Friction. Chapter Friction. Introduction. Types of Friction

Transcription

1 8 riction Chpter 5 riction Introduction If we slide or try to slide body over surfce, the otion is resisted by bondin between the body nd the surfce. This resistnce is represented by sinle force nd is clled friction force. The force of friction is prllel to the surfce nd opposite to the direction of intended otion. Types of riction () Sttic friction : The opposin force tht coes into ply when one body tends to ove over the surfce of nother, but the ctul otion hs yet not strted is clled sttic friction. (i) If pplied force is nd the body reins t rest then sttic friction =. (ii) If body is t rest nd no pullin force is ctin on it, force of friction on it is zero. (iii) Sttic friction is self-djustin i. 5. force becuse it chnes itself in ccordnce with the pplied force nd is lwys equl to net externl force. () Liitin friction : If the pplied force is incresed, the force of sttic friction lso increses. If the pplied force exceeds certin (xiu) vlue, the body strts ovin. This xiu vlue of sttic friction upto which body does not ove is clled liitin friction. (i) The nitude of liitin friction between ny two bodies in contct is directly proportionl to the norl rection between the. l or l s (ii) Direction of the force of liitin friction is lwys opposite to the direction in which one body is t the vere of ovin over the other (iii) Coefficient of sttic friction : s is clled coefficient of sttic friction nd is defined s the rtio of force of liitin friction nd norl rection s Diension : [ M L T ] Unit : It hs no unit. Vlue of depends on teril nd nture of surfces in contct tht ens whether dry or wet ; rouh or sooth polished or nonpolished. (e) Vlue of does not depend upon pprent re of contct. () Kinetic or dynic friction : If the pplied force is incresed further nd sets the body in otion, the friction opposin the otion is clled kinetic friction. (i) Kinetic friction depends upon the norl rection. k or k k where k is clled the coefficient of kinetic friction (ii) Vlue of k depends upon the nture of surfce in contct. (iii) Kinetic friction is lwys lesser thn liitin friction k s i.e. coefficient of kinetic friction is lwys less thn coefficient of sttic friction. Thus we require ore force to strt otion thn to intin it inst friction. This is becuse once the otion strts ctully ; inerti of rest hs been overcoe. lso when otion hs ctully strted, irreulrities of one surfce hve little tie to et locked in into the irreulrities of the other surfce. (iv) Kinetic friction does not depend upon the velocity of the body. (v) Types of kinetic friction Slidin friction : The opposin force tht coes into ply when one body is ctully slidin over the surfce of the other body is clled slidin friction. e.. flt block is ovin over horizontl tble. ollin friction : When objects such s wheel (disc or rin), sphere or cylinder rolls over surfce, the force of friction tht coes into ply is clled rollin friction. ollin friction is directly proportionl to the norl rection () nd inversely proportionl to the rdius (r) of the rollin cylinder or wheel. rollin r r k l

2 orce of friction riction 9 r is clled coefficient of rollin friction. It would hve the diensions of lenth nd would be esured in etre. ollin friction is often quite sll s copred to the slidin friction. Tht is why hevy lods re trnsported by plcin the on crts with wheels. In rollin the surfces t contct do not rub ech other. The velocity of point of contct with respect to the surfce reins zero ll the ties lthouh the centre of the wheel oves forwrd. Grph etween pplied orce nd orce of riction () rt O of the curve represents sttic friction ( s ). Its vlue increses linerly with the pplied force () t point the sttic friction is xiu. This represent liitin friction ( l ). () eyond, the force C of friction is seen to decrese slihtly. The portion C of the s curve represents the kinetic friction ). l k ( k (4) s the portion C O pplied force of the curve is prllel to x-xis therefore kinetic friction does i. 5. not chne with the pplied force, it reins constnt, whtever be the pplied force. riction is Cuse of Motion It is enerl isconception tht friction lwys opposes the otion. No doubt friction opposes the otion of ovin body but in ny cses it is lso the cuse of otion. or exple : () While ovin, person or vehicle pushes the round bckwrds (ction) nd the rouh surfce of round rects nd exerts forwrd force due to friction which cuses the otion. If there hd been no friction there will be slippin nd no otion. () Durin cyclin, the rer wheel oves by the force ction counicted to it by pedllin while front wheel oves by itself. So, i. 5. when pedllin bicycle, the force exerted by rer wheel on round kes force of friction ct on it in the forwrd direction (like wlkin). ront wheel ovin by itself experience force of friction in bckwrd direction (like rollin of bll). [However, if pedllin is stopped both wheels ove by theselves nd so experience force of friction in bckwrd direction]. While pedllin riction edllin is stoped i. 5.4 () If body is plced in vehicle which is ccelertin, the force of friction is the cuse of otion of the body lon with the vehicle (i.e., the body will rein t rest in the ccelertin vehicle until s). If there hd been no friction between body nd vehicle, the body will not ove lon with the vehicle. i. 5.5 ro these exples it is cler tht without friction otion cnnot be strted, stopped or trnsferred fro one body to the other. dvntes nd Disdvntes of riction () dvntes of friction (i) Wlkin is possible due to friction. (ii) Two body sticks toether due to friction. i. 5.6 i. 5.7 (iii) rke works on the bsis of friction. (iv) Writin is not possible without friction. (v) The trnsfer of otion fro one prt of chine to other prt throuh belts is possible by friction. () Disdvntes of friction (i) riction lwys opposes the reltive otion between ny two bodies in contct. Therefore extr enery hs to be spent in over coin friction. This reduces the efficiency of chine. (ii) riction cuses wer nd ter of the prts of chinery in contct. Thus their lifetie reduces. (iii) rictionl force result in the production of het, which cuses de to the chinery. Methods of Chnin riction We cn reduce friction () y polishin. () y lubriction. () y proper selection of teril. (4) y strelinin the shpe of the body. (5) y usin bll berin. lso we cn increse friction by throwin soe snd on slippery round. In the nufcturin of tyres, synthetic rubber is preferred becuse its coefficient of friction with the rod is lrer. nle of riction s nle of friction y be defined s the nle which the resultnt of liitin friction nd norl rection kes with the norl rection. S i. 5.8

