Tiêu đề 02. FRICTION ( 31 - 54 ).pdf ✅

NISHITH Multimedia India (Pvt.) Ltd., 3 1 JEE - ADVANCED - VOL - II CURRENT ELECTRICITY NISHITH Multimedia India (Pvt.) Ltd., FRICTION SYNOPSIS Take a plane sheet of paper over a smooth table and place a book over it. Now pull the sheet slowly. What do you find? Book also moves along with the sheet, let us see the motion of book, initial velocity of book is zero but it moves with same velocity, means its veloc- ity has changed in horizontal direction means book has horizontal acceleration. Which indicates some horizontal force must have acted on the book. What is that force?. That force is friction. If I ask you whether friction opposes motion of book your answer in this case is no, as friction is the force causing motion of book. But when we carefully see, we find that when sheet tends to move, some horizontal force acted on sheet to oppose the motion of sheet but at the same time reaction of that horizontal force in opposite di- rection acted on book to move it. Now one thing you can observe that friction is the force that opposes the relative motion be- tween the bodies. F friction friction Friction is the force that acts at the contact points to oppose the relative motion between the sur- faces in a direction parallel to surface. It always acts as action reaction pair between surfaces. When a force is applied on a body and the body tends to move (but does not move), then the frictional force is called force of static friction. When the body is in motion, then the frictional force is called force of kinetic friction. Generally, the force of kinetic friction is slightly less than force of maximum static friction, for a given normal reaction. The force of friction comes into action only when there is a relative motion or there is a tendency of relative motion between the two contact surfaces. STATIC FRICTION: The force of static friction, which develops in a direction opposite to the applied force, is a self adjusting force. Consider a block of weight W = Mg placed on a rough horizontal surface. It is found that (a) When F = 0, then f s = 0. (b) When F  0 and small, then f s = F till f s becomes equal to some (f s ) max. . Once f s = (f s ) max. , then f s does not increase further. It is found that (f s ) max. = μs N (μs = coefficient of static friction) F N Mg fs (f s ) max. is also called the limiting friction. This μs is a dimensionless constant which depends on the nature of surfaces and the cohesive or adhesive forces. It does not depend of the area of surfaces in contact. The force of static friction can be expressed as : f s < μsN. Hence, μs = max. limiting friction [( ) ] normal reaction ( ) s f N f s is a self-adjusting force in the sense that when F < (f s ) max. then force of friction f s = F. But once F > (f s ) max. , then force of friction f s = (f s ) max. = μsN. The force of static friction is proportional to the normal force that keeps the two surfaces in contact with each other. It is almost independent of the area of contact between the two surfaces. The static frictional force is given by, f s  μsN, where μs is the static coefficient of friction. The “less than equal to” sign in the above equation represents adjusting nature of the force of static friction. The equality sign in the equation holds only when it has its maximum value. In cases where there is no relative motion be- tween the surfaces in contact, friction is known as static friction. FRICTION
Jr Chemistry E/M FRICTION 3 2 NISHITH Multimedia India (Pvt.) Ltd., JEE - ADVANCED - VOL - II NISHITH Multimedia India (Pvt.) Ltd., Static friction is an adjustable force which can take any value from zero to certain maximum values. Under a given case the maximum possible value of this static friction is known as limiting static friction. 0  f s  Limiting static friction. (Liming static friction)  (Normal reaction between the surfaces in contacts) L.S.F.  sN where s is a constant, characteristic of the surfaces in contact thus, 0  f s  sN Let us consider a case to understand it. A block of mass 2 kg lies over a rough horizontal surface. The coefficient of static friction between the block and surface is 0.5 s  N  Mg 0  f s  sN 10N Now a horizontal force say F is applied on block. F is gradually increased from zero Friction for F = 0 f = 0 for F = 5 N f = 5 N for F = 9.99 N f = 9.99 N See friction is adjustable for F = 10 N f = 10 N when F > 10 N relative motion starts and friction becomes kinetic. Kinetic Friction: When the applied force F exceeds the limiting friction, i.e. (f s ) max. , then the body begins to move. During motion the force of friction decreases slightly. The frictional force during motion is called the force of kinetic friction (fk ). It can be expressed as fk = μkN, where μk is called the coefficient of kinetic friction. μk is a dimensionless constant. Usually μk < μs . Also, μk is independent of the relative velocities of the two objects. When we try to slide an object on a surface, then the force of friction that develops as a function of applied force is shown in figure. Till F < (f s ) max. , the force of friction f s = F. But as F exceeds (f s ) max. (= μsN), the body begins to move and force of friction decreases to f k = μk N and remains so thereafter. The force of kinetic friction is proportional to the normal force, which presses the two surfaces together. f k = μkN, where μk is the coefficient of kinetic friction. It is almost independent of the surface area of contact. It is almost independent of the speed of sliding provided that the resulting heat does not alter the condition of the surface. The graph shown in the figure shows the variation of the force of friction with the applied force. ( )fs max Relative Motion Rest f O F 45° The variation of the friction force with the applied force. When the block remains at rest the force of static friction f s balances the applied force F until it reaches the maximum value (f s ) max . When the block starts moving, it is acted upon by the force of kinetic friction. The coefficient of kinetic friction is less than the coefficient of static friction μk < μs , for a given pair of surfaces. Whenever there is relative motion between the surfaces in contact, friction is known as kinetic friction (f ) k which is a constant force such that, k k f   N, where k is known as the coefficient of kinetic friction between the surface. In most of the cases k  s but if in a problem only  is given, s  k   Let us consider the same case as discussed ear- lier for 0.48 k  for F 10N f k  kN  9.6N Friction suddenly decreases from 10 N to 9.6 N just as motion starts for LSF F  f f fs fk = 45o F L.S.F. s f reduces from s f to k f suddenly, plot of friction against applied force is as shown above Some Important Points Regarding Friction Because limiting force is higher than kinetic
