORCE /here /here are are,, asi asial all l,, fiv fivee fore fores, s, !hi !hih h are are o"" o""onl onl  eno enount unter ered ed in in "eha "ehani nis s.. ea rth attrats it. It is also alled the fore of gravit Weight : eight of an o+et is the fore !ith !hih earth or the gravitational fore.

1. (i#

(ii#

th e e3ert fores on eah other that is alled ontat Contact Force : hen t!o odies o"e in ontat the fores. (a# Normal orce !N" : It is the o"ponent o"pon ent of ontat fore nor"al to the surfae. It "easures ho! strongl the surfaes in ontat are pressed to together gether.. (# Frictional orce : It is the o"ponent of ontat fore parallel to the surfae. It opposes the relative "otion (or atte"pted "otion# of o f the t!o surfaes in ontat.

(iii#

Ten#ion : /he fore e3erted  the end of a taut string, rope or hain is alled the tension. /he diretion of tension is to pull the t he od !hile that of nor"al nor"a l reation is to push the od.  od.

(iv#

S$ring orce : /he fore e3erted  a spring is given  F 4 5 3, !here 3 is the hange in length len gth and  is the stiffness onstant or spring onstant (units %" 51#.

2.

NEWTON%S LAWS LAWS Ne&ton%# Fir#t La& : Ever partile ontinues in its state of rest or of unifor" "otion in a straight line unless it is o"pelled to hange that t hat state  the ation of an applied fore.

.

Ne&ton%# Second La& :

.

Ne&ton%# Third La& : henever t!o odies interat the e3ert fores on eah other !hih are e7ual in "agnitude and opposite in diretion. o !henever od A e3erts a fore F on od $, $ e3erts e3 erts a fore 5 F on A.



Fnet

 "a



%e!t on8ss first la! is valid is alled an inertial 'nertial Reerence Frame : A referene fra"e in !hih %e!ton8 referene fra"e. An inertial fra"e is either at rest or "oving !ith unifor" veloit. Non('nertial Frame : An aelerated fra"e of referene is alled a non-inertial fra"e. '+ets in noninertial fra"es do not oe oe  %e!ton8s first la!. la!.

reogni9 ed onl  a non-inertial non-inertia l oserver to e3plain )#e*do Force : It is an i"aginar fore !hih is reogni9ed the phsial situation aording ao rding to %e!ton8s la! la!.. /he "agnitude of this fore F: is e7ual to the produt of the "ass " of the o+et and aeleration aeleratio n a of the fra"e of referene. /he diretion of the fore is opposite to the diretion of aeleration. F: 4 5 "a /he orce o riction o"es into ation onl !hen there is a relative "otion et!een  et!een the t!o ontat surfaes or !hen an atte"pt is "ade to have hav e it. /he fore of frition on eah od is in a diretion opposite to its "otion (e3isting or i"pending# relative to other od.

ETOOS Academy Ltd. : F-106, Road no.2, Indraprastha Industrial Area, End of Evergreen Motors (Mahindra ho!roo"#, $%& 'ffie &ane, )hala!ar Road, *ota, Ra+asthan (200# [2]

.

Static friction : /he fritional fore ating et!een an t!o surfaes at rest !ith respet to eah other is alled the fore of stati frition (f s#.

f s  s % !here s is the stati oeffiient of frition. 6.

Kinetic friction : /he fritional fore ating et!een surfaes in relative "otion !ith respet to eah other is alled the fore of ineti frition or sliding frition (f  #.

f  3  % !here  is the oeffiient of ineti frition.

s 4  Angle of friction () : Mathe"atiall, the angle of frition (# "a e defined as the angle et!een the nor"al reation % and the resultant of the "a5i"u" frition fore f and the nor"al reation.

