NEWTON'S LAWS OF MOTION

Transcription

1 5 EWO'S LAWS O MOIO EWO S IS LAW O MOIO (O GALLEO S LAW O IEIA) Every body continues its stte of rest or uniform motion in striht line unless compelled by n externl force to chne its stte. his fundmentl property of body is clled inerti t rest. his lw defines the force nd sttes tht the force is fctor which cn chne the stte of object. Definition of force from ewton s first lw of motion orce is the push or pull which chnes or tends to chne the stte of rest or of uniform motion. Exmple : A block of 5 k is restin on frictionless plne. It is struck by jet relesin wter t rte of 3 k/s t speed of 4 m/s. Clculte the initil ccelertion of the block. Sol. orce exertin on block dm v dt k IEIA Inerti is the property of body due to which it opposes the chne in its stte. Inerti of body is mesured by mss of the body. Inerti mss EWO S SECOD LAW O MOIO te of chne in momentum of body is lwys equl to the unblnced externl force pplied on it. dp d dv dm (mv) or m + v dt dt dt dt If m constnt then If v constnt then dm dv 0 0 dt dt dv dm i.e. m m i.e. v dt dt (e.. conveyor belt, rocket) * he chne in momentum lwys tkes plce in the direction of force. * his lw ives the mnitude of force. Exmple 1 : A force (6i ˆ 8j ˆ + 10k) ˆ produces ccelertion of 1 ms in body. Clculte the mss of the body. Sol. Accelertion m m 10 k 1 So ccelertion of the block 1.4 m / s m 5 IMPULSE When lre force ct for n extremely short durtion, neither the mnitude of the force nor the time for which it cts is importnt. In such s cse, the totl effect of force is mesured. he totl effect of force is clled impulse (mesure of the ction of force). his type of force is enerlly vrible in mnitude nd is sometimes clled impulsive force. If lre force ct on body or prticle for smller time : then the impulse product of force with time. Suppose force cts for short time dt then impulse dt t or finite internl of time t 1 to t then the impulse dt t 1 If constnt force cts for n intervl t then Impulse t Exmple 3 : A hmmer of mss 1 k movin with speed of 6 m/s strikes wll nd comes to rest in 0.1s. Clculte. () Impulse of the force (b) Avere retrdin force tht stops the hmmer. (c) Avere retrdtion of the hmmer. Sol. () Impulse t m (v u) 1 (0 6) 6 s (b) Avere retrdin force tht stops the hmmer Impulse 6 60 time (c) Avere retrdtion, 60 m / s SMA SUDY MAEIAL : PHYSICS 1 EWO'S LAWS O MOIO

2 Exmple 4 : A bll of 0.0 k hits wll t n nle of 45 with velocity of 5m/s. If the bll rebounds t 90 to the direction of incidence, clculte the chne in momentum of the bll. Sol. Chne in momentum ( mv cos 45 ) (mv cos 45 ) mv cos 45 mv cos θ v mv cos θ v θ θ θ 45 p mv cos s EWO S HID LAW O MOIO he first nd second lws re sttements bout sinle object, wheres the third lw is sttement bout two objects. A A * Accordin to this lw, every ction hs equl nd opposite rection. Action nd rection ct on different bodies nd they re simultneous. here cn be no rection without ction. * If n object A exerts force on n object B, then B exerts n equl nd opposite force ( ) on A. * ewton s III lw contrdicts theory of reltivity, becuse it sttes tht force sinls cn trvel with infinite speed while theory of reltively sttes tht nothin cn trvel with velocity reter thn velocity of liht. * Action nd rection never blnce ech other. * ewton s III lw cn be derived from II lw. (s iven) If two prticles of msses nd m re movin under ction of their mutully interctin forces with ech other, such tht no externl force cts on the system. Let force on 1 st due to nd is dp (i) dt nd force on nd due to 1 st dp is 1... (ii) dt Addin the two equtions, we hve dp1 dp d (p1 + p ) dt dt dt B B Since no externl force cts on the system, the totl of momentum of the system must be constnt. EE BODY DIAGAM A free body dirm is dirm showin the chosen body by itself, free of its surroundins, with vectors drwn to show the mnitudes nd directions of ll the forces pplied to the body by the vrious other bodies tht interct with it. Be creful to include ll the forces ctin on the body, but the eqully creful not to include ny forces tht the body exerts on ny other body. In prticulr, the two forces in n ctionrection pir must never pper in the sme free-body dirm becuse they never ct on the sme body. [orces tht body exerts on itself re never included, since these cn t ffect the body s motion.] COAC OCE Contct forces rises when one body is in physicl contct with nother. Exmple : orces exerted by ropes or sprins, the force involved in collisions, the force of friction between two surfces, nd the force exerted by fluid on its continer. wo bodies in contct : wo blocks of msses nd m plced in contct with ech other on frictionless horizontl surfce. Cse I : Let force be pplied on block of mss. Accelertion of both the blocks, m m1 + m Let the force of contct By BD of m1 + m 1 m1 m m + m m + m 1 1 Cse II : If force is pplied on block of mss m m BD of SMA SUDY MAEIAL : PHYSICS EWO'S LAWS O MOIO

3 Common ccelertion, m By BD of m, 1 m or 1 m or 1 m m + m 1 + m 1 m1 m1 1 m + m m + m 1 1 m BD of m hree bodies in contct : Cse I : hree blocks of msses, m nd m 3 plced in contct on smooth horizontl surfce. Let force be pplied on block of mss. Let contct force between nd m is 1 nd the contct force between m nd m 3 is. m m Accelertion of ll the blocks, m + m + m rom BD, (m + m 3) m + m + m 1 3 Cse II : If force is pplied on mss m 3 : m m Common ccelertion, m + m + m rom BD, 1 3 (m1 + m ) m + m + m 1 3 SYSEM O MASSES IED BY SIGS ension in strin : It is n intermoleculr force between the toms of strin, which cts or rects when the strin is stretched. Importnt points bout the tension in strin : () orce of tension ct on body in the direction wy from the point of contct or tied ends of the strin. (b) (i) Strin is ssumed to be inextensible so tht the mnitude of ccelertion of ny number of msses connected throuh strins is lwys sme. M 1 M (ii) If the strin is extensible the ccelertion of different msses connected throuh it will be different until the strin cn stretch. m m (c) (i) Strin is mssless nd frictionless so tht tension throuhout the strin remins sme. Mssless nd friction less strin (ii) If the strin is mssless but not frictionless, t every contct tension chnes. M 1 1 Mssless strin but there is friction between strin nd pulley (iii) If the strin is liht tension t ech point will be different dependin on the ccelertion of the strin. 1 here is friction between strin nd pulley nd strin used in not liht. (d) If force is directly pplied on strin s sy mn is pullin tied strin from the other end with some force the tension will be equl to the pplied force irrespective of the motion of the pullin ent, irrespective of whether the box will move or not, mn will move or not. 3 4 SMA SUDY MAEIAL : PHYSICS 3 EWO'S LAWS O MOIO

