Synopsis : FRICTION. = μ s R where μ s is called the coefficient of static friction. It depends upon the nature

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1 FRICTION Synopsis : 1. When a body is in otion over another srace or when an object oves throgh a viscos edi like air or water or when a body rolls over another, there is a resistance to the otion becase o the interaction o the object with its srrondings. Sch a resistance orce is called orce o riction.. is a reslt o oleclar interaction. According to odern view, the case o riction is largely de to atoic and oleclar orces between the two sraces at the point o contact. TYPES OF FRICTIONAL FORCE : 3. STATIC FRICTION : The rictional orce, which is eective beore otion starts between two planes in contact with each other, is known as static riction. Note: 1) Static rictional orce is a sel adjsting one. ) The axi rictional orce when the body is ready to start is called liiting rictional orce. 4. DYNAMIC FRICTION: The rictional orce, which is eective when two sraces in contact with each other are in relative otion with respect to each other, is known as dynaic riction. 5. ROLLING FRICTION: The rictional orce, which is eective when a body rolls or rotates on a srace, is known as rolling riction. Fs A B al orce State o rest Static Dynaic State o otion O D C Plling orce 6. Liiting riction (F s ) is independent o the area o contact o the sraces. Rolling riction depends on the area o contact. 7. Liiting riction is directly proportional to the noral reaction between the sraces in contact. R I R F= μ s R λ otion F s R Fs = μ s R where μ s is called the coeicient o static riction. It depends pon the natre o the sraces in contact and their state o roghness. 8. The angle between R and the resltant o R and F (i.e., R and R l ) is called the angle o riction λ. Tan λ = μ 9. Characteristics o static riction: 1

2 a) μ s between two given sraces is independent o the noral orce between the two sraces. b) μ s > 0, it can also be greater than one, bt in ost o the cases it is less than one c) I s is the angle o liiting riction between two sraces tan s = μ s 10. When one body oves over the other, the orce o riction acting between the two sraces is called kinetic riction. 11. The orce o kinetic riction is independent o the area o the sraces in contact and is proportional to the noral reaction F k R. F k = μ k. R Where μ k is coeicient o kinetic riction. 1. When one body oves over another body, the coeicient o riction is less than liiting coeicient o riction and is called the coeicient o kinetic riction. 13. F k is independent o the velocity o sliding provided the velocity is low. 14. When a body rolls over another, the rictional orce developed is called rolling rictional orce and the corresponding coeicient o riction is called coeicient o rolling riction (μ r ). 15. Rolling riction: a) Rolling riction coes into play when a body sch as a wheel rolls on a srace. b) Rolling riction arises ot o the deoration o the two sraces in contact with each other. c) Greater the deoration greater is the rolling rictional orce. d) The rolling rictional orce is inversely proportional to the radis o the rolling body. e) The rolling rictional orce between two given sraces is lesser than kinetic and liiting rictional orces. ) I μ R is the coeicient o rolling riction μ R < μ k < μ s or a given pair o sraces. g) Ball bearings are sed in achinery parts becase rolling riction is least. h) Radial tyres sed in cars redce rolling riction. 16. When lbricants or viscos liqids are introdced between the sraces o two solids in contact, they redce rictional orces becase interoleclar orces in liqids are ch weaker than those in solids. 17. Plling a block or roller a) I the plling orce is sch that F cos< s, ( s is liiting riction) the block will be at rest and the orce o riction between block and the srace is = F cos N F sin F (plling F cos b) The noral orce is N = - F sin c) Force needed to jst slide the body is F= sraces. μs sinφ = cos + μs sin cos( φ) Where φ is the angle o riction between the two

