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1 or ore Study Material and Latest Questions related to IIT-JEE visit www. ICTION Introduction If we slide or try to slide a body over a surface, the otion is resisted by a bonding between the body and the surface. This resistance is represented by a single force and is called friction force. The force of friction is parallel to the surface and opposite to the direction of intended otion. Types of riction. Static friction: The opposing force that coes into play when one body tends to ove over the surface of another, but the actual otion has yet not started is called static friction.. If applied force is and the body reains at rest then static friction =.. If a body is at rest and no pulling force is acting on it, force of friction on it is zero. 3. Static friction is a self-adjusting force because it changes itself in accordance with the applied force and is always equal to net external force.. Liiting friction: If the applied force is increased, the force of static friction also increases. If the applied force exceeds a certain (axiu) value, the body starts oving. This axiu value of static friction up to which body does not ove is called liiting friction.. The agnitude of liiting friction between any two bodies in contact is directly proportional to the noral reaction between the. l or l s. Direction of the force of liiting friction is always opposite to the direction in which one body is at the verge of oving over the other 3. Coefficient of static friction : 3. s is called coefficient of static friction and is defined as the ratio of force of liiting friction and noral reaction s Diension : [ M L T ] 3.3 Unit: It has no unit. 3.4 Value of depends on aterial and nature of surfaces in contact that eans whether dry or wet ; rough or sooth polished or non-polished. 3.5 Value of does not depend upon apparent area of contact. g ig. 5. or ore Study Material and Question ank visit www.

2 or ore Study Material and Latest Questions related to IIT-JEE visit www. C. Kinetic or dynaic friction: If the applied force is increased further and sets the body in otion, the friction opposing the otion is called kinetic friction.. Kinetic friction depends upon the noral reaction. k or k k where k is called the coefficient of kinetic friction. Value of k depends upon the nature of surface in contact. 3. Kinetic friction is always lesser than liiting friction k l k s i.e. coefficient of kinetic friction is always less than coefficient of static friction. Thus we require ore force to start a otion than to aintain it against friction. This is because once the otion starts actually; inertia of rest has been overcoe. lso when otion has actually started, irregularities of one surface have little tie to get locked again into the irregularities of the other surface. 4. Kinetic friction does not depend upon the velocity of the body. 4. Types of kinetic friction 4.. Sliding friction : The opposing force that coes into play when one body is actually sliding over the surface of the other body is called sliding friction. e.g. flat block is oving over a horizontal table. 4.. olling friction : When objects such as a wheel (disc or ring), sphere or a cylinder rolls over a surface, the force of friction that coes into play is called rolling friction. olling friction is directly proportional to the noral reaction () and inversely proportional to the radius (r) of the rolling cylinder or wheel. is called coefficient of rolling friction. It would have rolling r r r the diensions of length and would be easured in etre. olling friction is often quite sall as copared to the sliding friction. That is why heavy loads are transported by placing the on carts with wheels. In rolling the surfaces at contact do not rub each other. The velocity of point of contact with respect to the surface reains zero all the ties although the centre of the wheel oves forward. GH ETWEEN LIED OCE ND OCE O ICTION. art O of the curve represents static friction ( s ). Its value increases linearly with the applied force. t point the static friction is axiu. This represent liiting friction ( l ). orce of friction s l k C O pplied force ig. 5. or ore Study Material and Question ank visit www.