3 0 riction y definition nle is clled the nle of friction tn l tn = [s s or tn ( ) L l we know s ] Hence coefficient of sttic friction is equl to tnent of the nle of friction. esultnt orce Exerted by Surfce on lock In the bove fiure resultnt force S ( ) ( ) S S when there is no friction ( 0) S will be iniu i.e. S = Hence the rne of S cn be iven by, S nle of epose nle of repose is defined s the nle of the inclined plne with horizontl such tht body plced on it is just beins to slide. y definition, is clled the nle of repose. In liitin condition So tn s tn tn sin nd cos [s we know s tn ] Thus the coefficient of liitin friction is equl to the tnent of nle of repose. s well s sin i.e. nle of repose = nle of friction. Clcultion of equired orce in Different Sitution If W = weiht of the body, = nle of friction, tn coefficient of friction Then we cn clculte required force for different sitution in the followin nner : () Miniu pullin force t n nle fro the horizontl i. 5.9 cos y resolvin in horizontl nd verticl direction (s shown in fiure) sin W i. 5. or the condition of equilibriu cos nd W sin y substitutin these vlue in cos ( W sin) sin cos ( W sin) [s tn ] cos sin W cos( ) () Miniu pushin force t n nle fro the horizontl y esolvin in horizontl nd verticl direction (s shown in the fiure) i. 5. plne sin W i. 5. or the condition of equilibriu cos nd W sin y substitutin these vlue in cos ( W sin) sin cos ( W sin) [s tn ] cos sin W cos( ) cos cos () Miniu pullin force to ove the body up on n inclined y esolvin in the direction i. 5.4 of the plne nd perpendiculr to the plne (s shown in the fiure) + sin cos + W sin i. 5.0 W W cos i. 5.5

4 riction or the condition of equilibriu sin W cos W cos sin nd W sin cos cos W sin y substitutin these vlues in nd solvin we et sin( ) W cos( ) (4) Miniu force to ove body in downwrd direction lon the surfce of inclined plne or the condition of equilibriu sin W cos W cos sin nd cos W sin W sin cos y substitutin these vlues in nd solvin we et sin( ) W cos( ) (6) Miniu force for otion lon horizontl surfce nd its direction i. 5.0 Let the force be pplied t n nle with the horizontl. y resolvin in horizontl nd verticl direction (s shown in fiure) + sin cos y esolvin in the direction of i. the 5.6 plne nd perpendiculr to the plne (s shown in the fiure) plne i. 5.7 or the condition of equilibriu sin W cos W cos sin nd cos W sin y substitutin these vlues in sin( ) W cos( ) cos + W sin nd solvin we et (5) Miniu force to void slidin of body down on n inclined y esolvin in the direction i. of 5.8 the plne nd perpendiculr to the plne (s shown in the fiure) + sin + sin W W cos + cos W sin W cos W or verticl equilibriu sin sin (i) nd for horizontl otion cos i.e. cos (ii) Substitutin vlue of fro (i) in (ii) cos ( sin) (iii) cos sin or the force to be iniu (cos sin) ust be xiu i.e. d [cos sin] 0 d sin cos 0 or tn tn ( ) nleof friction i.e. or iniu vlue of its nle fro the horizontl should be equl to nle of friction s nd tn so fro the fiure, cos i. 5. sin y substitutin these vlue in eqution (iii) i. 5. i. 5.9

5 riction Work done = force distnce = s = s It is cler tht work done depends upon in ccelertion of lock inst riction () ccelertion of block on horizontl surfce When body is ovin under ppliction of force, then kinetic friction opposes its otion. Let is the net ccelertion of the body ro the fiure k k k () ccelertion of block slidin down over rouh i. 5. inclined plne When nle of inclined plne is ore thn nle of repose, the body plced on the inclined plne slides down with n ccelertion. ro the fiure sin sin sin cos sin cos ccelertion [sin cos] Note : or frictionless inclined plne 0 i. 5.4 sin. () etrdtion of block slidin up over rouh inclined plne When nle of inclined plne is less thn nle of repose, then for the upwrd otion sin sin cos sin + cos etrdtion [sin cos] Note : or frictionless inclined plne 0 Work done inst friction () Work done over rouh inclined surfce i. 5.5 sin If body of ss is oved up slowly on rouh inclined plne throuh distnce s, then Work done = force distnce = s = [sin + cos ]s s[sin cos] s (i) Weiht of the body. (ii) Mteril nd nture of surfce in contct. (iii) Distnce oved. Motion of Two odies one estin on the Other When body of ss is restin on body of ss M then two conditions re possible () force is pplied to the upper body, () force is pplied to the lower body : M i. 5.8 We will discuss bove two cses one by one in the followin nner () force is pplied to the upper body, then followin four situtions re possible (i) When there is no friction The body will ove on body with ccelertion (/). / The body will rein t rest 0 If L is the lenth of s shown in fiure, will fll fro fter tie t L L t s s t nd / (ii) If friction is present between nd only nd pplied force is less thn liitin friction ( < l) ( = pplied force on the upper body, = liitin friction between nd l, = Kinetic friction between nd ) k The body will not slide on body till i.e. Cobined syste ( + M) will ove toether with coon ccelertion M (iii) If friction is present between nd only nd pplied force is reter thn liitin friction ( > l) In this condition the two bodies will ove in the se direction (i.e. of pplied force) but with different ccelertion. Here force of kinetic friction k will oppose the otion of while cuse the otion of. s i. 5.7 L l s sin + cos () Work done over horizontl i. surfce 5.6 In the bove expression if we put = 0 then k ree body dir of k

6 riction i.e. k ( k) k M ree body dir of (where = seudo force on body nd = liitin friction l between body nd ) oth the body will ove toether with coon ccelertion M seudo force on the body, i.e. k M k M Note : s both the bodies re ovin in the se direction. ccelertion of body reltive to will be M k ( M) M So, will fll fro fter tie t L ML M ( M) (iv) If there is friction between nd floor (where k l ( M ) = liitin friction between nd floor, k = kinetic friction between nd ) will ove only if k l nd then k l M l i. 5.9 However if does not ove then sttic friction will work (not liitin friction) between body nd the floor i.e. friction force = pplied force (= k) not l. () force is pplied to the lower body, then followin four situtions re possible (i) When there is no friction will ove with ccelertion (/M) while will rein t rest (reltive to round) s there is no pullin force on. nd 0 M s reltive to, will ove bckwrds with ccelertion (/M) nd so will fll fro it in tie t. t M L ML (ii) If friction is present between nd only nd < l L M i. 5.0 M K K nd l s M l s M s ( M) So both bodies will ove toether with ccelertion if s [ M] M (iii) If friction is present between nd only nd > l (where l = s = liitin friction between body nd ) oth the body will ove with different ccelertion. Here force of kinetic friction k will oppose the otion of while will cuse the otion of. i.e. i.e. k k k M [ k] M ree body dir of ree body dir of Note : s both the bodies re ovin in the se direction ccelertion of body reltive to will be k ( M) M Netive sin iplies tht reltive to, will ove bckwrds nd will fll it fter tie t L ML ( M) k (iv) If there is friction between nd floor nd > l : (where l = s(+m) = liitin friction between body nd surfce) The syste will ove only if The entire cse (iii) will be vlid. However if '' l then replcin by. l the syste will not ove nd friction between nd floor will be while between nd is zero. K M k

