Vibrations - Friction

Preface		Friction
Preface		We are familiar with the idea that it is easier to move over a smooth surface than a rough one. When one examines closely even the smoothest looking surface one finds that on a molecular scale it is very rough. This means that the intermolecular forces that are averaged out in the bulk of the solid can exert powerful influences on the molecules in neighbouring surfaces. These forces contribute to the phenomenon of friction. It is as if each free surface has a set of tiny flexible hooks attached to them that will grab similar hooks on nearby surfaces if they have a chance. Once the surfaces are close enough the hooks interlock and the surfaces resist sliding motion. A block on a slope resists slipping down if the slope is not too steep. At some stage if the slope is increased the pull of gravity overcomes the frictional effects of the interlocking hooks and the block breaks free and slides down the hill. However as it slides frictional forces are still operating albeit with less strength. Once in motion the hooks find it harder to interlock with each other. Not all surfaces have the same kind of molecular hooks. Those between snow on wood are weaker which is why snow is slippery. This characteristic of friction, responsible for the surface forces retarding sliding once it is initiated and varying with the speed of relative motion of the surfaces, is very general. The magnitude of the force pressing the surfaces together determines the magnitude of the "sliding" frictional force when the relative motion is non-zero which is less than the friction force that resists the onset of relative motion. This latter force is the "static" friction in the plane of the surfaces. It determines the value of the friction when there is no relative motion between the surfaces. This dependence of friction on relative motion can give rise to intermittent motion in a host of phenomena that experience friction in one form other. A simple example illustrates the general features of friction induced intermittent motion. Consider a block at rest on a stationary conveyor belt but attached to a fixed wall by a stretched horizontal spring. Since the block is at rest the elastic force in the spring tending to pull the block towards the wall must be less than the force due to static friction between the block and the conveyor belt. Suppose the conveyor belt is slowly set in motion in a direction that carries the block away from the fixed wall. Then initially the block will not move relative to the belt since the friction force continues to increase to compensate for the increasing tension in the spring as it extends. (It is as if the frictional hooks that bind the base of the block to the belt extend to keep the two in contact). However at some stage the force in the spring exceeds the maximum frictional force that the surfaces can exert on each other and the block starts to slip relative to the moving belt. However the friction is still present but slightly less than before. Relative to the belt the block now moves under the combined force of the spring and sliding friction. The sliding friction retards its motion and it will eventually slow down enough for the static friction to bring it to rest relative to the belt. The whole cycle can now repeat with the block intermittently sticking and slipping under the combined effects of friction and spring force. This kind of motion is sometimes referred to as a "slip-stick" or relaxation vibration.