NISHITH Multimedia India (Pvt.) Ltd., 3 3 JEE - ADVANCED - VOL - II CURRENT ELECTRICITY NISHITH Multimedia India (Pvt.) Ltd., FRICTION friction, hence we require more force to start a motion than to maintain it against friction. When a body rolls on a surface, the resistance offered by the surface is called rolling friction. In rolling the surfaces in contact do not rub each other. The velocity of the point of contact with respect to surface remains zero all the time, although the centre of the body moves forward. Rolling friction is negligible as compared to static or kinetic friction, i.e. μR < μk < μs If the normal force remains constant, then the force of friction does not depend on the area of surfaces in contact and their relative velocity. If lubricants are used the force of friction generally decreases. If a rubber wheel is rolling on a road, then lesser is the deformation in it, lesser is the friction. Friction is a non-conservative force, i.e., work done against friction is a path dependent. In its presence, mechanical energy is not conserved. Due to frictional forces, heat is produced. Frictional forces are essential in many walks of life. For example, the walking process can only take place because there is friction between the shoes and ground. In the process of walking, in order to set forward, you must press your foot backward on the ground. A friction force tends to oppose this movement of the foot and the ground pushes you forward which allows you to walk. When there is no friction, as on ice or polished granite or oily surface, walking is difficult.When a person is pedaling a bicycle and the bicycle is moving towards east, then direction of frictional force on the front wheel is towards west and on the rear wheel is towards east. However, if paddling is stopped, both wheels move themselves and so experience a force of friction is backward direction. Angle Of Friction (): Mathematically, the angle of friction () may be defined as the angle between the normal reaction N and the resultant of the friction force f and the normal reaction.  N mg F f s Thus,tan = f/N Since f = μN, therefore tan  = μ mg (sin  – μ cos ) > FP > mg (sin  + μ cos ) LEVEL -V SINGLE ANSWER QUESTIONS 1. A block of mass m slides down an inclined plane of inclination with uniform speed. The coefficient of friction between the block and plane is  . The contact force between the block and the plane is (A) mg (B) 2 mgsin 1    (C) mgsin  (D) 2 2 (mgsin ) ( mg cos )     2. Two men weighing 100 kg and 50 kg run a 100 m race. The coefficient of friction between their shoes and ground is 0.5. They run with maximum possible acceleration. Who will win the race. (A) 100 kg man (B)50 kg man (C) Both will finish at same time (D) Data given is insufficient to answer question 3. A force F is applied on a block of mass m as shown in the figure. What will be the maximum value of F such that the block will not move. The coefficient of friction between block and floor is    cons t tan  m  F (A) sin mg F    (B) cos sin mg F       (C) cos mg  (D) sin cos mg    
Jr Chemistry E/M FRICTION 3 4 NISHITH Multimedia India (Pvt.) Ltd., JEE - ADVANCED - VOL - II NISHITH Multimedia India (Pvt.) Ltd., 4. The minimum acceleration (from the given option) that must be imparted to the cart in the figure so that the block A will not fall (given  = 0.2 is the coefficient of friction between the surfaces of block and cart) is given by  m A (A)25m/s2 (B) 15 m/s2 (C) 5.4 m/s2 (D) 50 m/s2 5. Two blocks of mass 20 kg is connected as shown in the figure then friction on the block exerted by horizontal surface is (system is released from rest) 20kg 20kg  = 0.6 (A) 140 N (B) 120 N (C) 130 N (D) 100N 6. A horizontal force of 10 N is necessary to just hold a block stationary against a wall the coefficient of friction between the block and the wall is 0.2. The weight of the block is 10 N (A) 2 N (B) 20 N (C) 50 N (D) 100 N 7. A cart of mass M has a block of mass m in contact with it is shown in figure. The coeffi- cient of friction between the block and car is  . The correct options are M m a (A) minimum acceleration of car, so that block m does not fall is g  (B) Minimum acceleration is g (C) Normal force between block and car is ma (D) The magnitude of friction force between block and cart is greater than mg. 8. A body of mass M is kept on a rough hori- zontal surface (friction coefficient   ). A person is trying to pull the body by applying a horizontal force but the body is not mov- ing. The force by the surface on the body is F where : A) F mg  B) 2 Mg F Mg   1  C) F Mg   D) 2 Mg F Mg   1  9. A body of mass 2 kg is held at rest against a rough vertical wall by passing a horizontal (nomal) force of 45 N. Coefficient of friction between wall and the block is equal to 0.5. Now a horizontal force of 15 N (tangential to wall) is also applied on the block. Then the block will : A) Move horizontally with acceleration of 2 5 / m s B) Start to move with an acceleration of magni- tude 2 1.25 / m s C) Remain stationary D) Start to move horizontally with acceleration greater than 2 5 / m s 10. Two blocks A & B attached to each other by a mass-less spring , are kept on a rough horizontal surface   0.1. A constant force F N  200 is applied on block B horizon tally as shown below. If at some instant the acceleration of 10 kg mass is 2 12 / , m s then the acceleration of 20 kg mass is : A B 10kg 20kg F A) 2 2 2.5 / 15.5 / m s or m s B) 2 2 4 / 10 / m s or m s C) 2 2 3.6 / 4.1 / m s or m s D) 2 2 1.2 / 1.3 / m s or m s