Friction

Slide 1 : P. K. BHARTI, I.I.T. KHARAGPUR FRICTION 01.07.2010 © 2007-10 P K Bharti, IIT Kharagpur APPLIED FORCE FRICTION LIMITING FRICTION fs, max = msN KINETIC FRICTION fk = mkN

Slide 2 : P K BHARTI, IIT KHARAGPUR Suppose a heavy box is kept on a rough surface. Now, suppose you want to move it. If you apply a force F1 of very small magnitude, you may find the block doesn’t move. As block doesn’t move, it means accln=0. Therefore from Newton’s 1st Law sum of all the forces must be zero. It means a force of magnitude F1 must act towards left to balance force F1 exerted by you. Where does this extra force F1 comes from? Well ! This extra force comes as a result of the roughness of the surface of contact. This additional force is known as frictional force. 2 Box F1 F1

Slide 3 : P K BHARTI, IIT KHARAGPUR Now if you slowly increase your force, you may find the box still remains stationary. It means a frictional force [magnitude = your applied force magnitude] is acting opposite to your applied force. Now, if u go on increasing your applied force, a stage will come when box will just tend to move. Suppose this value of applied force be F. At this stage a friction of magnitude F will act opposite to your applied force F. This frictional force of magnitude F is the maximum magnitude of frictional force. Thus, before this maximum value F of friction, magnitude of friction = magnitude of applied force. Frictional force before starting of the motion has got a special name. It is known as STATIC FRICTION. Now, if u further increase your applied force, the box will start moving. 3

Slide 4 : P K BHARTI, IIT KHARAGPUR When box starts moving, you will find from your experience that the magnitude of friction force is less than maximum frictional force F and remains almost constant. This frictional force which acts during motion is called KINETIC FRICTION. So, from this experiment we observed: BEFORE START OF MOTION : Friction is known as STATIC Friction. Magnitude of static friction = magnitude of applied force. Maximum value of static friction (F here) is known as LIMITING FRICTION. AFTER START OF MOTION: Friction is known as KINETIC friction. Magnitude of kinetic friction < magnitude of limiting friction. Kinetic friction magnitude almost remains constant.

Graph of friction vs. applied force : P K BHARTI, IIT KHARAGPUR Graph of friction vs. applied force From O to A particle remains stationary. Thus in part OA Static friction acts. Here, Static friction = Applied force, therefore angle =45o . Length AB represents maximum friction, i.e., Limiting friction. After A, point start moving thus in this part kinetic friction acts. Length CD represents almost constant kinetic friction in this part. . 5 APPLIED FORCE FRICTION 45o LIMITING FRICTION O A KINETIC FRICTION B C D

Slide 6 : P K BHARTI, IIT KHARAGPUR 6 Static friction fs acts on a body before it starts moving when a force is applied. Kinetic friction fk comes into play after the body starts its motion.

STATIC FRICTION : P K BHARTI, IIT KHARAGPUR STATIC FRICTION 1. The magnitude of the Static Friction fs is given by where ms = a constant known as coefficient of static friction between the body and the surface of contact. It depends upon roughness of the surface. Rough the surface have more ms . & N = Normal force on the object from the surface. 2. STATIC FRICTION MAGNITUDE = MAGNITUDE OF APPLIED FORCE. 3. Limiting Friction = Maximum value of Static Friction Limiting Friction = fs, max = msN. 7 m N Applied force fs mg Rough surface

KINETIC FRICTION : P K BHARTI, IIT KHARAGPUR KINETIC FRICTION The magnitude of the kinetic friction fk is given by fk = µkN where mk = a constant known as coefficient of kinetic friction between the body and the surface of contact. It depends upon roughness of the surface. More rough the surface is, more will be mk . & N = Normal force on the object from the surface. 8 m Body moving on Rough surface fk N mg

Graph of friction vs. applied force [Revised] : P K BHARTI, IIT KHARAGPUR Graph of friction vs. applied force [Revised] From O to A particle remains stationary. Thus in part OA Static friction acts. Here, Static friction = Applied force, therefore angle =45o . Length AB represents maximum friction, i.e., Limiting friction, fs, max = msN . After A, point start moving thus in this part kinetic friction acts. Length CD represents almost constant kinetic friction fk = mkN in this part. . 9 APPLIED FORCE FRICTION 45o LIMITING FRICTION fs, max = msN O A KINETIC FRICTION fk = mkN B C D

SOME IMPORTANT FACTS : P K BHARTI, IIT KHARAGPUR SOME IMPORTANT FACTS The coefficients of friction depend on the nature of the surface. The frictional force is nearly independent of the contact area between the objects. The kinetic friction force is usually less than the maximum static friction force (Limiting friction). 10

Finding the DIRECTION of friction : P K BHARTI, IIT KHARAGPUR Finding the DIRECTION of friction RULE: Only think if the surface were frictionless, then in which direction the body should move. Friction direction will be just to opposite to it. Example 1: Let us find direction of friction force exerted by rough surface on block. Clearly, if surface were assumed frictionless, then block would have moved rightward under the action of force F. Therefore direction of friction will be opposite to this, i.e., friction will act in leftward direction. . 11 F f N mg