4 Box Mn (e) Strin is ssumed to be mssless unless stted, hence tension in it every where remins the sme nd equl to pplied force. However, if strin hs mss, tension t different points will be different bein mximum ( pplied force) t the end throuh which force is pplied nd minimum t the other end connected to body. M min mx (f) In order to produce tension in strin two equl nd opposite stretchin forces must be pplied. he tension thus produced is equl in mnitude to either pplied force (i.e. ) nd is directed inwrds opposite to. Here it must be noted tht strin cn never be compressed like sprin. () If strin is cut so tht element b is replced by strin scle (the rest of the strin bein undisturbed), the scle reds the tension. b c hree smll elements of strin,, b, c c (h) Every strin cn ber mximum tension, i.e. if the tension in strin is continuously incresed it will brek if the tension is incresed beyond certin limit. he mximum tension which strin cn ber without brekin is clled brekin strenth. It is finite for strin nd depends on its mteril nd dimension. Exmple 5 : A uniform rope of lenth L is pulled by constnt force. W h t i s t h e t e n s i o n i n t h e r o p e t d i s t n c e l from the end where it is pplied? Sol. Let be tension in the rope t point P, then ccelertion of rope, M A P B Eqution of motion of prt PB is (ml) P B M l (ml) ( l) 1 L M L Exmple 6 : he system shown in fiure re in equilibrium. If the sprin blnce is clibrted in newtons, wht does it record in ech cse? ( 10 m/s ) Sol. 10 k (A) one weiht cts s support nother cts s weiht so tension k 10 k 10 k (B) k 30º (C) sin30º ½ 50 MOIO O BODIES COECED BY SIGS wo bodies : Let us consider the cse of two bodies of msses nd m connected by thred nd plced on smooth horizontl surfce s shown in fiure. A force is pplied on the body of mss m in forwrd direction s shown. Our im is to consider the ccelertion of the system nd the tension in the thred. he force ctin seprtely on two bodies re lso shown in fiure : rom fiure SMA SUDY MAEIAL : PHYSICS 4 EWO'S LAWS O MOIO

5 m 1 m m 3 3 m ( + m )...(i)...(ii) 1 m 1 m m nd m1 m1 + m m 1 + m hree bodies : In cse of three bodies, the sitution is shown in fiure Accelertion, m + m + m 1 3 m 1 1 m m 3 Sol. (i) Accelertion of the system 10 m + m + m m/s 1 3 (ii) ( + m ) (5 + 10) 4 60 AME O EEECE (i) Inertil frmes of reference : A reference frme which is esier t rest or in uniform motion lon the striht line. A non-ccelertin frme of reference is clled n inertil frme of reference. (ii) on-inertil frme of reference : A ccelertin frme of reference is clled non-inertil frme of reference. ewton s lw of motion re not directionl pplicble in such frmes, before ppliction we must use pseudo force. ote : A rottin frme of references is non-inertil frme of reference, becuse it is lso n ccelertion one due to its centripetl ccelertion. PSEUDO OCE he force on body due to ccelertion of non-inertil frme is clled fictitious or pprent or pseudo force nd is iven by m0 where 0 is ccelertion of non-inertil frme with respect to n inertil frme nd m is mss of the prticle or body. m1 1 m1 m + m + m 1 3 O O' m 1 m 1 or block of mss m 3, m 3 1 m m 3 m 3 m m + m + m 1 3 (m1 + m ) m + m + m 1 3 m 3 Exmple 7 : hree blocks re connected by strin s shown in fiure, nd re pulled by force If 5 k, m 10 k nd m 3 15 k. Clculte the ccelertion of the system nd 1 nd. he direction of pseudo force must be opposite to the direction of ccelertion of the non-inertil frme. When we drw the free body dirm of mss, with respect to n inertil frme of reference we pply only the rel forces (forces which re ctully ctin on the mss). But when the free body dirm is drwn from non-inertil frme of reference pseudo force (in ddition to ll rel forces) hs to be pplied to mke the eqution m to be vlid in this frme lso. SMA SUDY MAEIAL : PHYSICS 5 EWO'S LAWS O MOIO

6 Exmple 8 : A pendulum of mss m is suspended from the ceilin of trin movin with n ccelertion s shown in fiure. ind the nle θ in equilibrium position. Cse (b) : If the lift is ccelerted (i.e., constnt upwrd) O' ' Sol. m.b.d. of bob m θ m cos θ m sin θ W M( + ) hen net forces ctin on the mn re (i) weiht W M downwrd (ii) fictitious force 0 M downwrd. So pprent weiht, W' W + 0 M + M M ( + ) Cse (c) : If the lift is ccelerted downwrd with ccelertion < : on-inertil frme of reference (rin).b.d. of bob w.r.t. trin (rel forces + pseudo force) : with respect to trin, bob is in equilibrium Σ y 0 cos θ m nd Σ x 0 sin θ m tn θ θ tn 1 MOIO I A LI he weiht of body is simply the force exerted by erth on the body. If body is on n ccelerted pltform, the body experiences fictitious force, so the weiht of the body ppers chned nd this new weiht is clled pprent weiht. Let mn of weiht W M be stndin in lift. Cse () : If the lift movin with constnt velocity v upwrds or downwrds. W M( ) < he fictitious force 0 M cts upwrd while weiht of mn W M lwys cts downwrd, therefore so pprent weiht, W ' W + 0 M M M ( ) Specil cse : If then W '0 condition of weihtlessness. hus, in freely fllin lift the mn will experience weihtlessness. Cse (d) : If lift ccelerted downwrd with ccelertion > : W M ( ) 0 > W M In this cse there is no ccelerted motion hence no pseudo force experienced by observer O' in side the lift. So pprent weiht W' Actul weiht W hen s in Cse C Apprent weiht W ' M ( ) is netive. i.e., the mn will be ccelerted upwrd nd will sty t the ceilin of the lift. SMA SUDY MAEIAL : PHYSICS 6 EWO'S LAWS O MOIO