7 4 riction Motion of n Insect in the ouh owl The insect crwl up the bowl, up to certin heiht h only till the coponent of its weiht lon the bowl is blnced by liitin frictionl force. cos Let = ss of the insect, r = i. rdius 5. of the bowl, = coefficient of friction for liitin condition t point cos...(i) nd l sin...(ii) Dividin (ii) by (i) tn l s l So r y y h r y r or y r, h r Miniu Mss Hun fro the Strin to Just Strt the Motion () When ss plced on rouh horizontl plne nother ss hun fro the strin connected by frictionless pulley, the tension (T) produced in strin will try to strt the otion of ss. l l r sin O y T h or or T (i) T sin T sin T sin cos (ii) ro eqution (i) nd (ii) [sin cos] this is the iniu vlue of to strt the otion Note : In the bove condition Coefficient of friction tn cos Mxiu Lenth of Hun Chin unifor chin of lenth l is plced on the tble in such nner tht its l ' prt is hnin over the ede of tble without slidin. Since the chin hve unifor liner density therefore the rtio of ss nd rtio of lenth for ny prt of the chin will be equl. We know ss hnin fro the tble ss lyin on the tble or this cse we cn rewrite bove expression in the followin nner lenthhnin fro the tble [s chin hve unifor liner lenthlyin on the tble ( l l ) density] l l l l by solvin l ( ) Coefficient of riction etween ody nd Wede is t. i. 5.4 body slides on sooth wede of nle nd its tie of descent l T S S t liitin condition T l i. 5. this is the iniu vlue of to strt the otion. Note : In the bove condition Coefficient of friction () When ss plced on rouh inclined plne nother ss hun fro the strin connected by frictionless pulley, the tension (T) produced in strin will try to strt the otion of ss. Sooth wede i. 5.5 i. 5.6 If the se wede de rouh then tie tken by it to coe down becoes n ties ore (i.e. nt) The lenth of pth in both the cses re se. or sooth wede, S u t t S ( sin) t (i) [ su 0 nd sin] ouh wede sin + t liitin condition T cos i. 5. T or rouh wede, S u t t S (sin cos)( nt) (ii) [ su 0 nd (sin cos)] ro eqution (i) nd (ii)

8 riction 5 ( sin ) t = sin (sin cos) n tn n (sin cos)( nt) Stoppin of lock Due to riction () On horizontl rod (i) Distnce trvelled before coin to rest : block of ss is ovin initilly with velocity u on rouh surfce nd due to friction, it coes to rest fter coverin distnce S. S v = 0 u etrdin force ro i. 5.7 v u S 0 u S S [s v 0, ] u S or [s oentu = u] (ii) Tie tken to coe to rest ro eqution v u t 0 u t t u [ sv 0, ] () On inclined rod : When block strts with velocity u its kinetic enery will be converted into potentil enery nd soe prt of it oes inst friction nd fter trvellin distnce S it coes to rest i.e. v = 0. We know tht retrdtion [sin cos] y substitutin the vlue of v nd in the followin eqution v u S i u [sin cos] S u S (sin cos) Stoppin of Two locks Due to riction When two sses copressed towrds ech other nd suddenly relesed then enery cquired by ech block will be dissipted inst friction nd finlly block coes to rest i.e., S = E [Where = riction, S = Distnce covered by block, E = Initil kinetic enery of the block] u S v = 0 S S i. 5.9 S [Where = oentu of block] S [s = ] S In the iven condition nd re se for both the blocks. So, S ; S S Velocity t the otto of ouh Wede body of ss which is plced t the top of the wede (of heiht h) strts ovin downwrd on rouh inclined plne. Loss of enery due to friction = L (Work inst friction) E t point = h KE t point = u y the lw of conservtion of v enery i.e. v v h L ( h L) Stickin of lock With ccelerted Crt When crt oves with soe ccelertion towrd riht then pseudo force () cts on block towrd left. This force () is ction force by block on crt. fll. i. 5.4 Now block will rein sttic w.r.t. crt. If friction force [ s ] in This is the iniu ccelertion of the crt so tht block does not nd the iniu force to hold the block toether in M ) ( ( M ) in in Stickin of erson with the Wll of otor L M CT i u = 0 h

9 6 riction person with ss stnds in contct inst the wll of cylindricl dru (rotor). The coefficient of friction between the wll nd the clothin is. If otor strts rottin bout its xis, then person thrown wy fro the centre due to centriful force t prticulr speed, the person stuck to the wll even the floor is reoved, becuse friction force blnces its weiht in this condition. ro the fiure. riction force () = weiht of person () = in in c [Here, c= centriful force] r r orce of friction is non-conservtive force. orce of friction lwys cts in direction opposite to tht of the reltive otion between the surfces. ollin friction is uch less thn the slidin friction. This knowlede ws used by n to invent the wheels. The friction between two surfces increses (rther thn to decrese), when the surfces re de hihly sooth. The toic nd oleculr forces of ttrction between the two surfces t the point of contct ive rise to friction between the surfces. Sttic nd liitin friction. The coefficient of friction nd the nle of friction re relted s sin cos tn tn. force of 98 N is required to just strt ovin body of ss 00 k over ice. The coefficient of sttic friction is block weihs W is held inst verticl wll by pplyin horizontl force. The iniu vlue of needed to hold the block is [M MT 99] i. 5.4 C Less thn W Greter thn W 4. The xiu sttic frictionl force is Equl to W Dt is insufficient Equl to twice the re of surfce in contct Independent of the re of surfce in contct Equl to the re of surfce in contct None of the bove 5. Mxiu vlue of sttic friction is clled Liitin friction Norl rection ollin friction [HU 995; ET 000] Coefficient of friction 6. ullin force kin n nle to the horizontl is pplied on block of weiht W plced on horizontl tble. If the nle of friction is, then the nitude of force required to ove the body is equl to [EMCET 987] W sin tn( ) W sin cos( ) W cos cos( ) W tn sin( ) 7. In the fiure shown, block of weiht 0 N restin on horizontl surfce. The coefficient of sttic friction between the block nd the surfce force of.5 N will keep the block in unifor s otion, once it hs been set in otion. horizontl force of N is pplied to the block, then the block will Move over the surfce with constnt velocity Move hvin ccelerted otion over the surfce Not ove irst it will ove with constnt velocity for soe tie nd then will hve ccelerted otion 8. Two sses nd of 0 k nd 5 k respectively re connected with strin pssin over frictionless pulley fixed t the corner of tble s shown. The coefficient of sttic friction of with tble is 0.. The iniu ss of C tht y be plced on to prevent it fro ovin is 5 k 0 k 5 k k 9. The liitin friction is lwys reter thn the dynic friction lwys less thn the dynic friction C T [M ET 984]

