It is easy to show that if the kinetic coefficient of friction between a block and a ramp is
and this ramp is a
straight line with slope
,
then this block will move along the ramp with constant speed. A natural question to
ask is the following: besides straight lines, are there other shapes of ramps such that
a block will go down the ramp with constant speed? Here we classify all possible
shapes of these ramps, and, surprisingly, we show that the planar ramps can be
parametrized in terms of elementary functions: trigonometric functions, exponential
functions and their inverses. They provide basic examples of curves explicitly
parametrized by arclength. A video explaining the main results in this paper can be
found at
http://youtu.be/iBrvbb0efVk.