7 Exmple 9 : A sprin weihin mchine inside sttionry lift reds 50k when mn stnds on it. Wht would hppen to the scle redin if the lift is movin upwrd with (i) constnt velocity, nd (ii) constnt ccelertion? Sol. (ii) In the cse of constnt velocity of lift, there is no fictitious force, therefore the pprent weiht ctul weiht. Hence the redin of mchine is 50 k wt. (ii) In this cse the ccelertion is upwrd, the fictitious force m cts downwrd, therefore pprent weiht is more thn ctul weiht i.e. W' W + m ( + ) Hence scle shows redin m ( + ) k. wt. Exmple 10 : wo objects of equl mss rest on the opposite pns of n rm blnce. Does the scle remin blnced when it is ccelerted up or down in lift? Sol. Yes, since both mss experience equl fictitious forces in mnitude s well s direction. PULLEY * Idel pulley is considered weihtless nd frictionless. * Idel strin is mssless nd inextensible. * he pulley my chne the direction of force in the strin but not the tension. Some cses of pulley Cse I : m m ension in the strin m Accelertion zero ection t the suspension of the pulley. m Accelertion net pullin force totl mss to be pulled ension Product of msses Sum of two msses Cse II : > m ow for mss, for mss m m m By (i) nd (ii)... (i)... (ii) m 1 m A A m B m B m1 m m1 + m (m1m ) nd (m1 + m ) ection t the suspension of pulley 4m1m ( + m ) Cse III : or mss : or mss m : m m Accelertion, m (m1 + m ) 1 nd m m ( + m ) Cse IV : ( > m ) ble 1 M 1 ble m 1 m m 1 M By (i), (ii) nd (iii)...(i)...(ii)...(iii) m m (m1 m ) (m1 + m + M) Cse V : Mss suspended over pulley from nother on n inclined plne. or mss :...(i) msin m m m cos m 1 SMA SUDY MAEIAL : PHYSICS 7 EWO'S LAWS O MOIO

8 or mss m : m sin θ m Accelertion,...(ii) (m1 m sin θ) m1m (1 + sin θ) (m1 + m ) ; (m1 + m ) Cse VI : Msses nd m re connected by strin pssin over pulley ( > m ) 1 1 m sin m cos 1 m 1 m cos m m (m1sin α msin β) Accelertion, (m1 + m ) m sin Cse (VIII) : rom cse (III) m1m ension (m1 + m ) If x is the extension in the sprin then kx m1m x k k(m1 + m ) YPES O ICIO Sttic friction (o reltive motion between objects) ICIO riction m 1 Dynmic friction (here is reltive motion between objects) m m m1m (sin α + sin β) ension, (m1 + m ) Cse VII : or mss : 1 or mss m : m + 1 m or mss m 3 : m 3 m 3...(i)...(ii)...(iii) Slidin friction (Kinetic friction) ollin friction SAIC ICIO * It is the frictionl force which is effective before motion strts between two plnes in contct with ech other. * It s nture is self djustin. * umericl vlue of sttic friction is equl to externl force which cretes the tendency of motion of body. * Mximum vlue of sttic friction is clled limitin friction. 1 1 A m B m m 3 m 3 (m + m3 ) Accelertion, (m1 + m + m 3) We cn clculte tensions 1 nd from bove equtions. LAWS O LIMIIG ICIO * he mnitude of the force of limitin friction (f L ) between ny two bodies in contct is directly proportionl to the norml rection () between them f L * he direction of the force of limitin friction is lwys opposite to the direction in which one body is on the vere of movin over the other. * he force of limitin friction is independent of the pprent contct re, so lon s norml rection between the two bodies in contct remins the sme. * Limitin friction between ny two bodies in contct depends on the nture of mteril of the surfces in contct nd their rouhness nd smoothness. * Its vlue is more thn the other types of frictionl force. DYAMIC ICIO If the body is in motion, the friction opposin its motion is clled dynmic friction. his is lwys slihtly less thn the limitin friction. SMA SUDY MAEIAL : PHYSICS 8 EWO'S LAWS O MOIO

9 COEICIE O ICIO he frictionl coefficient is dimensionless sclr vlue which describes s the rtio of the force of friction between two bodies nd the norml force pressin them toether. Coefficient of sttic friction µ s f k Coefficient of slidin (kinetic) friction µ k he vlues of µ s nd µ k depend on the nture of both the surfces in contct. ote : * riction lwys opposes the tendency of reltive motion. * he force of sttic friction exctly blnces the pplied force durin the sttionry stte of the body therefore it is known s self djustin. * µ s nd µ k cn exceed unity, lthouh commonly they re less thn one. * Sttic friction is self-djustin force, the kinetic friction is not self djustin force. * he frictionl force is contct force prllel to the surfces in contct nd directed so s to oppose the reltive motion or ttempted reltive motion of the surfces. * When two hihly polished surfces re pressed hrd, then sitution similr to weldin occurs. It is clled cold weldin. * When two copper pltes re hihly polished nd plced in contct with ech other, then insted of decresin, the force of friction increses. his rises due to the fct tht for two hihly polished surfces in contct, the number of molecules comin in contct increses nd s result the cohesive/ dhesive forces increses. his in turn, increses the force of friction. ote : Let f is the force nd is the norml rection, then the net force pplied by the surfce on the object is surfce + f Its minimum vlue (when f 0) is M nd mximum vlue (when f µ) is M 1+ µ Grph between pplied force nd force of friction : If we slowly increse the force with which we re pullin the box, rph shows tht the friction force increses with our force upto certin criticl vlue, f L, the box suddenly beins to move, nd s soon s it strts movin, smller force is required to mintin its motion s in motion friction is reduced. he friction vlue from 0 to f L is known s sttic friction, which blnces the externl force on the body nd prevent it from slidin. he vlue f L is the mximum limit up to which the sttic friction cts is known s limitin friction, fter which body strts slidin nd friction reduces to kinetic friction. f L Y orce of friction O Sttic friction A B Limitin friction Applied force C Kinetic friction Exmple 11 : A block of mss 1 k is t rest on rouh horizontl surfce hvin coefficient of sttic friction 0. nd kinetic friction 0.15, find the frictionl forces if horizontl force, () I (b).5, is pplied on the block m 3 Sol. Mximum force of friction or limitin friction f L () or ext 1, ext < f L So, body is in rest mens sttic friction is present nd hence f s ext 1 (b) or ext.5 so ext > f L ow body is in movin condition rictionl force f L k µ k µ k m Exmple 1 : Lenth of chin is L nd coefficient of sttic friction is µ. Clculte the mximum lenth of the chin which cn be hun from the tble without slidin. Sol. Let y be the mximum lenth of the chin cn be hold outside the tble without slidin. f (L y) W' Lenth of chin on the tble (L y) Weiht of prt of the chin on tble W ' M (L y) L Weiht of hnin prt of the chin y X W M L y SMA SUDY MAEIAL : PHYSICS 9 EWO'S LAWS O MOIO