10 riction 7 Equl to the dynic friction Soeties reter nd soeties less thn the dynic friction 0. Which is suitble ethod to decrese friction ll nd berins olishin Lubriction ll the bove

11 8 riction. unifor rope of lenth l lies on tble. If the coefficient [M ET 994] of friction is, then the xiu lenth l of the prt of this rope which cn overhn fro the ede of the tble without slidin down is [DMT 00] l l l k 0. k 5 k l l. Which of the followin stteents is not true [CMC Vellore 989] The coefficient of friction between two surfces increses s the surfce in contct re de rouh The force of friction cts in direction opposite to the pplied force ollin friction is reter thn slidin friction The coefficient of friction between wood nd wood is less thn. block of k is stopped inst wll by pplyin force perpendiculr to the wll. If 0. then iniu vlue of will be [M MT 00] 0 k 6. Work done by frictionl force is Netive Zero ositive ll of the bove 7. unifor chin of lenth L chnes prtly fro tble which is kept in equilibriu by friction. The xiu lenth tht cn withstnd without slippin is l, then coefficient of friction between the tble nd the chin is l L l L l l L l L L l [EMCET (En.) 995] 8. When two surfces re coted with lubricnt, then they Stick to ech other [MC 998, 99; IIMS 00] Slide upon ech other 980 N 49 N oll upon ech other None of these 98 N 490 N 4. hevy unifor chin lies on horizontl tble-top. If the coefficient of friction between the chin nd tble surfce is 0.5, then the xiu frction of lenth of the chin, tht cn hn over one ede of the tble is[cse MT 990] 0% 5% 5% 5% 5. The blocks nd re rrned s shown in the fiure. The pulley is frictionless. The ss of is 0 k. The coefficient of friction of with the horizontl surfce is 0.0. The iniu ss of to strt the otion will be 9. 0 k block is initilly t rest on rouh horizontl surfce. horizontl force of 75 N is required to set the block in otion. fter it is in otion, horizontl force of 60 N is required to keep the block ovin with constnt speed. The coefficient of sttic friction is [MU 999] block with ss 00 k is restin on nother block of ss 00 k. s shown in fiure horizontl rope tied to wll holds it. The coefficient of friction between nd is 0. while coefficient of friction between nd the round is 0.. The iniu required force to strt ovin will be

12 [ET 999] 5 N riction 9 5 N 900 N 00 N 00 N 00 N. To void slippin while wlkin on ice, one should tke sller steps becuse of the [HU 999; CECE 004] riction of ice is lre Lrer norl rection riction of ice is sll Sller norl rection. box is lyin on n inclined plne wht is the coefficient of sttic friction if the box strts slidin when n nle of inclintion is 60 o [KCET 000] 6. body of ss k is kept by pressin to verticl wll by force of 00 N. The coefficient of friction between wll nd body is 0.. Then the frictionl force is equl to [Oriss JEE 00] 6 N 0 N 600 N 700 N 7. horizontl force of 0 N is necessry to just hold block sttionry inst wll. The coefficient of friction between the block nd the wll is 0.. the weiht of the block is [IEEE 00] N 0 N 0 N N. block of ss k is kept on the floor. The coefficient of sttic friction is 0.4. If force of.5 Newtons is pplied on the block s shown in the fiure, the frictionl 8. The coefficient of sttic friction, s, between block of ss k nd the tble s shown in the fiure is 0.. force between the block nd the floor will be Wht would be the xiu ss vlue of block so [M ET 000] tht the two blocks do not ove? The strin nd the.5 N pulley re ssued to be sooth nd ssless. 5 N ( 0 / s ) 7.84 N 0 N 4. Which one of the followin is not used to reduce friction Oil Snd ll berins Grphite [Kerl (En.) 00] 5. If ldder weihin 50N is plced inst sooth verticl wll hvin coefficient of friction between it nd floor is 0., then wht is the xiu force of friction vilble t the point of contct between the ldder nd the floor [IIMS 00] 50 N.0 k 4.0 k 0. k 0.4 k k [CSE MT 004] 9. If ss of 0 k, coefficient of sttic friction = 0., coefficient of kinetic friction = 0.. Then ss of to strt otion is [Oriss MT 004] 0 k 75 N 50 N k

13 40 riction. k 4.8 k unifor etl chin is plced on rouh tble such tht one end of chin hns down over the ede of the tble. When one-third of its lenth hns over the ede, the chin strts slidin. Then, the coefficient of sttic friction is 4 4 [Kerl ET 005]. lift is ovin downwrds with n ccelertion equl to ccelertion due to rvity. body of ss kept on the floor of the lift is pulled horizontlly. If the coefficient of friction is, then the frictionl resistnce offered by the body is [DMT 004] Zero. If ldder weihin 50 N is plced inst sooth verticl wll hvin coefficient of friction between it nd floor is 0., then wht is the xiu force of friction vilble t the point of contct between the ldder nd the floor [HU 004] 75 N 5 N 50 N 5 N Kinetic riction. Which one of the followin stteents is correct. cr is ovin lon striht horizontl rod with speed v 0. If the coefficient of friction between the tyres nd the rod is, the shortest distnce in which the cr cn be stopped is [M ET 985; HU 00] v0 v0 v0 4. block of ss 5 k is on rouh horizontl surfce nd is t rest. Now force of 4 N is iprted to it with neliible ipulse. If the coefficient of kinetic friction is 0.4 nd 9.8 / s, then the ccelertion of the block is 0.6 / s 0.69 / s v / s 0.88 / s 5. body of ss k is bein dred with unifor velocity of /s on rouh horizontl plne. The coefficient of friction between the body nd the surfce is 0.0. The ount of het enerted in 5 sec is ( J 4. joule/ cl nd 9.8 / s ) 9. cl.67 cl 0. cl.4 cl [MH CET (Med.) 00] 6. Two crts of sses 00 k nd 00 k on horizontl rils re pushed prt. Suppose the coefficient of friction between the crts nd the rils re se. If the 00 k crt trvels distnce of 6 nd stops, then the distnce trvelled by the crt weihin 00 k is [CMT 989; DMT 00] ollin friction is reter thn slidin friction ollin friction is less thn slidin friction ollin friction is equl to slidin friction ollin friction nd slidin friction re se. The xiu speed tht cn be chieved without skiddin by cr on circulr unbnked rod of rdius 6 4 nd coefficient of sttic friction, is [NCET 990] 7. body lies on sooth horizontl tble nd nother body is plced on. The coefficient of friction between