3 or ore Study Material and Latest Questions related to IIT-JEE visit www. 3. eyond, the force of friction is seen to decrease slightly. The portion C of the curve represents the kinetic friction ( k ). 4. s the portion C of the curve is parallel to x-axis therefore kinetic friction does not change with the applied force, it reains constant, whatever be the applied force. riction is a Cause of Motion It is a general isconception that friction always opposes the otion. No doubt friction opposes the otion of a oving body but in any cases it is also the cause of otion. or exaple: a) While oving, a person or vehicle pushes the ground backwards (action) and the rough surface of ground reacts and exerts a forward force due to friction which causes the otion. If there had been no friction there will be slipping and no otion. ction riction b) During cycling, the rear wheel oves by the force counicated to it by pedalling while front wheel oves by itself. So, when pedalling a bicycle, the force exerted by rear wheel on ground akes force of friction act on it in the forward direction (like walking). ront wheel oving by itself experience force of friction in backward direction (like rolling of a ball). [However, if pedalling is stopped both wheels ove by theselves and so experience force of friction in backward direction]. ig. 5.3 While pedalling ig. 5.4 edalling is stoped c) If a body is placed in a vehicle which is accelerating, the force of friction is the cause of otion of the body along with the vehicle (i.e., the body will reain at rest in the accelerating vehicle until a sg ). If there had been no friction between body and vehicle, the body will not ove along with the vehicle. ro these exaples it is clear that without friction otion cannot be started, stopped or transferred fro one body to the other. or ore Study Material and Question ank visit www. 3

4 or ore Study Material and Latest Questions related to IIT-JEE visit www. DVNTGES ND DISDVNTGES O ICTION. dvantages of friction I. Walking is possible due to friction. II. Two body sticks together due to friction. III. rake works on the basis of friction. IV. Writing is not possible without friction. V. The transfer of otion fro one part of a achine to other part through belts is possible by friction.. Disadvantages of friction I. riction always opposes the relative otion between any two bodies in contact. Therefore extra energy has to be spent in over coing friction. This reduces the efficiency of achine. II. riction causes wear and tear of the parts of achinery in III. contact. Thus their lifetie reduces. rictional force results in the production of heat, which causes daage to the achinery. C. Methods of Changing riction We can reduce friction I. y polishing. II. y lubrication. III. y proper selection of aterial. a IV. y strealining the shape of the body. sg V. y using ball bearing. VI. lso we can increase friction by throwing soe sand on slippery ground. In the anufacturing of tyres, synthetic rubber ig. 5.5 is preferred because its coefficient of friction with the road is larger. ngle of riction ngle of friction ay be defined as the angle which the resultant of liiting friction and noral reaction akes with the noral reaction. y definition angle is called the angle of friction tan l ] l tan = s [s we know s ig. 5.6 ig. 5.7 S g ig. 5.8 a or ore Study Material and Question ank visit www. 4

5 or ore Study Material and Latest Questions related to IIT-JEE visit www. or tan ( L) Hence coefficient of static friction is equal to tangent of the angle of friction. esultant orce Exerted by Surface on lock In the above figure resultant force S S S ( g ) ( g ) g when there is no friction ( 0) S will be iniu i.e. S = g Hence the range of S can be given by, g S g ngle of epose ngle of repose is defined as the angle of the inclined plane with horizontal such that a body placed on it is just begins to slide. y definition, is called the angle of repose. g sin In liiting condition g sin and g cos So tan s tan tan [s we know s tan Thus the coefficient of liiting friction is equal to the tangent of angle of repose. s well as i.e. angle of repose = angle of friction. Calculation of equired orce in Different Situation If W = weight of the body, = angle of friction, tan coefficient of friction Then we can calculate required force for different situation in the following anner: () Miniu pulling force at an angle fro the horizontal ] g ig. 5.9 g cos ig. 5.0 y resolving in horizontal and vertical direction (as shown in figure) sin cos W ig. 5. or the condition of equilibriu cos and W sin y substituting these value in or ore Study Material and Question ank visit www. 5

6 or ore Study Material and Latest Questions related to IIT-JEE visit www. cos ( W sin) sin cos ( W sin) cos [s tan ] sin W cos ( ) () Miniu pushing force at an angle fro the horizontal y esolving in horizontal and vertical direction (as shown in the figure) ig. 5. cos sin W ig. 5.3 or the condition of equilibriu cos and W sin y substituting these value in cos ( W sin) sin cos ( W sin) cos sin W cos ( ) [s tan ] (3) Miniu pulling force to ove the body up on an inclined plane ig. 5.4 y esolving in the direction of the plane and perpendicular to the plane (as shown in the figure) + sin cos + W sin W W cos ig. 5.5 or the condition of equilibriu or ore Study Material and Question ank visit www. 6