3 d) I the applied orce is greater than the above vale, block slides with acceleration and the orce o riction between the block and the srace is k. e) The ini possible orce aong all directions reqired to jst ove the body is μs sinφ (or) where φ is the angle o riction. The orce st be applied at 1+ μs angle to the horizontal at an angle eqal to angle o riction φ. 18. Pshing a block or Roller: a) I the pshing orce is sch that, Fcos< s, the block will be rest and the orce o riction between the block and the srace is = F cos. N F sin F cos F (pshing b) The noral orce is N = + F sin c) Force needed to jst slid the body is μs μssinφ F= = cos μs sin cos( + φ) where φ is the angle o riction. d) Plling is easier than pshing becase lower rictional orce, in the case o plling need to be overcoe. e) I the angle ade by the pshing orce with the vertical is lesser than or eqal to angle o riction, the block cannot be oved, irrespective o the agnitde o the applied orce. 19. A nior chain o length L lies on a table. I the coeicient o riction is μ, then the axi length o the chain which can overhang ro the edge o the table withot μl sliding down is. μ Block on a rogh ixed horizontal srace a) I we contine to apply a orce F = s, the block slides with an acceleration given by a = (μ s μ k ) g b) Once the block slides, orce o riction on the block is kinetic rictional orce ( k ) c) I the block slides with an acceleration nder the inlence o an external orce F, the acceleration o the block is a = F k 1. Sliding block on a horizontal srace coing to rest: x v = a) I a block having initial velocity slides on a rogh horizontal srace and coes it rest, the acceleration o the block is a = μ k g b) Distance traveled by the block beore coing rest is S = 3 μkg

4 c) Tie taken by the block to coe to rest is t =. Motion on a rogh horizontal plane : (a) Plled with a horizontal orce F: (i) body oving with nior velocity F = μ k. (ii) body oving with nior acceleration F = ( μk g + a). (b) Plled with a orce F inclined at an angle with the horizontal and the body oving with nior velocity. μk F = cos + μk sin c) Pshed with a orce F inclined at an angle with the horizontal and the body oving with nior velocity: μk F =. cos μk sin μ k g 3. Block on a rogh inclined plane a) Angle o repose α: It is the angle o inclination o the N inclined plane with the horizontal or which block jst begins to slide down. sin b) I α is the angle o repose μ s = tanα c) The angle o repose is the angle o static riction d) The angle o inclination is () less than (α), the block does not slide down, it is at rest. The orce o riction < s and is cos eqal to = sin [ sin < s] e) I the angle o inclination is [] eqal to [α]. Then the block is in liiting eqilibri. The orce o riction is = s = μ s cos α [ sin = s] ) I the block slides down the inclined plane with nior velocity μ k = tan where is the angle o inclination o the inclined plane. Sliding down the inclined plane: g) I the inclination is aintained at α, the block will eventally slide down with an [ μs μk ] acceleration eqal to a = g 1+ μs h) I α, the block slides down with an acceleration given by a = g [sin - μ k cos] [ sin > s] i) I α, and the block slides down ro the top o the inclined plane. Velocity at the botto o the plane is V = gl(sin μk cos = gh(1 μk cot ) j) In the above case tie o descent is L t = g(sin μ k cos) 4

5 k) The tie taken by a body to slide down on a rogh inclined plane is 'n' ties the tie taken by it to slide down on a sooth inclined plane o sae inclination and length, 1 then coeicient o riction is μ = tan 1 n Moving p the inclined plane: l) I a block is projected p a rogh inclined plane, the acceleration o the block is a = g [sin + μ k cos] ) Force opposing the otion o the block is F = sin + μ k cos n) The distance traveled by the block p the plane beore the velocity becoes zero is S = g(sin + μk cos) o) The tie o ascent is t =. In the above case the block will coe down g(sin +μk cos ) sliding only i α. p) In the above case i tie o decent is n ties the tie o ascent, then n 1 μ = tan n + 1 q) Force needed to be applied parallel to the plane to ove the block p with constant velocity is F = sin + μ k cos r) Force needed to be applied parallel to the plane to ove the block p with an acceleration a is F = sin + μ k cos + a s) I block has a tendency to slide, the orce to be applied on the block parallel and p the plane to prevent the block ro sliding is F = sin - μ s cos 4. Block on a sooth inclined plane a) N = cos N b) Acceleration o sliding block (a = g sin ) sin c) I l is the length o the inclined plane and h is the height. The tie taken to slide down starting ro rest ro the top is cos 1 1 h t = = gsin sin g d) Sliding block takes ore tie to reach the botto than to all reely ro the top o the incline. e) Velocity o the block at the botto o the inclined plane is V = glsin = gh sae as the speed attained i block alls reely ro the top o the inclined plane. ) I a block is projected p the plane with a velocity, the acceleration o the block is a = - g sin g) Distance traveled p the plane beore its velocity becoes zero is S = gsin h) Tie o ascent is t = gsin 5