14 riction 4 nd is. Wht ccelertion iven to will cuse slippin to occur between nd nle of 0 to the upwrd drwn verticl which cuses the block to just slide is [ISM Dhnbd 994] / 9.4 N 9.6 N /.96 N 94. N k body is pushed with just enouh force to strt it ovin cross floor nd the se force continues to ct fterwrds. The coefficient of sttic friction nd slidin friction re 0.5 nd 0.4 respectively. The ccelertion of the body is 6 / s.9 / s 4.9 / s / s 9. cr turns corner on slippery rod t constnt speed of 0 / s. If the coefficient of friction is 0.5, the iniu rdius of the rc in eter in which the cr turns is otorcyclist of ss is to neotite curve of rdius r with speed v. The iniu vlue of the coefficient of friction so tht this neotition y tke plce sfely, is v r r v v r v r [Hryn CEE 996]. On rouh horizontl surfce, body of ss k is iven velocity of 0 /s. If the coefficient of friction is 0. nd distnce of / s, the body will stop fter coverin 5 50 [M MT 999]. block of ss 50 k cn slide on rouh horizontl surfce. The coefficient of friction between the block nd the surfce is 0.6. The lest force of pull ctin t n. body of 0 k is cted by force of 9.4 N if 9.8 / sec. The ccelertion of the block is 0 / s. Wht is the coefficient of kinetic friction[emcet 994] ssuin the coefficient of friction between the rod nd tyres of cr to be 0.5, the xiu speed with which the cr cn ove round curve of 40.0 rdius without slippin, if the rod is unbnked, should be [MU 995] 5 /s 4 /s 9 /s /s 5. Consider cr ovin lon striht horizontl rod with speed of 7 k/h. If the coefficient of kinetic friction between the tyres nd the rod is 0.5, the shortest distnce in which the cr cn be stopped is [ 0 s ] [CSE MT 99] k horse pulls crt of ss 500 k lon level rod with n ccelertion of s. If the coefficient of slidin friction is 0., then the force exerted by the horse in forwrd direction is [SC 998] 000 N 5000 N 4000 N 6000 N 7. The xiu speed of cr on rod turn of rdius 0; if the coefficient of friction between the tyres nd the rod is 0.4; will be [MH CET (Med.) 999] 9.84 /s 7.84 /s 0.84 /s 5.84 /s

15 4 riction 8. block of ss 50 k slides over horizontl distnce of. If the coefficient of friction between their surfces is 0., then work done inst friction is horizontl force of 00 N is ctin on it, then ccelertion of the block will be [IIMS 00] 0.5 /s 5 /s 98 J 56 J [HU 00; CSE MT 999, 000; IIMS 000] 7J 4 J 0 /s 5 /s 4. It is esier to roll brrel thn pull it lon the rod. This stteent is [V 00] 9. On the horizontl surfce of truck ( = 0.6), block of ss k is plced. If the truck is ccelertin t the rte of 5/sec then frictionl force on the block will be [CSE MT 00] 5 N 6 N lse True Uncertin Not possible 5. rble block of ss k lyin on ice when iven velocity of 6 /s is stopped by friction in 0s. Then the coefficient of friction is [IEEE 00] 5.88 N 8 N vehicle of ss is ovin on rouh horizontl rod with oentu. If the coefficient of friction between the tyres nd the rod be, then the stoppin distnce is [CSE MT 00]. body of weiht 64 N is pushed with just enouh force to strt it ovin cross horizontl floor nd the se force continues to ct fterwrds. If the coefficients of sttic nd dynic friction re 0.6 nd 0.4 respectively, the ccelertion of the body will be (ccelertion due to rvity = ) [EMCET 00]. When body is ovin on surfce, the force of friction is clled [M ET 00] Sttic friction Liitin friction Dynic friction ollin friction. block of ss 0 k is plced on rouh horizontl surfce hvin coefficient of friction = 0.5. If horizontl force of 9.4 N is pplied on 0 k block which rests on horizontl surfce. If the coefficient of friction is 0., the ccelertion should be 9.8 / s.6 / s 0 / s 9.6 / s k weiht is dred on horizontl surfce by rope upto etres. If coefficient of friction is 0. 5, the nle of rope with the surfce is 60 nd 9.8 / sec, then work done is [M ET 995] 94 joules 588 joules 5 joules 97 joules 8. cr hvin ss of 000 k is ovin t speed of 0 etres/sec. rkes re pplied to brin the cr to rest. If the frictionl force between the tyres nd the rod surfce is 5000 newtons, the cr will coe to rest in [M MT 995] 5 seconds seconds 0 seconds 6 seconds 9. If s, k nd r re coefficients of sttic friction, slidin friction nd rollin friction, then [EMCET (En.) 995] s k r k r s r k s r k s

16 0. body of ss 5k rests on rouh horizontl surfce of coefficient of friction 0.. The body is pulled throuh distnce of 0 by horizontl force of 5 N. The kinetic enery cquired by it is ( = 0 s ) 0 J 00 J 50 J 50 J [EMCET (Med.) 000]. otorcycle is trvellin on curved trck of rdius 500. If the coefficient of friction between rod nd tyres is 0.5, riction 4 5. Consider cr ovin on striht rod with speed of 00 /s. The distnce t which cr cn be stopped is [ k 0.5] [IEEE 005] cylinder of 0 k is slidin in plne with n initil velocity of 0 /s. If the coefficient of friction between the surfce nd cylinder is 0.5 then before stoppin, it will the speed voidin skiddin will be [MH cover. CET (Med.) 00] ( 0 / s ) [b. MT 004] 50 /s 75 /s /s 5 /s firen of ss 60 k slides down pole. He is pressin the pole with force of 600 N. The coefficient of friction between the hnds nd the pole is 0.5, with wht ccelertion will the firen slide down ( = 0 /s ) /s.5 /s 0 /s 5 /s [b. MT 00]. block of ss M 5 k is restin on rouh horizontl surfce for which the coefficient of friction is 0.. When force 40 N is pplied, the ccelertion of the block will be ( 0 / s ) [M MT 004] / sec / sec / sec / sec 4. body is ovin lon rouh horizontl surfce with n initil velocity 6 / s. If the body coes to rest fter trvellin 9, then the coefficient of slidin friction will be M 0 Motion on Inclined Surfce. When body is lyin on rouh inclined plne nd does not ove, the force of friction is equl to is reter thn is less thn is equl to. When body is plced on rouh plne inclined t n nle to the horizontl, its ccelertion is (sin cos) (sin cos) ( sin cos) (sin cos). block is t rest on n inclined plne kin n nle with the horizontl. s the nle of the incline is incresed, the block strts slippin when the nle of inclintion becoes. The coefficient of sttic friction between the block nd the surfce of the inclined plne is or body strts slidin down t n nle to horizontl. Then coefficient of friction is equl to [CSE MT 99] sin cos [CECE 004] tn Independent of 4. iven object tkes n ties s uch tie to slide down 45 rouh incline s it tkes to slide down perfectly

