Friction

Everyone knows it’s hard to push a heavy object on a rough surface.  Most of the resistance comes from friction, a force between object and surface that resists motion (for kinetic friction) or attempted motion (for static friction).  The standard model describing the amount of friction posits that

fk = ?kN  (for kinetic friction), and

fs ? ?sN  (for static friction)

where N is the normal force between object and surface and ?k,s are unitless constants that depend on the surface / object interaction.  This site has a nice introduction to friction, including a section focusing on the coefficient of friction between car tires and road.  I suggest you read it now, since you won’t have much time later while you’re skidding across a rain- or ice-slick road.  In particular – just to pick an example – while you’re driving back to Amherst from South Hadley over the Notch on a wet day when the temperature is just above freezing in the lower parts of the Valley.

Although different tires behave differently, typical static coefficients of friction vary dramatically with road conditions (see table).   For normal tires, the maximum braking force drops by almost a factor of 2 in rain, by another factor of 2 on snow, and by yet another factor of 2 on ice.  Note that the stopping distance is inversely proportional to braking force; check your constant acceleration formulas to see why.

There is a whole discipline devoted to deducing vehicle speeds from skidmark length, primarily for use in court cases; this requires knowledge of the kinetic coefficient of friction for a skidding tire. If you are unlucky enough to be in a rollover accident, apparently the police may drag your car around on its roof to measure the kinetic coefficient of friction between roof and road.

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