10 or equilibrium : Limitin force of friction weiht of hnin prt of the chin µ W µw ' W µ M L (L y) M L y µ L µl µy y y 1+ µ AGLE O ICIO he nle of friction is the nle which the resultnt of limitin friction f L nd norml rection mkes with the norml rection. It is represented by λ. S + S tn L µ λ µ or smooth surfce λ 0 W m AGLE O EPOSE (θ) If body is plced on n inclined plne nd if its nle of inclintion is rdully incresed, then t some nle of inclintion θ the body will just on the point to slide down. he nle is clled nle of repose (θ). m s in m S m cos L m sinθ nd m cosθ L So, tn θ or µ tnθ eltion between nle of friction (λ) nd nle of repose (θ) : We know tht tn λ µ ndµ tn θ hence tn λ tn θ θ λ hus, nle of repose nle of friction ACCELEAIO O A BLOCK O A OUGH ICLIE Cse 1: When plne is inclined to the horizontl t n nle θ, which is reter thn the nle of repose, the mss m plced on the inclined plne slides down with n ccelertion. f µ µ mcosθ f mcos m m msin rom BD of block m sinθ f m m sinθ µ m cosθ m sinθ µ cosθ here < Cse : When plne is inclined to the horizontl t n nle θ, which is less thn the nle of repose, then the minimum force required to move the body up the inclined plne is mcos m m f msin m sinθ + f m sinθ + µm cosθ where f µ µ mcosθ nd its upwrds ccelertion et force (sin θ + µ cos θ) n ote : (i) Pedlin: In the cyclin, rer wheel move by the force communicted to it by pedlin, while front wheel moves by itself, therefore, like in wlkin force of friction on rer wheel is in forwrd direction nd cts s supportin force. As front wheel moves by itself, force of friction on front wheel is in the bckwrd direction (nture opposin force). (ii) on-pedlin : When pedlin is stopped, both the wheels moves by themselves so the force of friction on both the wheels is in bckwrds direction. f 1 f f 1 f iure : Pedlin on-pedlin SMA SUDY MAEIAL : PHYSICS 10 EWO'S LAWS O MOIO

11 ADDIIOAL EXAMPLES Exmple 1 : A cricket bll of mss 150 is movin with velocity of 1m/s nd is hit by bt so tht the bll is turned bck with velocity of 0m/s. If the durtion of contct between the bll nd bt is 0.01s, find their impulse nd the vere force exerted on the bll by the bt. p p f p i m (v u) [0 ( 1)] So by time vered definition of force in cse of impulse v I p t t 0.01 Exmple : A bird with mss m perches t the middle of stretched strin. Show tht the tension in the strin is iven by Assume tht ech hlf of the strin is striht. m sin θ. Sol. Initil position of wire AOB. inl position of wire ACB. Let θ be the nle mde by wire with horizontl, which is very smll. A cos O sin C cos w m esolvin tension of strin in horizontl nd verticl directions, we note tht the horizontl components cncel while verticl components dd nd blnce the weiht. or equilibrium sin θ W m W sin θ B Exmple 3 : A body of mss M is kept on rouh horizontl surfce (friction coefficient µ). A person is tryin to pull the body by pplyin horizontl force, but the body is not movin. Wht is the force by the surfce on A. Sol. Let f is the force of friction nd is the norml rection, then the net force by the surfce on the body is + f Let the pplied force is ' (vryin), pplied horizontlly then f µ s (djustble with f ' ). ow if ' is zero, f 0 nd min M nd when ' is incresed to mximum vlue permissible for no motion f µ s, ivin + µ M 1+ µ therefore we cn mx s s M M 1 + µ s Exmple 4 : A motor cr hs width 1.1 m between wheels. Its centre of rvity is 0.6 m bove the round nd the coefficient of friction between the wheels nd the rod is 0.8. Wht is the mximum possible speed, if the centre of rvity inscribes circle of rdius 15 m? (od surfce is horizontl) (A) 7.64 m/s (B) 6.8 m/s (C) m/s (D) 11.3 m/s Sol. (C). v µ r m/s Exmple 5 : A child weihin 5 k slides down rope hnin from the brnch of tll tree. If the force of friction ctin inst him is, wht is the ccelertion of the child (ke 9.8 m/s ) (A).5 m/s (B) 8 m/s (C) 5 m/s (D) 9.7 m/s Sol. (D).et downwrd force Weiht riction m m/s 5 SMA SUDY MAEIAL : PHYSICS 11 EWO'S LAWS O MOIO