17 44 riction sooth 45 incline. The coefficient of kinetic friction 0.4 nd 0. respectively, then the frictionl force ctin on between the object nd the incline is iven by [ET the 999; block MU is 000] [SC 994] n n n n 5. The force required just to ove body up n inclined plne is double the force required just to prevent the body slidin down. If the coefficient of friction is 0.5, the nle of inclintion of the plne is Strtin fro rest, body slides down 45 inclined plne in twice the tie it tkes to slide down the se distnce in the bsence of friction. The coefficient of friction between the body nd the inclined plne is [CSE MT 990].7 N.7 N The coefficient of friction between body nd the surfce of n inclined plne t 45 is 0.5. If ccelertion of the body downwrds in / s, the / s is [EMCET 994] brick of ss k beins to slide down on plne inclined t n nle of 45 o with the horizontl. The force 8. box is plced on n inclined plne nd hs to be pushed down. The nle of inclintion is of friction will be [EMCET 994] [CMT 000] 9.6 sin 45 o 9.6 cos 45 o Equl to nle of friction 9.8 sin 45 o 9.8 cos 45 o More thn nle of friction Equl to nle of repose Less thn nle of repose 9. force of 750 N is pplied to block of ss 0 k to prevent it fro slidin on plne with n inclintion nle 0 with the horizontl. If the coefficients of sttic friction nd kinetic friction between the block nd the plne re 750 N 45 N 500 N 50 N 0. block is lyin on n inclined plne which kes 60 with the horizontl. If coefficient of friction between block nd plne is 0.5 nd 0 / s, then ccelertion of the block when it oves lon the plne will be[et 997].50 / s 7.4 / s 5.00 / s 8.66 / s. body of ss 00 is slidin fro n inclined plne of inclintion 0. Wht is the frictionl force experienced if.7 [HU 998].7 N.7 N. body tkes just twice the tie s lon to slide down plne inclined t 0 o to the horizontl s if the plne were frictionless. The coefficient of friction between the body nd the plne is [JIME 999] The upper hlf of n inclined plne of inclintion is perfectly sooth while the lower hlf is rouh. body strtin fro the rest t top coes bck to rest t the botto if the coefficient of friction for the lower hlf is iven by = sin = cos 4 = cot = tn [b. MT 000]

18 riction body is slidin down n inclined plne hvin coefficient of friction 0.5. If the norl rection is twice tht of the resultnt downwrd force lon the incline, the nle between the inclined plne nd the horizontl is [EMCET (En.) 000] 00 J Zero. k ss strts fro rest on n inclined sooth surfce with inclintion 0 o nd lenth. How uch will it trvel before coin to rest on frictionl surfce with frictionl coefficient of 0.5 [ 5 o 0 o o 60 o 6. body of ss 0 k is lyin on rouh plne inclined t n nle of 0 o to the horizontl nd the coefficient of friction is 0.5. the iniu force required to pull the body up the plne is [JIME 000] 94 N 9.4 N 8. block rests on rouh inclined plne kin n nle of o 0 with the horizontl. The coefficient of sttic friction between the block nd the plne is 0.8. If the frictionl force on the block is 0 N, the ss of the block (in k) is (tke 0 / s ) [IEEE 004] 9.4 N 0.94 N block of ss k slides down on rouh inclined plne of inclintion 60 o strtin fro its top. If the coefficient of kinetic friction is 0.5 nd lenth of the plne is, then work done inst friction is (Tke = 9.8 /s ) [MC 000; KCET 00] 9.8 J 4.94 J.45J.96 J 8. block of ss 0 k is plced on n inclined plne. When the nle of inclintion is 0 o, the block just beins to slide down the plne. The force of sttic friction is [Kerl (En.) 00] 0 k wt 89 k w 49 k wt 5 k wt.6.5. body tkes tie t to rech the botto of n inclined plne of nle with the horizontl. If the plne is de rouh, tie tken now is t. The coefficient of friction of the rouh surfce is tn 4 tn 4 tn tn 4. block is kept on n inclined plne of inclintion of lenth l. The velocity of prticle t the botto of inclined is (the coefficient of friction is ) l ( cos sin ) l (sin cos) l (sin cos) l (cos sin ) 9. body of 5 k weiht kept on rouh inclined plne of nle 0 o strts slidin with constnt velocity. Then the coefficient of friction is (ssue = 0 /s ) [JIME 00] / / Joule of work is done in slidin up k block on n inclined plne to heiht of 0 etres. Tkin vlue of ccelertion due to rvity to be 0 /s, work done inst friction is [M MT 00] 00 J 00 J. block of ss lyin on rouh horizontl plne is cted upon by horizontl force nd nother force Q inclined t n nle to the verticl. The block will rein in equilibriu, if the coefficient of friction between it nd the surfce is [Hryn CEE 996]

19 46 riction ( Q sin) ( Q cos) ( cos Q) Q ( Q sin) M ( Q cos) ( Q sin) ( sin Q) ( Q cos). Which of the followin is correct, when person wlks on rouh surfce [IIT 98] The frictionl force exerted by the surfce keeps hi ovin The force which the n exerts on the floor keeps hi ovin 0 N N 0 N 5 N 6. block of ss is plced on frictionless horizontl surfce. nother block Q of se ss is kept on nd connected to the wll with the help of sprin of sprin constnt k s shown in the fiure. s is the coefficient of friction between nd Q. The blocks ove toether perforin SHM of plitude. The xiu vlue of the friction force between nd Q is [IIT-JEE (Screenin) 004] The rection of the force which the n exerts on floor keeps hi ovin None of the bove. block of ss 0. k is held inst wll by pplyin horizontl force of 5 N on the block. If the coefficient of friction between the block nd the wll is 0.5, the nitude of the frictionl force ctin on the block is[iit 994] 7. body of ss rests on horizontl surfce. The.5 N 4.9 N 0.98 N 0.49 N 4. body of ss M is kept on rouh horizontl surfce (friction coefficient ). person is tryin to pull the body by pplyin horizontl force but the body is not ovin. The force by the surfce on the body is, where M Mf M M M M [M ET 997] 5. Wht is the xiu vlue of the force such tht the block shown in the rrneent, does not ove 60 =k [IIT-JEE Screenin 00] k k Zero s coefficient of friction between the body nd the surfce is. If the ss is pulled by force s shown in the fiure, the liitin friction between body nd surfce will be Sooth surfce [HU 004] k slb rests on frictionless floor s shown in the fiure. 0 k block rests on the top of the slb. The sttic coefficient of friction between the block nd slb is 0.60 while the kinetic friction is The 0 k block is cted upon by horizontl force 00 N. If 9.8 / s, the resultin ccelertion of the slb will be [NCET 98] Q 0