7 or ore Study Material and Latest Questions related to IIT-JEE visit www. sin W cos W cos sin and W sin cos cos W sin y substituting these values in and solving we get sin( ) W cos ( ) (4) Miniu force to ove a body in downward direction along the surface of inclined plane y esolving in the direction of the plane and perpendicular to the plane (as shown in the figure) or the condition of equilibriu sin W cos W cos sin and cos W sin y substituting these values in and solving we get sin( ) W cos ( ) cos + ig sin W ig. 5.7 W cos (5) Miniu force to avoid sliding of a body down on an inclined plane ig. 5.8 y esolving in the direction of the plane and perpendicular to the plane (as shown in the figure) + sin + cos W sin W cos W ig. 5.9 or ore Study Material and Question ank visit www. 7

8 or ore Study Material and Latest Questions related to IIT-JEE visit www. or the condition of equilibriu sin W cos W cos sin and cos W sin W sin cos y substituting these values in and solving we get sin( ) W cos ( ) (6) Miniu force for otion along horizontal surface and its direction Let the force be applied at an angle with the horizontal. y resolving in horizontal and vertical direction (as shown in figure) or vertical equilibriu sin g g sin and for horizontal otion cos i.e. cos (ii) Substituting value of fro (i) in (ii) cos ( g sin) g cos sin (iii) (i) or the force to be iniu (cos sin) ust be axiu i.e. d [cos sin] 0 d sin cos 0 ig sin g ig. 5. cos tan or tan ( ) angle of friction ig. 5. i.e. or iniu value of its angle fro the horizontal should be equal to angle of friction s tan so fro the figure, sin or ore Study Material and Question ank visit www. 8

9 or ore Study Material and Latest Questions related to IIT-JEE visit www. and cos y substituting these value in equation (iii) g in g g cceleration of a lock gainst riction () cceleration of a block on horizontal surface When body is oving under application of force, then kinetic friction opposes its otion. a Let a is the net acceleration of the body k ro the figure a k k a () cceleration of a block sliding down over a rough inclined plane When angle of inclined plane is ore than angle of repose, the body placed on the inclined plane slides down with an acceleration a. ro the figure a g sin a g sin cceleration a g [sin cos ] Note : or frictionless inclined plane 0 a g sin. (3) etardation of a block sliding up over a rough inclined plane When angle of inclined plane is less than angle of repose, then for the upward otion a g sin a g sin g cos a g ig. 5.3 g sin g cos g ig. 5.4 a g sin + g cos g etardation a g[sin cos ] ig. 5.5 Note : or frictionless inclined plane 0 a g sin Work done against friction () Work done over a rough inclined surface If a body of ass is oved up slowly on a rough inclined plane through distance s, then or ore Study Material and Question ank visit www. 9

10 or ore Study Material and Latest Questions related to IIT-JEE visit www. Work done = force distance = a s = g [sin + cos ]s g s[sin cos ] a s () Work done over a horizontal surface In the above expression if we put = 0 then Work done = force distance = s = g s It is clear that work done depends upon g sin + g cos g ig. 5.6 (i) Weight of the body. (ii) Material and nature of surface in contact. (iii) Distance oved. Motion of Two odies one esting on the Other When a body of ass is resting on a body of ass M then two conditions are possible () force is applied to the upper body, () force is applied to the lower body We will discuss above two cases one by one in the following anner : () force is applied to the upper body, then following four situations are possible (i) When there is no friction (a) The body will ove on body with acceleration (/). a / (b) The body will reain at rest a 0 (c) If L is the length of as shown in figure, will fall fro after tie t t L a M L g s ig. 5.7 L ig. 5.8 s s a t and a / (ii) If friction is present between and only and applied force is less than liiting friction ( < l ) or ore Study Material and Question ank visit www. 0