Example 2 : P K BHARTI, IIT KHARAGPUR Example 2 Block A Clearly if all surfaces are assumed frictionless, then A will moves rightward under the action of force F. Therefore, friction forces [here two friction forces, 1st from floor and 2nd from block B] direction will be towards left. Block B: Only friction that will act on block B will be exerted by block A. And, from Newton’s 3rd law, this friction will be nothing but f2 in right direction. 12 A B F A f1 from floor f2 from block B B f2 from block A f1 from floor on A f2 from block B on A f2 from block A on B

Finding magnitude of friction : P K BHARTI, IIT KHARAGPUR Finding magnitude of friction 13 Stationary Body [Static friction] fs = magnitude of applied force or Limiting friction, fs, max = msN. Translating Body [Kinetic friction] fk = mkN. We illustrate some examples to find f in next slides.

Slide 14 : P K BHARTI, IIT KHARAGPUR 14 Example 3: Let us find expressions for frictional force in example 1. Solution: Let us draw FBD of block. First we find N. Along vertical direction, we have: N – mg = 0 ? N = mg. Now two cases arises: CASE 1: If Block remains stationary. Here, static friction f = applied force ? f = F. Alternatively : CASE 2. If Block moves forward. Kinetic friction f = mkN = mkmg. F f N mg

Slide 15 : P K BHARTI, IIT KHARAGPUR Example 4: We will find expression for magnitude forces of example 2. [Assume blocks are moving] Solution: We draw FBD of A and B. NOTE: SAME COLOURED FORCES REPRESENT ACTION-REACTION PAIRS OF NEWTON’S 3rd LAW. 15 A f1 f2 B f2 F A B F mBg N1 mAg N2 N2

Slide 16 : P K BHARTI, IIT KHARAGPUR First we find N1 & N2 . Along vertical direction from FBD of A and B we get: N1 -N2 - mAg= 0 & N1 - mBg = 0 . Thus from these two eqns. we get: N1 = (mA+ mB )g & N2 =mBg . Now let the coefficients of kinetic friction between A and floor be m1 & between A and B be m2 . Therefore, f1 = kinetic friction exerted by floor on A ? f1 = m1N1 [Why we are using N1 , why not N2 or N1- N2 etc here ? Because, f1 is the friction from floor, therefore N should be also due to that of floor, i.e., N should be N1] ? f1 = m1(mA+ mB )g And, f1 = kinetic friction exerted by (B on A) or (A on B) ?f2 = m2N2 [Why we are using N2 , why not N1 here ???] ?f2 = m2mBg. NOTE : Please grasp these concepts clearly before moving ahead. 16

Slide 17 : P K BHARTI, IIT KHARAGPUR 17 EXAMPLE 5: A particle of mass m is resting on a horizontal surface. The static and kinetic friction coefficients between block and surface are m1and m2 respectively. Find the magnitude of friction acting on the block. Ans: Zero. Explanation: Idea here is that the block is stationary. Therefore, static friction is acting on the block. As, there is no applied force in the horizontal direction. Therefore, magnitude of friction force = applied force = 0 m

Slide 18 : P K BHARTI, IIT KHARAGPUR Example 6. Solve example 5 again if the block rests on an inclined plane making angle q with horizontal. SOLUTION: Body is resting so static friction is acting. Its direction will certainly upward the incline(why??) We draw FBD of block. Now, we draw our coordinate system . Resolve mg. Along x-axis: mg sinq – f = 0 ? f = mg sin q. [Ans] [Surprise!!!, we did not used any formula for friction, FBD done all]. 18 m y x N f mg mg cosq mg sinq q q

Some discussion on Example 6 : P K BHARTI, IIT KHARAGPUR Some discussion on Example 6 We could also solved this problem as: Along y-axis: N-mg cos q = 0 ? N = mg cos q As friction is static, therefore f = mN ? f = mmg cos q . But correct answer is f = mg sinq. For Limiting friction: f = mN = mmg cos q ...(1) Also from previous part: f = mg sinq …(2) Dividing (1) by (2) we get, tan? = m . This is the process by which we get coefficients of static friction practically. 19

Exercises : P K BHARTI, IIT KHARAGPUR Exercises H. C. Verma (Chapter: Friction) Worked out examples 1 to 8. Page no. 97-99 Try to solve all exercises problems. 20

Exercises : P K BHARTI, IIT KHARAGPUR Exercises Q. A block of mass m is at rest on a rough wedge as shown in figure. What is the force exerted by the wedge on the block? 21 m q

Exercises : P K BHARTI, IIT KHARAGPUR Exercises Q. A particle of mass m is kept on a rough horizontal surface (friction coefficient = µ). A person is trying to pull the particle by applying a horizontal force but the body is not moving. The force by the surface on the particle is F where 22

Slide 23 : P K BHARTI, IIT KHARAGPUR 23 Next class Why (and How) to Join My Classes on Physics? Friday, July 02 2010 8:30 PM (IST)

Slide 24 : P. K. BHARTI, I.I.T. KHARAGPUR FRICTION 01.07.2010 © 2007-10 P K Bharti, IIT Kharagpur APPLIED FORCE FRICTION LIMITING FRICTION fs, max = msN KINETIC FRICTION fk = mkN