20 riction / s.47 / s.5 / s 6. / s 00 N 0 k 40 k 9. block of ss k rests on rouh inclined plne kin n nle of 0 with the horizontl. The coefficient of sttic friction between the block nd the plne is 0.7. The frictionl force on the block is [IIT 980; J & K CET 004] 9.8 N ed the ssertion nd reson crefully to rk the correct option out of the options iven below: If both ssertion nd reson re true nd the reson is the correct explntion of the ssertion. If both ssertion nd reson re true but reson is not the correct explntion of the ssertion. If ssertion is true but reson is flse. If the ssertion nd reson both re flse. (e) If ssertion is flse but reson is true N. ssertion : On riny dy, it is difficult to drive cr or 9.8 N bus t hih speed N 0. When bicycle is in otion, the force of friction exerted by the round on the two wheels is such tht it cts [IIT 990; Mnipl MEE 995; M ET 996] In the bckwrd direction on the front wheel nd in the forwrd direction on the rer wheel In the forwrd direction on the front wheel nd in the bckwrd direction on the rer wheel In the bckwrd direction on both front nd the rer wheels In the forwrd direction on both front nd the rer wheels. n insect crwls up heisphericl surfce very slowly (see the fiure). The coefficient of friction between the insect nd the surfce is /. If the line joinin the centre of the heisphericl surfce to the insect kes n nle with the verticl, the xiu possible vlue of is iven by [IIT-JEE 00] eson : The vlue of coefficient of friction is lowered due to wettin of the surfce.. ssertion : When bicycle is in otion, the force of friction exerted by the round on the two wheels is lwys in forwrd direction. eson : The frictionl force cts only when the bodies re in contct.. ssertion : ullin lwn roller is esier thn pushin it. eson : ushin increses the pprent weiht nd hence the force of friction. 4. ssertion : nle of repose is equl to nle of liitin friction. eson : When the body is just t the point of otion, the force of friction in this ste is clled s liitin friction. cot tn sec cosec 5. ssertion : Two bodies of sses M nd (M > ) re llowed to fll fro the se heiht if the ir resistnce for ech be the se then both the bodies will rech the erth siultneously. eson : or se ir resistnce, ccelertion of both the bodies will be se. 6. ssertion : riction is self djustin force.

21 48 riction eson : riction does not depend upon ss of the body. b b c c 7 8 d 9 d 0 c 7. ssertion : The vlue of dynic friction is less thn the liitin friction. eson : Once the otion hs strted, the inerti of rest hs been overcoe. 8. ssertion : The ccelertion of body down rouh inclined plne is reter thn the ccelertion due to rvity. b 4 d 5 c 6 b 7 c 8 d b Criticl Thinkin Questions c b 4 c 5 6 b 7 c c eson : The body is ble to slide on inclined plne only when its ccelertion is reter thn ccelertion due to rvity. ssertion & eson e 4 b 5 d 6 d 7 8 d Sttic nd Liitin riction c d c 4 b 5 6 c 7 c d c c b d 7 c 8 b 9 0 c c b 4 c 5 6 b 7 8 d 9 0 d d Kinetic riction b d 4 d 5 6 c 7 8 d 9 0 b b d c 4 c 5 b 6 d 7 b d d b b 4 b 5 d 6 b 7 b 8 d 9 c 0 b d 4 b 5 d 6 d Motion on Inclined Surfce

22 46 riction 8. Surfces lwys slide over ech other Coefficient of friction s l. Sttic nd Liitin riction Here pplied horizontl force cts s norl rection or holdin the block orce of friction = Weiht of block f W W W W s W 7. l s N i.e. iniu 4N force is required to strt the otion of body. ut pplied force is only N. So the block will not ove. 8. or liitin condition C 5k C C C 0. ll nd berin produce rollin otion for which force of friction is low. Lubriction nd polishin reduce rouhness of surfce.. or iven condition we cn pply direct forul l l. Slidin friction is reter thn rollin friction. W N 0. ' 0.5 l 4. l 0% l l of l k 0 6. Work done by friction cn be positive, netive nd zero dependin upon the sitution. 7. Lenhtof chin hnin fro the tble Lenhtof chin lyin on the tble W f l L l. f f G G( ) (00) N. tn (nle of repose) tn pplied force.5 N Liitin friction N or the iven condition pplied force is very sller thn liitin friction. Sttic friction on body = pplied force =.5 N 4. Snd is used to increse the friction N 6. or the iven condition, Sttic friction = pplied force = Weiht of body 0 0 N W W 0. 0 N s k 9. s 0. k s l l Lenht of the chin hnin fro the tble Lenthof the chin lyin on the tble / l / l / l / Kinetic riction.. In the iven condition the required centripetl force is provided by frictionl force between the rod nd tyre. f G f v v. etrdin force Now fro eqution of otion Ground v u s 0 u u u s s v0

23 riction Net force = pplied force riction force / s 5. Work done = orce Displceent ( v t) W ( 0.) joule W Het enerted Q J 6. or iven condition s cl 4. s s s s There is no friction between the body nd surfce of the tble. If the body is pulled with force then ( ) Due to this force upper body will feel the pseudo force in bckwrd direction. f ut due to friction between nd, body will not ove. The body will strt ovin when pseudo force is ore thn friction force. i.e. for slippin, 8. Liitin friction s s N Kinetic friction k k N orce pplied on the body = 00 N nd if the body is ovin then, Net ccelertin force =pplied force Kinetic friction / s 60 v v r r u (0). S or liitin condition f f sin0 ( cos0), y solvin 94. N. Net force on the body = pplied force riction k k v r / s f cos 0 sin 0 u (0) 5. s Net force in forwrd direction = ccelertin force + riction ( ) ( )( 0. 0) N 7. v r / s 8. W S J 9. l N 0. seudo force on the block = 5 5 N seudo is less then liitin friction hence sttic force of friction = 5 N. u u S. Weiht of the body = 64N.. 4. so ss of the body 6. 4 k, 0. 6, 0. 4 Net ccelertion s ppliedforce - Kinetic friction Mss of the body s k ( s k ) ( ) 0. ppliedforce Kinetic friction ss / s 0 u 6 5. v u t u t t ro the reltion / s 0 7. Let body is dred with force, kin n nle 60 with the horizontl. sin 60 Kinetic friction in the otion = k ro the fiure k cos 60 nd sin60 cos60 ( sin60) k k k cos60 N cos 60 k k Work done k s 5 Joule N