/hus tan 3

f %

ine f 3  %, therefore, tan  3 


OBJECTIVE QUESTION BANK ONLY ONE OPTION IS CORRECT. Tae a!!"#$. 2 %&'()e* +#" a'*,e"&'g ea /(e*)&#'. /.1 A oo is at rest on a tale. hat is the 3reation4 fore aording to %e!ton5s third la! to the gravitational fore 6 the earth on the oo7 (A# the nor"al fore e8erted 6 the tale on the oo ($# the nor"al fore e8erted 6 the tale on the ground (9# the nor"al fore e8erted 6 the ground on the tale (:# the gravitational fore e8erted on the earth 6 the oo Ans.

/.2

A !eight an e hung in an6 of the follo!ing four !a6s 6 string of sa"e t6pe. In !hih ase is the string "ost liel6 to rea7

(A# A

($# $

(9 ) 9

(:# :

Ans.

/.,

A rope of "ass  g is "oving vertiall6 in vertial position !ith an up!ards fore of 100 % ating at the upper end and a do!n!ards fore of ;0 % ating at the lo!er end.
Ans.

ETOOS Academy Ltd. : F-106, Road no.2, Indraprastha Industrial Area, End of Evergreen Motors [4] (Mahindra ho!roo"#, $%& 'ffie &ane, )hala!ar Road, *ota, Ra+asthan (200#

/.-

A stunt "an +u"ps his ar over a rater as sho!n (neglet air resistane# (A ) during the !hole flight the driver e0perienes !eightlessness ($# during the !hole flight the driver never e0perienes !eightlessness (# during the !hole flight the driver e0perienes !eightlessness onl at the highest point (3# the apparent !eight inreases during up!ard +ourne

Ans.

/.

A fle0i4le hain of !eight 5 hangs 4et!een t!o fi0ed points A  $ !hih are at the sa"e hori7ontal level. 8he inlination of the hain !ith the hori7ontal at 4oth the points of support is. 5hat is the tension of the hain at the "id point9 (A#

5 2

. ose 

($#

5 2

. tan 

( )

5 2

ot 

(3# none

Ans.

/.6

5hat should 4e the "ini"u" fore : to 4e applied to the string so that 4lo; of "ass " +ust 4egins to "ove up the fritionless plane. (A# Mg tan



2

($# Mg ot



2

(#

Mg os  1  sin 

(3# %one

Ans.

/.<

A spring of fore onstant ; is ut into t!o piees suh that one piee suh that one piee is dou4le the length of the other. 8hen the long piee !ill have a fore onstant of (A# (2=,# ; ($# (,=2# ; (# ,; (3# 6;

Ans.


/.

Find the aeleration of  g "ass !hen aeleration of 2 g "ass is 2 "s 2 as sho!n in figure. (A#  "s 2 ($ ) 2 "s 2 (3# 0. "s 2 (4# 5ero

Ans.

/.6

$lo of 1 g is initiall7 in e8uili9riu" and is hanging 97 t!o idential springs A and $ as sho!n in figures. If spring A is ut fro" lo!er point at t:0 then, find aeleration of 9lo in "s 2 at t : 0. (A )  ($# 10 (3# 1 (4# 0

Ans.

/.10

If the string ; all the pulle7s are ideal, aeleration of "ass " is (A#

g

($# 0

2 (3# g

(4# dependent on "

Ans.

Q(e*)&#' N#. 11 )# 10 0 /(e*)&#'* A partile of "ass " is onstrained to "ove on <-a
/.11

>hat is the period of the "otion?

 2A"    F  

(A ) 

 2A"    F  

($# 2

 2A"   (3#   F  

(4# %one


Ans.

/.12

eloit  ti"e graph of the partile is

(A )

($#

(3#

(4#

Ans.

/.1

A Find "ini"u" ti"e it !ill ta5e to reah fro" 6 7  to 0. 2

(A#



"A

2

F

( 2  1# ($ )

"A F

( 2  1#

(3# 2

"A F

( 2  1#

(4# %one

Ans.

/.1-

8!o 9lo5s are onneted 9 a spring. 8he o"9ination is suspended, at rest, fro" a string attathed to the eiling, as sho!n in the figure. 8he string 9rea5s suddenl. I""ediatel after the string 9rea5s, !hat is the initial do!n!ard aeleration of the upper 9lo5 of "ass 2" : (A# 0 ($ ) g;2 (3# g (4# 2g

Ans.


