Static and Kinetic Friction

FIGURE 3.12

It is common experience that it takes a certain minimum force to start an object sliding over a surface. Once the sliding has started, the force needed to keep it moving at constant velocity is lower. In 1748 Leonhard Euler distinguished be­tween static friction and kinetic friction. In Fig. 3.11 a force is applied to a block on a horizontal surface. The force of static friction opposes the tendency of the block to move relative to the surface. If the block does not move, the force of static friction f _s must be exactly equal to the applied force F _app. As the applied force is increased, f _s also increases and stays equal to F _app, as shown in Fig. 3.12, but only until a critical value, f _s(max), is reached. For a larger applied force, the block starts to slide and is then subject to kinetic friction. As sliding commences, the frictional force rapidly falls at low speeds. At higher speeds, the force of kinetic friction f _k either stays constant or decreases gradually as the speed increases. In many cases the friction at low speeds is characterized by a combination of static and kinetic friction. This produces a jerky "stick-slip" motion that can often be heard in creaking doors or planks, tire squeal, and squeaky wheels.

The fact that the frictional force is proportional to the load allows us to define two coefficients of friction. The force of kinetic friction f _k may be related to the normal force between the sliding surfaces by the equation

f _k= μ _k N (3.15)

where μ _k, the coefficient of kinetic friction, is a dimensionless number. Notice that Eq.6.1 is not a vector equation. As was mentioned above, the force of static friction does not have a fixed value. However, its maximum value is simply related to the normal force:

f _(max)= μ _s N or f _s ≤ μ _s N (3.16)

where μ _s is the coefficient of static friction. Make a careful note of the difference in form between Eqs. 3.15 and 3.16. In general, μ _s > μ _k, but there are exceptions.

The above relations are not exactly true. The coefficients are not really con­stants for any pair of surfaces; they depend on roughness, cleanliness (grease or oxide films), temperature, humidity, and so on.

CHAPTER 4

Work and Mechanical Energy

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