1. Friction Objectives –Make simple measurements of distance and time –Learn graphing skills and understand graphical relationships –Understand the meaning and use of the slope in a motion diagrams. –Study friction and its affect on acceleration. –Understand Applications of Newton’s 2 nd Law F = m a

2. Friction Forces Frictional forces oppose motion –Usually proportional to the velocity –Dependent upon the normal force F N –Dependent upon the two surfaces through the coefficient of friction (  ) A: Max Normal Force, maximum friction B: Normal Force with surface decreased, friction decreased C: No Normal Force, No Friction A BC F F F FNFN f

3. Coefficient of Friction Depends upon the nature of the two surfaces –Quantified by the coefficient of friction  Does not depend upon the surface area or weight of the sliding object, only on the nature of the surfaces.  is LARGE for things like wood or sand paper  is SMALL for things like plastic or teflon

4. Static and Kinetic Friction In the static region, the frictional force equals the applied force. The frictional force depends upon the coefficient of static friction  s. In the kinetic region, the object begins to move and the frictional force decreases slightly to a constant value dependent upon the coefficient of kinetic friction  k.

5. Smart Pulley System The Smart Pulley allows us to make measurements of displacement (  d) and time (  t). By plotting velocity (  d/  t) of a laboratory cart, acceleration can be experimentally determined as the slope in a motion diagram of velocity versus time (  v/  t).

6. Forces Forces on block mass M (including friction) Normal Force (F N = M g) Gravity (weight) Tension (from hanging mass weight) Friction F f =  F N Forces on hanging mass (m) Gravity (weight) m a = F - F f Tension(M + m) a = m g -  F N  = {mg - (M+m)a}/Mg g ~ 10 m/s 2

7. Constant Acceleration? With constant non-zero acceleration…  Velocity versus Time is linear.  Velocity changes uniformly.  Change in Velocity (  v) over change in time (  t) is average acceleration. Average acceleration =  v/  t

8. Constant Acceleration Motion Displacement Time Velocity Time Slope = acceleration