/.1

A lo is pro+eted up!ards on an inlined plane of inlination ,3 along the line of greatest slope of  4 0. !ith veloit5 of  "s. 7he lo 1st stops at a distane of 8888888888 fro" starting point (A# 1.2 " ($# 2. " (9# 10 " (:# 12. "

Ans.

/.16

A lo of "ass 2 g slides do!n an inline plane of inlination ,03. 7he oeffiient of frition et!een lo and plane is 0.. 7he ontat fore et!een lo and plan is ; (A# 20 %t

($# 10 , %t

(9#   %t

(: )  1 %t

Ans.

/.1

A od5 is plaed on a rough inlined plane of inlination. As the angle  is inreased fro" 03 to <03 the ontat fore et!een the lo and the plane (A# re"ains onstant ($# first re"ains onstant then dereases (9# first dereases then inreases (:# first inreases then dereases

Ans.

/.1=

A fore F  >i  - +> ats on lo sho!n. 7he fore of frition ating on the lo is ; (A# ? >i ($# ? 1.= >i 

(9# ? 2.- >i

(:# ? , >i

Ans.

/.1<

$lo $ of "ass 100 g rests on a rough surfae of frition oeffiient  4 1,. A rope is tied to lo $ as sho!n in figure. 7he "a@i"u" aeleration !ith !hih o5 A of 2 g an li"s on rope !ithout "aing lo "ove is ; -g g g ,g (A# ($ ) (9# (:# , , 2


Ans.

/.20

A lo plaed on a rough inlined plane of inlination (03# an +ust e pushed up!ards 4 appl4ing a fore 5F5 as sho!n. If the angle of inlination of the inlined plane is inreased to (  603#, the sa"e lo an +ust e prevented fro" sliding do!n 4 appliation of a fore of sa"e "agnitude. he oeffiient of frition et!een the lo and the inlined plane is (A#

 1  1

($#

2  1  1

(7 )

 1  1

(8# %one of these

Ans.

/.21

9ith !hat "ini"u" veloit4 should lo e pro+eted fro" left end A to!ards end $ suh that it reahes the other end $ of onve4er elt "oving !ith onstant veloit4 v. Frition oeffiient et!een lo and elt is . (A#

g&

($ )

(7#

g&

(8# 2

2g&

g&

Ans.

3#" Q. 22 )# Q.26 "e+e" +&g("e-1. /(e*)&#'* /.22 9hen F  2%, the fritional fore et!een  g lo and ground is (A ) 2% ($# 0 (7# : % (8# 10 % Ans.


/.2

9hen F  2%, the fritional fore et!een 10 g lo and  g lo is (A ) 2% ($# 1 % (7# 10 % (8# %one

Ans.

/.2-

he "a;i"u" 5F5 !hih !ill not ause "otion of an4 of the los. (A ) 10 % ($# 1 % (7# data insuffiient

(8# %one

he "a;i"u" aeleration of  g lo (A# 1 "
(8# %one

Ans.

/.2

(7 ) 0

Ans.

/.26

he aeleration of 10 g lo !hen F  0% (A ) 2 "
(8# %one

Ans.


NEWTONS LAW 3ORCE 5 3RICTION SUBJECTIVE LEVEL - I /.1

Figure sho!s three los in ontat and ept on a s"ooth horiontal surfae. 3hat is ratio of fore e4erted 5 lo A on $ to that of $ on .

Ans.

/.2

Ans.

/.

A force F appli ed to an object of mass m1 produes an aeleration of .00 "7s2. 8he sa"e fore

applied to a seond o+et of "ass "2 produes an aeleration of 1.00 "7s2. (a# 3hat is the value of the ratio "1 7 "2 9 (# If "1 and "2 are o"ined, find their aeleration under the ation of the fore F.