11 or ore Study Material and Latest Questions related to IIT-JEE visit www. ( = pplied force on the upper body, l = liiting friction between and, k = Kinetic friction between and ) (a) The body will not slide on body till i.e. g a a (b) Cobined syste ( + M) will ove together with coon acceleration M (iii) If friction is present between and only and applied force is greater than liiting friction ( > l ) In this condition the two bodies will ove in the sae direction (i.e. of applied force) but with different acceleration. Here force of kinetic friction otion of while cause the otion of. l s kg will oppose the i.e. i.e. k a k a ( kg) a k M a k a M kg a M ree body diagra of a ree k body diagra of Ma Note : s both the bodies are oving in the sae direction. cceleration of body relative to will be a a a M kg ( M) M So, will fall fro after tie t L a ML M g ( M) k (iv) If there is friction between and floor (where l ( M ) g = liiting friction between and floor, k = kinetic friction between and ) will ove only if k l and then k l M a l Ma ig. 5.9 K However if does not ove then static friction will work (not liiting friction) between body and the floor i.e. friction force = applied force (= k ) not l. () force is applied to the lower body, then following four situations are possible (i) When there is no friction K or ore Study Material and Question ank visit www.

12 or ore Study Material and Latest Questions related to IIT-JEE visit www. (a) will ove with acceleration (/M) while will reain at rest (relative to ground) as there is no pulling force on. M a and 0 a (b) s relative to, will ove backwards with acceleration (/M) and so will (c) fall fro it in tie t. M L t L a ML ig (ii) If friction is present between and only and < l (where = seudo force on body and l = liiting friction between body and ) (a) oth the body will ove together with coon acceleration a (b) seudo force on the body, a l s M (c) l s g M and g s ( M) g So both bodies will ove together with acceleration s [ M] g a a M M (iii) If friction is present between and only and > l (where l = s g = liiting friction between body and ) oth the body will ove with different acceleration. Here force of kinetic friction kg will oppose the otion of while will cause the otion of. Note : s both the bodies are oving in the sae direction cceleration of body relative to will be a a a k g( M) M Negative sign iplies that relative to, will ove backwards and will fall it after tie t L a ML g( M) k (iv) If there is friction between and floor and > l : (where l = s (+M)g = liiting friction between body and surface) '' The syste will ove only if l then replacing by l. The entire case (iii) will be valid. However if the syste will not ove and friction between and floor will be while between and is zero. if or ore Study Material and Question ank visit www.

13 or ore Study Material and Latest Questions related to IIT-JEE visit www. Motion of an Insect in the ough owl The insect crawl up the bowl, up to a certain height h only till the coponent of its weight along the bowl is balanced by liiting frictional force. l r O y g cos g g sin h ig. 5.3 Let = ass of the insect, r = radius of the bowl, = coefficient of friction for liiting condition at point g cos...(i) and l g sin...(ii) Dividing (ii) by (i) tan l s l So r y y or y h r y r r, h r Miniu Mass Hung fro the String to Just Start the Motion () When a ass placed on a rough horizontal plane nother ass hung fro the string connected by frictionless pulley, the tension (T) produced in string will try to start the otion of ass. l g T T ig. 5.3 g t liiting condition T l g g g this is the iniu value of to start the otion. Note : In the above condition Coefficient of friction () When a ass placed on a rough inclined plane nother ass hung fro the string connected by frictionless pulley, the tension (T) produced in string will try to start the otion of ass. T T g sin + g cos g or ore Study Material and Question ank visit www. 3

14 or ore Study Material and Latest Questions related to IIT-JEE visit www. in t liiting condition or T g (i) or T g sin T g sin T g sin g cos (ii) ro equation (i) and (ii) [sin cos ] this is the iniu value of to start the otion Note : In the above condition Coefficient of friction tan cos itj ee. ass lying on the table ac ki Maxiu Length of Hung Chain unifor chain of length l is placed on the table in such a anner that its l' part is hanging over the edge of table without sliding. Since the chain have unifor linear density therefore the ratio of ass and ratio of length for any part of the chain will be equal. ass hanging fro the table We know or this case we can rewrite above expression in the following anner length hanging fro the table [s chain have unifor linear density] ( l l ) by cr length lying on the table l l l solving l l ( ) l ig Coefficient of riction etween a ody and Wedge body slides on a sooth wedge of angle and its tie of descent is t. S S Sooth wedge ough wedge ig ig If the sae wedge ade rough then tie taken by it to coe down becoes n ties ore (i.e. nt) The length of path in both the cases are sae. or ore Study Material and Question ank visit www. 4