12 Q.1 ewton s first lw of motion describes the followin (A) Enery (B) Work (C) Inerti (D) Moment of inerti Q. A prticle is movin with constnt speed lon striht line pth. A force is not required to (A) Increse its speed (B) Decrese the momentum (C) Chne the direction (D) Keep it movin with uniform velocity Q.3 A body of mss k is hun on sprin blnce mounted verticlly in lift. If the lift descends with n ccelertion equl to the ccelertion due to rvity, the redin on the sprin blnce will be (A) k (B) (4 ) k (C) ( ) k (D) Zero Q.4 If the tension in the cble of 1000 k elevtor is 1000 k weiht, the elevtor (A) Is ccelertin upwrds (B) Is ccelertin downwrds (C) My be t rest or ccelertin (D) My be t rest or in uniform motion Q.5 An elevtor weihin 6000 k is pulled upwrd by cble with n ccelertion of 5m/s. kin to be 10m/s, then the tension in the cble is (A) 6000 (B) 9000 (C) (D) Q.6 A body is imprted motion from rest to move in striht line. If it is then obstructed by n opposite force, then (A) he body my necessrily chne direction (B) he body is sure to slow down (C) he body will necessrily continue to move in the sme direction t the sme speed (D) one of these Q.7 A body of mss k is movin with velocity 8 m/s on smooth surfce. If it is to be brouht to rest in 4 seconds, then the force to be pplied is (A) 8 (B) 4 (C) (D) 1 Q.8 A 30 m bullet initilly trvellin t 10 m/s penetrtes 1cm into wooden block. he vere resistnce exerted by the wooden block is (A) 850 (B) 00 (C) 000 (D) 1800 Q.9 If rope of lift breks suddenly, the tension exerted by the surfce of lift ( ccelertion of lift) (A) m (B) m ( + ) (C) m ( ) (D) 0 Q.10 A monkey of mss 0k is holdin verticl rope. he rope will not brek when mss of 5 k is suspended from it but will brek if the mss exceeds 5 k. Wht is the mximum ccelertion with which the monkey cn climb up lon the rope ( 10 m/s ) QUESIO BAK EXECISE - 1 (A) 10 m/s (B) 5 m/s (C).5 m/s (D) 5 m/s Q.11 he liner momentum p of body movin in one dimension vries with time ccordin to the eqution p + bt where nd b re positive constnts. he net force ctin on the body is (A) A constnt (B) Proportionl to t (C) Inversely proportionl to t (D) Proportionl to t Q.1 A force of 100 dynes cts on mss of 5 rm for 10 sec. he velocity produced is (A) 000 cm/sec (B) 00 cm/sec (C) 0 cm/sec (D) cm/sec Q.13 A body of mss m collides inst wll with velocity v nd rebounds with the sme speed. Its chne of momentum is (A) mv (B) mv (C) mv (D) Zero Q.14 When we jump out of bot stndin in wter it moves (A) orwrd (B) Bckwrd (C) Sidewys (D) one of the bove Q.15 wo forces of mnitude hve resultnt of the sme mnitude. he nle between the two forces is (A) 45 (B) 10 (C) 150 (D) 60 Q.16 If two forces of 5 ech re ctin lon X nd Y xes, then the mnitude nd direction of resultnt is (A) 5, π / 3 (B) 5, π / 4 (C) 5, π / 3 (D) 5, π / 4 Q.17 wo bodies of mss 3 k nd 4 k re suspended t the ends of mssless strin pssin over frictionless pulley. he ccelertion of the system is ( 9.8 m/s ) (A) 4.9 m/s (B).45 m/s (C) 1.4 m/s (D) 9.5 m/s Q.18 he mss of body mesured by physicl blnce in lift t rest is found to be m. If the lift is oin up with n ccelertion, its mss will be mesured s (A) (B) + (C) m (D) Zero Q.19 A cr is movin with uniform velocity on rouh horizontl rod. herefore, ccordin to ewton s first lw of motion (A) o force is bein pplied by its enine (B) A force is surely bein pplied by its enine (C) An ccelertion is bein produced in the cr (D) he kinetic enery of the cr is incresin SMA SUDY MAEIAL : PHYSICS 1 EWO'S LAWS O MOIO