6 5. When the body oves on a rogh horizontal srace, the orce o riction is μ. I s is the displaceent, the work done against riction = μ s. This work is converted into heat. 6

7 6. Block pressed against a vertical wall : A body o ass '' is pressed against a vertical wall with a horizontal orce 'F'. The noral orce is F. I the coeicient o static riction is μ s, then a) Block will be abot to slide down i μ s F =. b) I μ s F, block will not slide and the rictional orce acting on the block is. c) I μ s F, block will slide and the rictional orce acting on the block will be μ s F A vehicle is oving on a horizontal srace. A block o ass '' is stck on the ront part o the vehicle. The coeicient o riction between the trck and the block is 'μ'. The ini acceleration with which the trck shold travel, so that the body ay not slide down is a = g/ μ. 8. Block in a lorry: a) When a block is lying on the loor o an accelerating lorry, the orce o riction acting on the block is in the direction o acceleration o the lorry. b) Relative to lorry, block experiences a psedo orce a opposite to the acceleration o the lorry (a = acceleration o lorry) c) The axi acceleration o the lorry or which block beings to slide on the loor o the lorry is a = μ s g [ a = μ a = μ g] s s d) I a < μ s g block does not slide and riction orce on the block is = a e) I a μs g block slips or slides on the loor. The acceleration (a) o the block relative to lorry is a 1 = a - μ k 1 a k = a 1 a μk = a 1 a = a μkg ) In the above case, acceleration o the block relative to earth is μ k. Block on Block: 9. Case I: (lower block plled and there is no riction between lower block and the horizontal srace) a) When the lower block is plled pper block is accelerated by the orce o riction acting pon it b) The axi acceleration o the syste o two blocks or the to ove together withot slipping is a = μ s g, where μ s is the coeicient o static riction between the two blocks. c) I a < μ s g blocks ove together and applied orce is F = ( B + )a d) I a < μ s rictional orce between the two blocks = a e) The axi applied orce or which both blocks ove together is F ax = μ s g ( + B ) ) I F > F ax blocks slip relative to each other and have dierent accelerations. The acceleration o the pper block is μ k g and lower block is a = F B + psedo orce F a observer R a F

8 30. Case - II (Upper block plled and there is no riction between lower block and the horizontal srace) a) When the pper block is plled, lower block is F accelerated by the orce o riction acting pon it. b) The axi acceleration o the syste o two blocks B or the to ove together withot slipping is a ax = μ s g (μ s = coeicient o static riction between the two blocks) B c) I a < a ax rictional orce between the two blocks is = M B a d) I a < a ax ' then applied orce on the pper block is F = ( B + ) a e) The axi orce or which both blocks ove together is F ax = μ s g ( + B ) B ) I F>F ax blocks slide relative to each other and hence have dierent accelerations. The accele-ration o the lower block is μ g and the acceleration o the pper block is ( F μkg). 31. When oistre is present between bodies, riction increases. 3. I the etal sraces o ball bearing are not hard, riction will be high. 33. riction is redced by sing alloys or aking the oving parts (alloys have low coeicient o riction) 34. Advantages o riction: i) Sae walking on the loor is possible becase o the riction between the loor and the eet. ii) Nails and screws are driven in the walls or wooden sraces de to riction. iii) help the ingers to hold a drinking water tbler or pen. iv) Vehicles ove on the roads withot sliding de to riction and they can be stopped de to riction. v) The echanical power transission o belt drive is possible de to riction. 35. Disadvantages o riction: i) reslts in the large aont o power loss in engines. ii) De to riction, the wear and tear o the achine increases. iii) De to riction, heat is generated which goes as a waste. 36. Methods o redcing riction: i) between two sraces o contact can be redced by polishing the sraces. ii) A lbricant is a sbstance which ors a thin layer between two sraces in contact and redces the riction. The process o redcing riction is called lbrication. Soap water, two in one oil and grease are the exaples o lbricants. iii) The ree wheels o vehicles like cycles, two wheelers, otor cars, shats o otors, dynaos etc., are provided with ball bearing to redce the riction. iv) Atoobiles and aeroplanes have special constrction i.e. they are strea lined to redce the riction de to air. k B 8

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For more Study Material and Latest Questions related to IIT-JEE visit 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