Sliding Friction

Laboratory Exercise no. 9

"Laboratory Manual for General Physics", Bernard D.Kern. Part One: Mechanics, Heat and Sound, Revised Printing, 1996 Copyright C 1968, 1971, 1996 by Bernard Donald Kern


Discussion

An object which is made of wood, when sliding on another object of wood, has its motion retarded by a frictional force. It is generally true that the frictional force is

Consider a wooden block which is being pulled with constant velocity by a horizontal force F applied along a horizontal plane; i.e., with zero acceleration, a = 0. The vertical reaction force on the block is N. Then by Newton's Second Law,

  equation19

  equation25

  equation29

where tex2html_wrap_inline67 is a proportionality constant called the coefficient of sliding friction. In this particular example, the reaction force N is equal and opposite to the weight W of the block, and

  equation34

The coefficient may be obtained directly by measuring the two forces.

If the plane is inclined, as in our case, see the diagran above, then a component F of the weight W acts to move the block and the other component tex2html_wrap_inline69 presses the block to the plane. Since the block does not move perpendicularly to the plane (the acceleration is zero), tex2html_wrap_inline71 . If the block is made to slide with constant velocity by the adjustment of the angle of inclination:

  equation39

  equation42

  equation45

We see the interesting result that the coefficient of friction can be measured in terms of the angle, and with no dependence upon the size and mass of the block itself.

The static frictional forces are always larger than the kinetic frictional forces and not so reproducible, experimentally. We can use Eqn.4, but assume that the block is at rest. As angle tex2html_wrap_inline73 is increased, an angle will be reached at which the block suddenly starts to slip. At this point the component, tex2html_wrap_inline75 , has become greater than the static frictional force, tex2html_wrap_inline77 , and it is difficult to determine by how much. However, by use of the concept of an inequality, we can rewrite Eqn.6 using the "equal to or greater than" and "less than or equal" symbols tex2html_wrap_inline79 and tex2html_wrap_inline81 :

  equation52

  equation55

This gives a measured upper limit limit to the coeficient of static friction, tex2html_wrap_inline83


Run Virtual Java Experiment "Sliding Frction"

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