13 Q.0 A mn of weiht m is movin up in rocket with ccelertion 4. he pprent weiht of the mn in the rocket is (A) Zero (B) 4 m (C) 5 m (D) m Q.1 A plyer kicks footbll of mss 0.5 k nd the footbll beins to move with velocity of 10 m/s. If the contct between the le nd the footbll lsts for 1/50 sec, then the force cted on the footbll should be (A) 500 (B) 150 (C) 50 (D) 65 Q. If the norml force is doubled, the coefficient of friction is (A)ot chned (B) Hlved (C) Doubled (D) ripled Q.3 A stone weihin 1 k nd slidin on ice with velocity of m/s is stopped by friction in 10 sec. he force of friction (ssumin it to be constnt) will be (A) 0 (B) 0. (C) 0. (D) 0 Q.4 A lift is movin downwrds with n ccelertion equl to ccelertion due to rvity. A body of mss M kept on the floor of the lift is pulled horizontlly. If the coefficient of friction is µ, then the frictionl resistnce offered by the body is (A) M (B) µm (C) µm (D) Zero Q.5 A body of mss k is movin on the round comes to rest fter some time. he coefficient of kinetic friction between the body nd the round is 0.. he retrdtion in the body is (A) 9.8 m/s (B) 4.73 m/s (C).16 m/s (D) 1.96 m/s Q.6 A cyclist moves in circulr trck of rdius 100 m. If the coefficient of friction is 0., then the mximum velocity with which the cyclist cn tke the turn with lenin inwrds is (A) 9.8 m/s (B) 1.4 m /s (C) 140 m/s (D) 14 m/s Q.7 A block of mss 5 k lies on rouh horizontl tble. A force of 19.6 is enouh to keep the body slidin t uniform velocity. he coefficient of slidin friction is (A) 0.5 (B) 0. (C) 0.4 (D) 0.8 Q.8 A boy stndin on weihin mchine observes his weiht s 00. When he suddenly jumpes upwrds, his friend notices tht the redin incresed to 400. he ccelertion by which the boy jumped will be- (A) 9.8 m/s (B) 9.4 m/s (C) 4.9 m/s (D) 14.7 m/s be - (in m/s ) (3i ˆ + j) ˆ (B) 1i ˆ + 18j ˆ ( A ) (C) 1 (i ˆ + ˆj) (D) i ˆ + 3j ˆ 3 Q.31 A cr of 1000 k movin with velocity of 18 km/hr is stopped by the brke force of he distnce covered by it before comin to rest is - (A) 1 m (B) 16 m (C) 1.5 m (D) 144 m Q.3 A mn fires the bullets of mss m ech with the velocity v with the help of mchine un, if he fires n bullets every sec, the rection force per second on the mn will be - (A) m v n (B) m n v (C) mv n (D) vn m Q.33 A body of mss 15 k movin with velocity of 10 m/s is to be stopped by resistive force in 15 sec, the force will be - (A) 10 (B) 5 (C) 100 (D) 50 Q.34 A force of is pplied on prticle for sec, the chne in momentum will be - (A) s (B) 4 s (C) 6 s (D) 3 s Q.35 A cricket bll of mss 150 is movin with velocity of 1m/sec nd is hit by bt so tht the bll is turned bck with velocity of 0 m/sec, the force on the bll cts for 0.01 sec, the vere force exerted by the bt on the bll- (A) 48 (B) 40 (C) 480 (D) 400 Q.36 A body of mss 0 k movin with velocity of 3 m/s, rebounds on wll with sme velocity. he impulse on the body is - (A) 60 s (B) 10 s (C) 30 s (D) 180 s Q.37 A mss of 10 k is hun to sprin blnce in lift. If the lift is movin with n ccelertion /3 in upwrd & downwrd directions. Choose the correct options relted to the redin of the sprin blnce. (1) 13.3 k () 6.67 k (3) 3.6 k (4) 0 (A) 1, nd 3 re correct (B) 1 nd re correct (C) nd 4 re correct (D) 1 nd 3 re correct Q.38 Choose the correct options (1) A reference frme in which ewton s first lw is vlid is Q.9 A force of (6 î + 8 ĵ ) cted on body of mss 10 k. he clled n inertil reference frme. () rme movin t constnt velocity reltive to known displcement fter 10 sec, if it strts from rest, will be - inertil frme is lso n inertil frme. (A) 50 m lon tn 1 4/3 with x xis (3) Idely, no inertil frme exists in the universe for (B) 70 m lon tn 1 3/4 with x xis prcticl purpose, frme of reference my be considered (C) 10 m lon tn 1 4/3 with x xis s Inertil if its ccelertion is neliible with respect to (D) one the ccelertion of the object to be observed. Q.30 A body whose mss 6 k is cted upon by two forces (4) o mesure the ccelertion of fllin pple, erth (8i ˆ + 10ˆj) nd (4i ˆ + 8j) ˆ. he ccelertion produced will cnnot be considered s n inertil frme. SMA SUDY MAEIAL : PHYSICS 13 EWO'S LAWS O MOIO

14 (A) 1, nd 3 re correct (B) 1 nd re correct (C) nd 4 re correct (D) 1 nd 3 re correct Q.39 A block of mss M is pulled lon horizontl frictionless surfce by rope of mss m. If force P is pplied t the free end of the rope. he force exerted by the rope on the block will be - (A) P (B) Pm M + m MP mp (C) (D) M + m M + m Q.40 A body of mss 50 k is pulled by rope of lenth 8 m on surfce by force of 108 pplied t the other end. he force tht is ctin on 50 k mss, if the liner density of rope is 0.5 k/m will be - (A) 108 (B) 100 (C) 116 (D) 9 SMA SUDY MAEIAL : PHYSICS 14 EWO'S LAWS O MOIO

15 EXECISE - Q.1 A disc of mss 10 m is kept horizontlly in ir by firin bullets of mss 5 ech t the rte of 10/s. If the bullets rebound with sme speed. he velocity with which the bullets re fired is - (A) 49 cm/s (B) 98 cm/s (C) 147 cm/s (D) 196 cm/s Q. A fire mn hs to crry n injured person of mss 40 k from the top of buildin with the help of the rope which cn withstnd lod of 100 k. he ccelertion of the firemn if his mss is 80 k, will be- (A) 8.17 m/s (B) 9.8 m/s (C) 1.63 m/s (D) m/s Q.3 A body of 0.0 k flls from heiht of 5 metre into pile of snd. he body penetrtes the snd distnce of 5 cm before stopin. Wht force hs the snd exerted on the body? (A) 1.96 (B) 19.6 (C) (D) Q.4 he mnitude of the force (in ewtons) ctin on body vries with time t (in microseconds) s shown in fi. AB, BC, nd CD re striht line sements. he mnitude of the totl impulse of the force on the body from t 4 µs to t 16 µs is... -s. orce () A B C E D ime(µs) (A) s (B) s (C) s (D) 5 10.s Q.5 A cricket bll of mss 50 m movin with velocity of 4 m/ s is hit by bt so tht it cquires velocity of 8 m/s in the opposite direction. he force ctin on the bll, if the contct time is 1/100 of second, will be - (A) 1300 in the finl direction of bll (B) 13 in the initil direction of bll (C) 130 in the finl direction of bll (D) 1.3 in the initil direction of bll Q.6 A block of mss k is plced on the floor. he coefficient of sttic friction is 0.4.A force of.5 is pplied on the block, s shown. Clculte the force of friction between the block nd the floor. ( 9.8 ms ) (A).5 (B) 5 (C) 7.84 (D) zero Q.7 wo crs of unequl msses use similr tyres. If they re movin t the sme initil speed, the minimum stoppin distnce - (A) is smller for the hevier cr (B) is smller for the lihter cr (C) is sme for both crs (D) depends on the volume of the cr Q.8 Mrk the correct sttements bout the friction between two bodies - () sttic friction is lwys reter thn the kinetic friction (b) coefficient of sttic friction is lwys reter thn the coefficient of kinetic friction (c) limitin friction is lwys reter thn the kinetic friction (d) limitin friction is never less thn sttic friction (A) b, c, d (B), b, c (C), c, d (D), b, d Q.9 A block is plced on rouh floor nd horizontl force is pplied on it. he force of friction f by the floor on the block is mesured for different vlues of nd rph is plotted between them () he rph is striht line of slope 45 (b) he rph is striht line prllel to the xis (c) he rph is striht line of slope 45º for smll nd striht line prllel to the -xis for lre. (d) here is smll kink on the rph (A) c, d (B), d (C), b (D), c Q.10 he contct force exerted by body A on nother body B is equl to the norml force between the bodies. We conclude tht - () the surfces must be smooth (b) force of friction between two bodies my be equl to zero (c) mnitude of norml rection is equl to tht of friction (d) bodies my be rouh (A) b, d (B), b (C) c, d (D), d Q.11 It is esier to pull body thn to push, becuse - (A) the coefficient of friction is more in pushin thn tht in pullin (B) the friction force is more in pushin thn tht in pullin (C) the body does not move forwrd when pushed (D) one of these Q1 A block of metl is lyin on the floor of bus. he mximum ccelertion which cn be iven to the bus so tht the block my remin t rest, will be - (A) µ (B) µ/ (C) µ (D) µ Q.13 A 600 k rocket is set for verticl firin. If the exhust speed is 1000 m/s. hen clculte the mss of s ejected per second to supply the thrust needed to overcome the weiht of rocket. (A) 5.88 k/s (B) 4.88 k/s (C).88 k/s (D) 3.88 k/s Q.14 A force of 50 cts in the direction s shown in fiure. he block of mss 5 k, restin on smooth horizontl surfce. ind out the ccelertion of the block. (A) 3 3 m / s (B) 3 m / s (C) 5 3 m / s (D) one of these SMA SUDY MAEIAL : PHYSICS 15 EWO'S LAWS O MOIO

