|
|
| Fig. 1 | Fig. 2 |
It is often not understood that even when dealing with static friction, application of less-than-critical sheering forces (that is, forces which do not cause breaking of static friction) creates an actual displacement between an object and the surface it rests on. The amount of movement is typically very small and barely if at all visible (displacement can be large enough to be seen when, for example, the surface is a rubber mat). When the sheering force is let off, static friction becomes a restoring force, returning the objects to its original position respective to the surface. This restoring force can be thought of as spring tension, and in this thinking ought to be proportional to object displacement. This experiment sought to verify the linear F = k x relationship of static frictional forces between various materials at less-than-critical sheering forces. Very precise measurements of displacement were measured using a Michelson-type interferometer. The results showed a definite linear relationship between applied force and displacement of the test object for Styrofoam and particleboard surfaces.
 |
| Fig. 3 |
The first goal achieved was forming the ‘fringing' patterns with the interferometer. The basic setup follows the Michelson interferometer design.
As shown in Fig. 1, the beam emitted by the Laser (while a laser pointer is shown, a HeNe laser was used for actual collection of data) passed through one or two Lenses. The Lenses simply made the laser beam diverge and created a larger beam for viewing. The beam then hit the Beam Splitter, separating into two partial beams. Each partial beam bounced from a mirror back onto the beam splitter so that they overlapped and projected as a spot of light on a viewing surface (in the direction of the sheet of paper in Fig. 1). The Reference Mirror held a fixed position and created a reference beam. The Test Mirror (see also (5) of Fig. 3) was attached to a movable Test Block, and the surface under the block could be changed.
More difficult was developing the apparatus to precisely add and measure sheer force to the Test Mirror. The resulting design is shown in Fig. 3. Two Static Pulleys (1) were attached to a solid base along with a Moveable Pulley (2). A taut Fishing Line (3) passed through the Static Pulleys and terminated on the hooks on the Force Probe (4) and the back of the Test Block (5) with the Test Mirror attached . The Moveable Pulley could then be pushed into the Fishing Line, causing a tension felt equally by both the Force Probe and Test Block (It should be noted that the Test Block and Force Probe were adjusted carefully so that they were directly aligned with the Fishing Line.). In this way, the Pulley system ensured that only the desired vector component of force was applied to the Probe and Block. When everything was secured properly, this system worked remarkably well and tension could be applied and held fairly precisely by hand.
A computer captured data directly from the calibrated Force Probe. To take a data run, the apparatus was first adjusted so that little or no force acted on the Test Mirror and Force Probe. The state (bright or dark) of the central dot (see Fig. 2) was noted, the force was captured and 0 was entered as the fringe number. The Moveable Pulley was then pushed into the Fishing Line until the central dot grew into a ring with its alternate state in the center. The force was again captured and entered as fringe # 1. For example, in Figure 2, the initial central dot is red. If tension were applied to the Test Block, it would grow into a ring with a dark spot in its center. The dark spot becomes the new central dot, and was counted as one fringe when it became the same size as the original bright spot.
This process was repeated for multiple surfaces, and for most runs it was verified that as tension was released the same number of fringes disappeared as had previously appeared. For the final run of a surface, the attempt was made to capture data until holding the Moveable Pulley became too difficult or the static friction bonds were broken and the Test Mirror slid out of position