8!o fores, F1 : (; 6i ;  j# % and F2 : ( ;  i < = j# %, at on a partile of "ass 2.00 g that is initiall5 at rest at oordinates (; 2.00 ", < .00 "#. (a# 3hat are the o"ponents of the partile>s veloit5 at t : 10.0 s9 (# In !hat diretion is the partile "oving at t : 10.0s9 (# 3hat displae"ent does the partile undergo during the first 10.0s9 (d# !hat are the oordinates of the partile at t : 10.0 s9

Ans.

/.

In the s5ste" sho!n in figure, a horiontal fore of "agnitude F4 ats on the ?.00 g o+et. 8he horiontal surfae is fritionless. (a# For !hat values of F4 does the 2.00 g o+et aelerate up!ard9 (# For !hat values of F4 is the tension in the ord ero9 (# @lot the aeleration of the ?.00 g o+et versus F4. Inlude values of F4 fro" ; 100 % to < 100 %.

Ans.


/.

A van aelerates do!n a hill (Fig.#, going fro" rest to 0.0 "7s in 6.00 s. uring the aeleration, a to5 (" : 0.100 g# hangs 5 a string fro" the vanBs eiling. 8he aeleration is suh that the string re"ains perpendiular to the eiling. eter"ine (a# the angle  and (# the tension in the string.

Ans.

/.6

$lo A of "ass "72 is onneted to one end of light rope !hih passes over a pulle5 as sho!n in the Fig. Man of "ass " li"s the other end of rope !ith a relative aeleration of g76 !ith respet to rope. Find aeleration of lo A and tension in the rope.

Ans.

/.=

(a# (#

8o point the side of a uilding, painter nor"all5 hoists hi"self up 5 pulling on the rope A as in figure. 8he painter and platfor" together !eigh 200%. 8he rope $ an !ithstand 00%. Find the "a4i"u" aeleration of the painter. tension in rope A (i# !hen painter is at rest (ii# !hen painter "oves up !ith an aeleration 2 "7s2.

Ans.


/.?

a"e spring is attahed !ith 2 g,  g and 1 g los in three different ases as sho!n in figure. If 41, 42 and 4 e the onstan e4tensions in the spring in these three ases then find the ratio of their e4tensions.

(a#

(#

(#

Ans.

/.C

3hat horiontal fore "ust e applied to the art sho!n in figure in order that the los re"ain stationar5 relative to the art9 Assu"e all surfaes, !heels, and pulle5 are fritionless.

Ans.

/.10

Inlined plane is "oved to!ards right !ith an aeleration of  "s ;2 as sho!n in figure. Find fore in ne!ton !hih lo of "ass  g e4erts on the inline plane. (All surfaes are s"ooth#

Ans.

/.11

Find fore in ne!ton !hih "ass A e4erts on "ass $ if $ is "oving to!ards right !ith  "s ;2. Also find "ass of A. (All surfaes are s"ooth#


Ans.

/.12

Fore F is applied on upper pulle5. If F : 0t !here t is ti"e in seond. Find the ti"e !hen "1 loses ontat !ith floor.

Ans.

/.1

onsider a large tru arr5ing a heav5 load, suh as steel ea". A signifiant haard for the driver is that the load "a5 slide for!ard, rushing the a, if the tru stops suddenl5 in an aident or even in raing. Assu"e, for e4a"ple, that a 10000 g load is loated on the flat ed of a tru "oving at 12.0 "7s. Assu"e the load is not tied do!n to the tru and assu"e that the oeffiient of frition et!een the load and the tru ed is 0.00. alulate the "ini"u" stopping distane for the tru for !hih the load !ill not slide for!ard relative to the tru.

Ans.

/.1

In the figure, !hat should e "ass " so that lo A slide up !ith a onstant veloit59

Ans.

/.1

A lo of "ass 1 g is horiontall5 thro!n !ith a veloit5 of 10 "7s on a stationar5 long plan of "ass 2 g !hose surfae has a  : 0.. @lan rests on fritionless surfae. Find the ti"e !hen "1 o"es to rest !.r.t. plan.