16 Q.15 wo msses 10 k nd 0 k respectively re connected by mssless sprin s shown in fiure force of 00 cts n the 0 k mss. At the instnt shown in fiure the 10 k mss hs ccelertion of 1 m/s, wht is the ccelertion of 0 k mss. 10 K 0 K 00 m (A) m/s (B) 6 m/s (C) 3 m/s (D) 4 m/s Q.16 Choose the correct options (1) Inerti mss () 1 ewton 10 5 dyne (3) hrust on rocket M v M t (4) Apprent weiht of body in the ccelerted lift is W m ( + ). (A) 1, nd 3 re correct (B) 1 nd re correct (C) nd 4 re correct (D) 1 nd 3 re correct Q.17 Choose the correct options (1) or equilibrium of body under the ction of concurrent forces n 0 () If the downwrd ccelertion of the lift is, then the body will enjoy weihtlessness. (3) If the downwrd ccelertion of the body is >, then the body will rise up to the ceilin of lift (4) If the downwrd ccelertion of the lift is >, then the body will enjoy weihtlessness. (A) 1, nd 3 re correct (B) 1 nd re correct (C) nd 4 re correct (D) 1 nd 3 re correct Q.18 A rope of lenth 15 m nd liner density k/m is lyin lenth wise on horizontl smooth tble. It is pulled by force of 5. he tension in the rope t the point 7 m wy from the point of ppliction, will be - (A) (B) (C) (D) one of these Q.19 wo blocks of mss m 1 k nd M k re in contct on frictionless tble. A horizontl force ( 3) is pplied to m. he force of contct between the blocks, will be- (A) (B) 1 (C) 4 (D) 5 Psse (Q.0-Q.) Pseudo orce is iminry force which is reconised only by non-inertil observer to explin the physicl sitution ccordin to ewton s Lws. Mnitude of pseudo force p is equl to the product of the mss m of the object nd the ccelertion of the frme of reference. he direction of the force is opposite to the direction of ccelertion. p m Q.0 A sprin weihin mchine inside sttionry lifts reds 50 k when mn stnd on it. Wht would hppen to the scle redin if the lift is movin upwrd with (i) constnt velocity (ii) constnt ccelertioin - (A) 50 k wt, (B) 50 k wt, (C) 50 k wt, SMA SUDY MAEIAL : PHYSICS 16 EWO'S LAWS O MOIO k wt k wt 50 k wt (D) 50 k wt, 50 k wt Q.1 A 5 k lift is supported by cble. he ccelertion of the lift when the tension in the cble is 175, will be - (A).8 m/s (B) 16.8 m/s (C) 9.8 m/s (D) 14 m/s Q. A body is suspended by strin from the cellin of n elevtor. It is observed tht the tension in the strin is doubled when the elevtor is ccelerted. he ccelertion will be - (A) 4.9 m/s (B) 9.8 m/s (C) 19.6 m/s (D).45 m/s Directions : Assertion-eson type questions. Ech questions contin SAEME-1 (Assertion) nd SAEME- (eson). Ech question hs 4 choices (A), (B), (C) nd (D) out of which OLY OE is correct. (A) Sttement- 1 is rue, Sttement- is rue, Sttement- is correct explntion for Sttement -1 (B) Sttement -1 is rue, Sttement - is rue ; Sttement- is O correct explntion for Sttement - 1 (C) Sttement - 1 is rue, Sttement- is lse (D) Sttement -1 is lse, Sttement - is rue Q.3 Sttement 1 : A mn stndin in lift which is movin upwrd, will feel his weiht to be reter thn when the lift ws t rest. Sttement : If the ccelertion of the lift is '' upwrd, then the mn of mss m shll feel his weiht to be equl to norml rection () exerted by the lift iven by m ( + ) (where is ccelertion due to rvity). Q.4 Sttement 1 : Accordin to the ewton's third lw of motion, the mnitude of the ction nd rection force in n ction rection pir is sme only in n inertil frme of reference. Sttement : ewton's lws of motion re pplicble in every inertil reference frme. Q.5 Sttement 1 : A body is lyin t rest on rouh horizontl surfce. A person ccelertin with ccelertion ˆ i (where is positive constnt nd î is unit vector in horizontl direction) observes the body. With respect to him, the block experience kinetic friction. Sttement : Whenever there is reltive motion between the contct surfces then kinetic friction cts.