15 or ore Study Material and Latest Questions related to IIT-JEE visit www. at or sooth wedge, S u t S ( g sin ) t [ su 0 and a g sin ] (i) at or rough wedge, S u t S g (sin cos )( nt) ro equation (i) and (ii) ( g sin = g (sin cos )( nt ) t sin (sin cos ) n tan n ) (ii) [ su 0 and a g (sin cos )] Stopping of lock Due to riction () On horizontal road (i) Distance travelled before coing to rest : block of ass is oving initially with velocity u on a rough surface and due to friction, it coes to rest after covering a distance S. ig etarding force a g ro v u as u S g a a g 0 u g S or S (ii) Tie taken to coe to rest ro equation v u a t 0 u t u g u S g v = 0 g t [s v 0, a g] [s oentu = u] [ sv 0, a g] () On inclined road : When block starts with velocity u its kinetic energy will be converted into potential energy and soe part of it goes against friction and after travelling distance S it coes to rest i.e. v = 0. We know that retardation a g [sin cos ] y substituting the value of v and a in the following equation u S v = 0 ig or ore Study Material and Question ank visit www. 5

16 or ore Study Material and Latest Questions related to IIT-JEE visit www. v u a S 0 u g [sin cos ] S u S g (sin cos ) Stopping of Two locks Due to riction When two asses copressed towards each other and suddenly released then energy acquired by each block will be dissipated against friction and finally block coes to rest i.e., S = E [Where = riction, S = Distance covered by block, E = Initial kinetic energy of the block] S g S S g [Where = oentu of block] [s = g] In the given condition and are sae for both the blocks. S S ; S So, Velocity at the otto of ough Wedge body of ass which is placed at the top of the wedge (of height h) starts oving downward on a rough inclined plane. Loss of energy due to friction = L (Work against friction) E at point KE at point = u = gh y the law of conservation of energy i.e. v gh L v ( gh L) S S ig v L ig u = 0 Sticking of a lock With ccelerated Cart When a cart oves with soe acceleration toward right then a pseudo force (a) acts on block toward left. h or ore Study Material and Question ank visit www. 6

17 or ore Study Material and Latest Questions related to IIT-JEE visit www. This force (a) is action force by a block on cart. a a M CT Now block will reain static w.r.t. cart. If friction force a g [ s a] a a in g g g This is the iniu acceleration of the cart so that block does not fall. and the iniu force to hold the block together ( M a in ) in g in ( M ) Sticking of a erson with the Wall of otor person with a ass stands in contact against the wall of a cylindrical dru (rotor). The coefficient of friction between the wall and the clothing is. If otor starts rotating about its axis, then person thrown away fro the centre due to centrifugal force at a particular speed, the person stuck to the wall even the floor is reoved, because friction force balances its weight in this condition. ro the figure. riction force () = weight of person (g) = g c g C [Here, c = g centrifugal force] r g ig. 5.4 in g g r in ig. 5.4 IMOTNT OINTS orce of friction is non-conservative force. orce of friction always acts in a direction opposite to that of the relative otion between the surfaces. olling friction is uch less than the sliding friction. This knowledge was used by an to invent the wheels. The friction between two surfaces increases (rather than to decrease), when the surfaces are ade highly sooth. The atoic and olecular forces of attraction between the two surfaces at or ore Study Material and Question ank visit www. 7

18 or ore Study Material and Latest Questions related to IIT-JEE visit www. the point of contact give rise to friction between the surfaces. or ore Study Material and Question ank visit www. 8