Ans.

/.16

$lo M slides do!n on fritionless inline as sho!n. Find the "ini"u" frition oeffiient so that " does not slide !ith respet to M.

Ans.

/.1=

8he oeffiient of stati and ineti frition et!een the t!o los and also et!een the lo!er lo and the ground are s : 0.6 and  : 0.. Find the value of tension 8 applied on the lo!er lo at !hih the upper lo egins to slip relative to lo!er lo.

Ans.

/.1?

Find the aeleration of the los and "agnitude D diretion of fritional fore et!een lo A and tale, if lo A is pulled to!ards left !itha fore of 0%.

Ans.

/.1C

oeffiient of frition et!een  g and 10 g lo is 0.. If frition et!een the" is 20 %. 3hat is the value of fore eing applied on  g. 8he floor is fritionless

Ans.


SUBJECTIVE LEVEL - II /.1

(a# (3# (#

he diagra" sho!s partiles A and $, of "asses 0.2 g and " g respetivel, onneted 3 a light ine4tensi3le string !hih passes over a fi4ed s"ooth peg. he sste" is released fro" rest, !ith $ at a height of 0.2 " a3ove the floor. $ desends, hitting the floor 0. s later. All resistanes to "otion "a 3e ignored. Find the aeleration of $ as it desends. Find the tension in the string !hile $ is desending and find also the value of ". 5hen $ hits the floor it o"es to rest i""ediatel, and the string 3eo"es sla. Find the length of ti"e for !hih $ re"ains at rest on the ground 3efore 3eing +ered into "otion again.

Ans.

/.2

A 1g 3lo $7 rests as sho!n on a 3raet A7 of sa"e "ass. 8onstant fores F1 9 20% and F2 9 :% start to at at ti"e t 9 0 !hen the distane of 3lo $ fro" pulle is 0". i"e !hen 3lo $ reahes the pulle is ;;;;;;;;;.

Ans.

/.

Tw o men of masses m1 and

"2 hold on the opposite ends of a rope passing over a fritionless pulle. he "ass "1 li"3s up the rope !ith an aeleration of 1.2 "
Ans.

/.-

In figure sho!n, pulles are ideal "1 > 2 "2. Initiall the sste" is in e?uili3riu" and string onneting "2 to rigid support 3elo! is ut. Find the initial aeleration of "2@


/.

(a# (3# (#

he sste" sho!n ad+aent is in euili3riu". Find the aeleration of the 3lo4s A, $ 5  all of eual "asses " at the instant !hen (Assu"e springs to 3e ideal# he spring 3et!een eiling 5 A is ut. he string (ine7tensi3le# 3et!een A 5 $ is ut. he spring 3et!een $ 5  is ut. Also find the tension in the string !hen the sste" is at rest and in the a3ove  ases.

Ans.

/.6

In the sste" sho!n. Find the initial aeleration of the !edge of "ass M. he pulles are ideal and the ords are ine7tensi3le. (there is no frition an!here#.

Ans.

/.8 (a# (3#

A 3lo4 of "ass " lies on !edge of "ass M as sho!n in figure. Ans!er follo!ing parts separatel. M 9ith !hat "ini"u" aeleration "ust the !edge 3e "oved to!ards  right hori:ontall so that 3lo4 " falls freel. Find the "ini"u" frition oeffiient reuired 3et!een !edge M and ground so that it does not "ove !hile 3lo4 " slips do!n on it.

Ans.

/.;

A ar 3egins to "ove at ti"e t < 0 and then aelerates along a straight tra4 !ith a speed given 3 =(t# < 2t2 "s >1 for 0 ? t ? 2 After the end of aeleration, the ar ontinues to "ove at a onstant speed. A s"all 3lo4 initiall at rest on the floor of the ar 3egins to slip at t < 1se. and stops slipping at t <  se. Find the oeffiient of stati and 4ineti frition 3et!een the 3lo4 and the floor.

Ans.


/.