17 PEVIOUS YEA AIEEE QUESIOS SECIO-1 Q.1 hree point msses A, B nd C re 66 rm ech re connected s shown. he ccelertion of system is 5 m/s. ension between B nd C is pproximtely-[aieee-00] (A) 0.33 ewton (B) 4 ewton (C) 5 ewton (D) 6 ewton Q. A person in n eroplne which is comin, down t ccelertion releses coin. After relese, the cclertion of coin with respect to observer on round nd in eroplne both will be respectively- [AIEEE-00] (A) nd ( ) (B) ( ), (C) ( + ), (D), ( + ) Q.3 A liht strin pssin over smooth liht pulley connects two blocks of msses nd m (verticlly). If the ccelertion of the system is /8, then the rtio of the msses is [AIEEE-00] (A) 8 : 1 (B) 9 : 7 (C) 4 : 3 (D) 5 : 3 Q.4 One end of mssless rope, which psses over mssless nd frictionless pulley P is tied to hook C while the other end is free. Mximum tension tht the rope cn ber is 360. With wht vlue of minimum sfe ccelertion (in ms ) cn mn of 60 k slide down the rope? [AIEEE-00] EXECISE - 3 (A) Pm M m (B) P P M P m (C) (D) M + m M + m Q.8 One end of liht sprin blnce hns from the hook of the other liht sprin blnce ttched to roof nd block of mss M k hns from the other end. hen the true sttement bout the scle redin is [AIEEE-003] (A) he scle of the lower one reds M k nd of the upper one zero (B) he redin of the two scles cn be nythin but the sum of the redin will be M k (C) Both the scles red M/ k ech (D) both the scles red M k ech Q.9 hree forces strt ctin simultneously on prticle movin with velocity v. these forces re represented in mnitude nd direction by the three sides of trinle ABC (s shown). he prticle will now move with velocity [AIEEE-003] (A) 16 (B) 6 (C) 4 (D) 8 Q.5 A sprin blnce is ttched to the ceilin of lift. A mn hns his b on the sprin nd the sprin reds 49, when the lift is sttionry. If the lift moves downwrd with n ccelertion of 5 m/s, the redin of the sprin blnce will be [AIEEE-003] (A) 74 (B) 15 (C) 49 (D) 4 Q.6 Let be the force ctin on prticle hvin position vector r, nd be the torque of this force bout the oriin. hen [AIEEE-003] (A) r. 0 nd. 0 (B) r. 0 nd. 0 (C) r. 0 nd. 0 (D) r. 0 nd. 0 Q.7 A block of mss M is pulled lon horizontl frictionless surfce by rope of mss m. If force P is pplied t the free end of the rope, the force exerted by the rope on the block is [AIEEE-003] (A) Greter thn v (B) v in the direction of the lrest force BC (C) v, reminin unchned (D) Less thn v Q.10 A mchine un fires bullet of mss 40 with velocity 100 ms 1. he mn holdin it cn exert mximum force of 144 on the un. How mny bullets cn he fire per second t the most? [AIEEE-004] (A) One (B) our (C) wo (D) hree Q.11 wo msses 5 k nd m 4.8 k tied to strin re hnin over liht fricitionless pulley. Wht is the ccelertion of the msses when left free to move? ( 9.8 m/s ) [AIEEE-004] (A) 0. m/s (B) 9.8 m/s (C) 5 m/s (D) 4.8 m/s Q.1 A prchutist fter bilin out flls 50 m without friction. When prchute opens, it decelertes t m/s. He reches the round with speed of 3 m/s. At wht heiht, did he bil out? [AIEEE-005] (A) 91 m (B) 18 m (C) 93 m (D) 111 m SMA SUDY MAEIAL : PHYSICS 17 EWO'S LAWS O MOIO

18 Q.13 A block is kept on frictionless inclined surfce with nle of inclintion 'α'. he incline is iven n ccelertion '' to keep the block sttionry. hen '' is equl to [AIEEE-005] (A) / tn α (B) cosec α (C) (D) tn α Q.14 A prticle of mss 0.3 k is subjected to force kx with k 15 /m. Wht will be its initil ccelertion if it is relesed from point 0 cm wy from the oriin? [AIEEE-005] (A) 3 m/s (B) 15 m/s (C) 5 m/s (D) 10 m/s Q.15 A plyer cuht cricket bll of mss 150 movin t rte of 0 m/s. If the ctchin process is completed in 0.1 s, the force of the blow exerted by the bll on the hnd of the plyer is equl to [AIEEE 006] (A) 30 (B) 300 (C) 150 (D) 3 SECIO- Q.16 A horizontl force of 10 ewton is necessry to just hold block sttionry inst wll. he coefficient of friction between the block nd the wll is 0.. he weiht of block is [AIEEE-003] Q.17 A mrble block of mss k lyin on ice when iven velocity of 6 m/s is stopped by friction is 10 s. hen the coefficient of friction is [AIEEE-003] (A) 0.03 (B) 0.04 (C) 0.06 (D) 0.0 Q.18 A block rests on rouh indined plne mkin n nle of 30 with the horizontl. he coefficient of sttic friction between the block nd the plne is 0.8. If the frictionl force on the block is 10, the mss of block (in k) is (ke 10 m/s ) [AIEEE-004] (A).0 (B) 4.0 (C) 1.6 (D).5 Q.19 A smooth block is relesed t rest on 45º incline nd then slides distnce 'd'. he time tken to slide is 'n' times s much to slide on rouh incline thn on smooth incline. he coefficient of friction is [AIEEE-005] (A) µ K 1 1 n 1 (B) µ k 1 n 1 1 (C) µ S 1 (D) µ n S 1 n Q.0 he upper hlf of n inclined plne with inclintion φ is perfectly smooth while the lower hlf is rouh. A body strtin from rest t the top will in come to rest t the bottom if the coefficient of friction for the lower hlf is iven by [AIEEE-005] (A) sin φ (B) cos φ (C) tn φ (D) tn φ Q.1 he fiure shows the position time (x t) rph of onedimensionl motion of body of mss 0.4 k. he mnitude of ech impulse is [AIEEE 010] x(m) (A) 50 (C) (B) 100 (D) 0 (A) 0.4 s (C) 1.6 s t(s) (B) 0.8 s (D) 0. s SMA SUDY MAEIAL : PHYSICS 18 EWO'S LAWS O MOIO

19 ASWE KEY EX ECIS E - 1 Q A C D D D D B B D D C D Q A B A B B B C C B C C A Q A B D D D C A A D C B A Q A C C B B A C B EX ECIS E - Q A B C B B A A C A A A B Q A A A C D A A B A A A B Q A D D D EXECISE - 3 Q. o A n s. A A B C D C C D C D A C D D A C C A A C B SMA SUDY MAEIAL : PHYSICS 19 EWO'S LAWS O MOIO