CE 201 - Statics

1. CE 201 - Statics Chapter 8 – Lecture 1

2. F Ff Fn FRICTION • We used to assume that surface of contact between two bodies are smooth • Reaction is assumed normal to surface of contact • In reality, surfaces are rough

3. Characteristics of Dry Friction What is friction? Friction is a force of resistance acting on a body preventing it from slipping. The friction force is always tangent to the surface at point of contact and its direction is opposite to the possible motion of the body.

4. W P Ff Nn Theory of Friction • Consider block of weight W on a rough surface • Surface of contact of the block is non-rigid or deformable • N is upward to balance W and Ff is to the left to prevent P from moving the block. • Close look at the contacting surfaces

5. a/2 a/2 W P h O F X N Equilibrium • For simplicity, the resultants N and F will be used. • F is tangent to the surface and opposite to P • N is found from the distribution of Nn and is upward to balance W • N acts at a distance X right to W line of action • X is necessary for the tipping effect • Take moment about O WX = Ph  X = Ph / W • The block will be on the verge of tipping if X = a/2

6. a/2 a/2 Impending Motion W P h O Fs X N Impending Motion • As P increase, F will increase till it reaches a maximum value Fs called the limiting static frictional force • Any further increase in P will cause deformation at the points of contact and consequently the block will move. Fs was found to be directly proportional to N Fs = s N Where s is the coefficient of static friction and is dimensionless.

7. a/2 a/2 Impending Motion W P h O Fk X N Motion If P was increased to be greater than Fs, the frictional force slightly drops to Fk called the kinetic frictional force. Since P > Fk , the block will move. Fk was found to be: Fk = k N Where k is the coefficient of kinetic friction and is approximately 25% less than s

8. Characteristics of Dry Friction • Frictional force is tangent to the surface opposite to motion • Maximum Fs is independent of the area of contact • Maximum Fs is greater than maximum Fk • If one body is moving with very low velocity, then Fs = Fk or s = k • When body is about to move, then Fs = s N • When body is moving, then Fk = k N

9. Angle of Friction • If block is stationary Fs s N • If block is on the verge of moving Fs = s N • If block is moving Fk = k N

10. W W Impending Motion Motion P P Fs Fk s k N N Rs Rk At equilibrium, Fs and N combine to have a resultant Rs, the angle of static friction s is:s = tan-1 ( Fs / N) = tan-1 (s N / N) = tan-1sIf the block is in motion, then the angle of kinetic friction :k = tan-1 ( Fk / N) = tan-1 (k N / N) = tan-1kBy comparison, s k Angle of Friction

11. Angle of Response To measure the coefficient of friction experimentally, a block is placed on a plane of different material than the block. • The plane is inclined to the angle s • The block is on the verge of moving • Fs = s N

12. s W s Fs = s N N Angle of Response At equilibrium Fs = W sin s N = W cos s Since Fs = s N W sin s = s ( W cos s ) s = tan-1s s is called the angle of response s = tan s