An inlined plane "aes an angle 0 !ith the hori3ontal. Agroove 'A 4  " ut in the plane "aes an angle 0 !ith '5. A short s"ooth 6linder is free to slide do!n the influene of gravit6. Find the ti"e taen 76 the 6linder to reah fro" A to '. ( g 4 10 "8s2#

Ans.

/.10

A thin rod of length 1 " is fi9ed in a vertial position inside a train, !hih is "oving hori3ontall6 !ith onstant aeleration - "8s2. A 7ead an slide on the rod, and frition oeffiient 7et!een the" is 182. If the 7ead is released fro" rest at the top of the rod, find the ti"e !hen it !ill reah at the 7otto".

Ans.

/.11

:hree idential rigid irular 6linders A, $ and ; are arranged on s"ooth inlined surfaes as sho!n in figure. Find the least value of  that prevent the arrange"ent fro" ollapse.

Ans.

/.12

A 7lo of "ass 0 g resting on a hori3ontal surfae is ated upon 76 a fore F !hih varies as sho!n in the figure. If the oeffiient of frition 7et!een the 7lo and surfae is 0.2, find the ti"e (in seond# !hen the 7lo !ill o"e to rest.

Ans.

/.1

Find "ini"u" nor"al fore to 7e applied 76 eah hand to hold three idential 7oos in vertial position. Eah 7oo has "ass <"< and value of oeffiient of frition 7et!een the 7oos as !ell as 7et!een hand and the 7oo is .

Ans.


OBJECTIVE QUESTION BANK ONLY ONE OPTION IS CORRECT.

/.1



/.2



/.

$

/.

A

/.



/.6

A

/.

$

/.3

$

/.4

A

/.10



/.11

A

/.12

A

/.1

$

/.1

$

/.1

A

/.16



/.1

$

/.13

A

/.14

$

/.20



/.21

$

/.22

A

/.2

A

/.2

A

/.2



/.26

A

(NEWTONS LAW O!CE " !ICTION# SUBJECTIVE LEVEL $ I 1

 (# a 7 8 "8s 2 9 (a# "2 

/.1

51

/.

(a#  "8s along negative :-a:is and 1 "8s along positive ;-a:is (#  7 tan <1

/.2

"1

  1    fro" positive :-a:is   

/.

(a# F: > 14.6 %

/.

(a# 0? (#

/.

(# F:  < 3. %



(# (22 =i   +=# "

(d# ( 22 =i  4 +=# "

(#

g

a7

(a# "8s2, (#(i#100 %, (ii# 120 %

/.3

:2 > :1 > : :1 5 :2 5 : 5 1 5 13 5 10

/.4

 " 2  g  (M  "1  "2#  "  1 

/.10



/.11

%, 1681 Bg

/.12

2 se

/.1

1."

/.1

1 Bg

/.1

8 se

/.16

8

/.1

0 %

/.13

10 =

/.14

0 %

2

4

,@7

1"g

/.6

13


SUBJECTIVE LEVEL $ II /.1

(a# 2 "s 2, (# 2.- %, 0. (# 0.2 s

/.2

0. se

/.

6. %, 1.-3 se

/.-

 "1  2" 2    g 2 "   2

/.

(a# aA4

g  2

4a$5 a405 74"g825

(# aA4 2g, a$ 4 2g, a 4 0, 7 4 05 (# aA4 a$ 4 g82, a 4 g, 7 4

/.6

2g82

/.

s 40.- , 9 4 0.

/.:

2 se

/.12

.60

/.1

%4

"g 2

5 7 4 2"g

/.3

(a# a 4 g ot , (# ""in 4

/.10

182 se

/.11

" sin  os  " os2   M

 1      

tan 1 

"g 2

ETOOS Academy Ltd. : F-106, Road no.2, Indraprastha Industrial Area, End of Evergreen Motors [%&] (Mahindra ho!roo"#, $%& 'ffie &ane, )hala!ar Road, *ota, Ra+asthan (200#

132519199 Newton s Laws Force Friction 291

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