ME 141. Lecture 7: Friction

Transcription

1 ME 141 Engineering Mechanic Lecture 7: riction Ahmad Shahedi Shail Lecturer, Dept. of Mechanical Engg, BUET Webite: teacher.buet.ac.bd/hail Courtey: Vector Mechanic for Engineer, Beer and Johnton

2 Introduction In preceding chapter, it wa aumed that urface in contact were either frictionle (urface could move freely with repect to each other) or rough (tangential force prevent relative motion between urface). Actually, no perfectly frictionle urface exit. or two urface in contact, tangential force, called friction force, will develop if one attempt to move one relative to the other. However, the friction force are limited in magnitude and will not prevent motion if ufficiently large force are applied. The ditinction between frictionle and rough i, therefore, a matter of degree. There are two type of friction: dry or Coulomb friction and fluid friction. luid friction applie to lubricated mechanim. The preent dicuion i limited to dry friction between nonlubricated urface.

3 The Law of Dry riction. Coefficient of riction Bloc of weight W placed on horizontal urface. orce acting on bloc are it weight and reaction of urface N. Small horizontal force P applied to bloc. or bloc to remain tationary, in equilibrium, a horizontal component of the urface reaction i required. i a tatic-friction force. A P increae, the tatic-friction force increae a well until it reache a maximum value m. N m urther increae in P caue the bloc to begin to move a drop to a maller inetic-friction force. N

4 The Law of Dry riction. Coefficient of riction Maximum tatic-friction force: N m Kinetic-friction force: N 0.75 Maximum tatic-friction force and ineticfriction force are: - proportional to normal force - dependent on type and condition of contact urface - independent of contact area

5 The Law of Dry riction. Coefficient of riction our ituation can occur when a rigid body i in contact with a horizontal urface: No friction, (P x = 0) No motion, (P x < m ) Motion impending, (P x = m ) Motion, (P x > m )

6 Angle of riction It i ometime convenient to replace normal force N and friction force by their reultant R: No friction No motion Motion impending Motion tan tan N m N N tan tan N N N

7 Angle of riction Conider bloc of weight W reting on board with variable inclination angle q. No friction No motion Motion impending Motion

8 Problem Involving Dry riction All applied force nown Coefficient of tatic friction i nown Determine whether body will remain at ret or lide All applied force nown Coefficient of tatic friction i nown Motion i impending Motion i impending Determine value of coefficient of tatic friction. Determine magnitude or direction of one of the applied force

9 Sample Problem 8.1 SOLUTION: Determine value of friction force and normal reaction force from plane required to maintain equilibrium. Calculate maximum friction force and compare with friction force required for equilibrium. If it i greater, bloc will not lide. A 100 lb force act a hown on a 300 lb bloc placed on an inclined plane. The coefficient of friction between the bloc and plane are = 0.25 and = Determine whether the bloc i in equilibrium and find the value of the friction force. If maximum friction force i le than friction force required for equilibrium, bloc will lide. Calculate inetic-friction force.

10 Sample Problem 8.1 SOLUTION: Determine value of friction force and normal reaction force from plane required to maintain equilibrium. x 100 lb lb 0 y 0 : 80 lb : N lb 0 N 240 lb Calculate maximum friction force and compare with friction force required for equilibrium. If it i greater, bloc will not lide. m N m 240 lb 48 lb 0.25 The bloc will lide down the plane.

11 Sample Problem 8.1 If maximum friction force i le than friction force required for equilibrium, bloc will lide. Calculate inetic-friction force. actual 0.20 N 240 lb actual 48 lb

12 Prob # 8.12 The 20-lb bloc A and the 30-lb bloc B are upported by an incline that i held in the poition hown. Knowing that the coefficient of tatic friction i 0.15 between all urface of contact, determine the value of θ for which motion i impending.

13 Prob # 8.19 Wire i being drawn at a contant rate from a pool by applying a vertical force P to the wire a hown. The pool and the wire wrapped on the pool have a combined weight of 20 lb. Knowing that the coefficient of friction at both A and B are μ = 0.40 and μ = 0.30, determine the required magnitude of the force P.

14 Wedge Wedge - imple machine ued to raie heavy load. orce required to lift bloc i ignificantly le than bloc weight. riction prevent wedge from liding out. Want to find minimum force P to raie bloc. Bloc a free-body N W or R 1 x y 0 : N 0 : N R2 W 0 N Wedge a free-body N N or x y 2 P R 0 : 2 P 0 0 : N N R3 co6 in 6 co6 in 6 0 0

15 Prob # 8.50 The elevation of the end of the teel beam upported by a concrete floor i adjuted by mean of the teel wedge E and. The bae plate CD ha been welded to the lower flange of the beam, and the end reaction of the beam i nown to be 100 N. The coefficient of tatic friction i 0.30 between two teel urface and 0.60 between teel and concrete. If the horizontal motion of the beam i prevented by the force Q, determine (a) the force P required to raie the beam, (b) the correponding force Q

16 Prob # 8.62 A 5 ο wedge i to be forced under a 1400-lb machine bae at A. Knowing that the coefficient of tatic friction at all urface i 0.20, (a) determine the force P required to move the wedge, (b) indicate whether the machine bae will move.

17 Prob # 8.65 A 15 ο wedge i forced under a 50-g pipe a hown. Knowing that the coefficient of tatic friction at both urface of the wedge i 0.20, determine the larget coefficient of tatic friction between the pipe and the vertical wall for which lipping will occur at A