24 48 riction 8. u v u t t [s v 0 ] u t 6 sec Kinetic enery cquired by body = (Totl work done on the body) (work inst friction) S S Joule. v r / s. Net downwrd ccelertion. ( ) / s 60 Weiht- rictionforce Mss Kinetic friction = 0.( sin0) k (50 0) 6 N cos 0 Kinetic friction ccelertion of the block Mss We know / s u u (6) s 0. s 0 9 u (00) 5. s Kinetic enery of the cylinder will o inst friction v = s u (0) s 0 (0.5) 0 Motion on Inclined Surfce. When the body is t rest then sttic friction works on it, which is less thn liitin friction ( )... Coefficient of friction = Tnent of nle of repose k tn sin 0 0 cos 0 W 600N 4. tn n [s 45 ] n 5. etrdtion in upwrd otion (sin cos) orce required just to ove up (sin cos) up Siilrly for down wrd otion (sin cos) orce required just to prevent the body slidin down dn (sin cos) ccordin to proble up (sin cos) (sin cos) sin cos sin cos cos sin tn tn () tn ( 0.5) tn (0.75) tn n dn 45 nd n (Given) tn (sin cos) 9.8(sin5 0.5 cos45 ) 4.9 / sec 8. ecuse if the nle of inclintion is equl to or ore thn nle of repose then box will utoticlly slides down the plne. 9. Net force lon the plne = sin = = 50 N Liitin friction = cos l s = cos 0 = 46 N s net externl force is less thn liitin friction therefore friction on the body will be 50 N. 0. (sin cos) 0(sin cos60) 7.4 / s. cos k k k k cos 0 s o cos.7. tn tn 0 n 4. or nle of repose, riction =Coponent of weiht lon the plne N o

25 riction 49 = sin 9.8 sin45 4. or upper hlf o o 9.6 sin45 v u l/ ( sin ) l / lsin or lower hlf 0 u l (sin cos) l sin l(sin cos) cos sin tn 5. esultnt downwrd force lon the incline (sin cos) Norl rection cos Given : cos (sin cos) y solvin o (sin cos) 0 9.8(sin0 0.5 cos0) 9.4 N. 7. W cos S J 8. sin0 50N 5k - wt. 9. tn Work done inst rvity h J. Work done inst friction = (Totl work done work done inst rvity) J v S ouh u s 0 sin0 v 0 Let it trvel distnce S before coin to rest v 0 S nle of repose tn ( ) tn (0.8) nle of inclined plne is iven 0. It ens block is t rest therefore, Sttic friction = coponent of weiht in downwrd direction 0 sin 0 N k 9 sin0. tn tn n 4 tn 4. ccelertion (sin cos ) nd s = l l/ l/ v s l (sin cos) Criticl Thinkin Questions. y drwin the free body dir of the block for criticl condition Q sin. ( Q cos) Q sin Q cos. Liitin friction s 0.5 (5). l 5 Since downwrd force is less thn liitin friction therefore block is t rest so the sttic force of friction will work on it. N s = downwrd force = Weiht N 4. Mxiu force by surfce when friction works 5. f Miniu force ( ) when there is no friction Hence rnin fro to We et, M M f cos 60 ( W sin60) Substitutin & W 0 we et 0N 6. When two blocks perfors siple hronic otion toether then t the extree position ( t plitude =) K estorin force K There will be no reltive otion between nd Q if pseudo force on block is less thn or just equl to liitin friction between nd Q. K i.e. Liitin friction Mxiu friction K 7. Norl rection sin0 f sin W 0 + sin 0 0 cos 60 + Q cos o cos 0 +Q sin 5N

26 50 riction opposite to its weiht. Thus weiht is reduced. So pullin is esier thn pushin the lwn roller. V Liitin friction between body nd surfce is iven by,. 8. Liitin friction between block nd slb s N ut pplied force on block is 00 N. So the block will slip over slb. Now kinetic friction works between block nd slb N k k This kinetic friction helps to ove the slb 9. ccelertion of slb 9. Liitin friction l cos / s l cos 0 N (pproxitely) ut when the block is lyin on the inclined plne then coponent of weiht down the plne sin 9.8 sin0 9.8 N It ens the body is sttionry, so sttic friction will work on it Sttic friction = pplied force = 9.8 N 0. (,c) In cyclin, the rer wheel oves by the force counicted to it by pedllin while front wheel oves by it self. So, while pedllin bicycle, the force exerted by rer wheel on round kes force of friction ct on it in the forwrd direction (like wlkin). ront wheel ovin by itself experience force of friction in bckwrd direction (like rollin of bll). [However, if pedllin is stopped both wheels ove by theselves nd so experience force of friction in bckwrd direction] The force ctin on the body of ss M re its weiht M ctin verticlly downwrds nd ir resistnce ctin verticlly upwrd. M ccelertion of the body, M Now, M >, therefore, the body with lrer ss will hve reter ccelertion nd it will rech the round first. 6. Only sttic friction is self djustin force. This is becuse force of sttic friction is equl nd opposite to pplied force (so lon s ctul otion does not strt). rictionl force = i.e. friction depends on ss. 7. W 8. ccelertion down rouh inclined plne H (sin cos) nd this is less thn. H V W M ssertion & eson. On riny dy, the rods re wet. Wettin of rods lowers the coefficient of friction between the tyres nd the rod. Therefore, rip of cr on the rod reduces nd thus chnces of skiddin increses.. (e) When bicycle is in otion, two cses y rise : (i) When the bicycle is bein pedlled. In this cse, the pplied force hs been counicted to rer wheel. Due to which the rer wheel pushes the erth bckwrds. Now the force of friction cts in the forwrd direction on the rer wheel but front wheel ove forwrd due to inerti, so force of friction works on it in bckwrd direction (ii) When the bicycle is not bein pedlled : In this cse both the wheels ove in forwrd direction, due to inerti. Hence force of friction on both the wheels cts in bckwrd direction.. Suppose the roller is pushed s in fiure. The force is resolved into two coponents, horizontl coponent which H helps the roller to ove forwrd, nd the verticl coponent ctin downwrds dds to the weiht. Thus weiht is incresed. ut in the cse of pull [fi ] the verticl coponent is