TOYS, TRICKS, AND TEASERS Friction. There’s the rub. By Donald E. Simanek
» Illusions and paradoxes never cease to fascinate.
When we perceive something that seems to behave in an unexpected
or impossible way, we realize that it’s something new to our experience and want to figure out what’s going on. Visual illusions are the
obvious example, but there are also tricks of physics and mechanics
that seem paradoxical when first experienced. They challenge us to
“puzzle out” what makes them work and are often the basis of magic
tricks, toys, and illusions, or, at least, instructive physics demonstrations. We’ll explore some of these tricks that may not be familiar to
readers, with an emphasis on those that you can do or make yourself.
I’ll include explanations, as well as web links to more detailed treatments. Readers are invited to contribute their own favorites to me at
Let us all give thanks for friction. Without it, our feet
would slide uncontrollably when we try to walk, cars
would spin their wheels and go nowhere, mountains
would subside, and weather patterns would be
vastly altered. Nearly everything in our world
would function differently without friction.
Friction has the unfortunate side effect of dissipating kinetic energy, converting it into heat, which
contributes to the inefficiency of machinery. Yet,
without friction, it’s hard to imagine how we could
even manufacture machinery. Some friction is a
good and useful thing. A lot of it is too much.
How many of us can claim we understand friction?
The details of intermolecular forces and surface
films are complex and won’t be dealt with here. But
in everyday life there are just a few basics you need
A Little Friction Physics
When bodies are touching, they experience contact
forces at their interface. These forces obey Newton’s
third law: If body A exerts a force on body B, then B
exerts an equal-sized but oppositely directed force
on A. The contact force acting on a body has two
components: one perpendicular to the interface
(called the “normal” force, symbol “N”) and one
tangential to the interface (called the “force due
to friction,” symbol “f”). If there’s no sliding at the
surfaces, the force due to friction can be anywhere
from zero in size to a maximum value f = μs N,
where μs is called the “static friction coefficient.” If
there is sliding, the force due to friction is given by
f = μk N, where μk is the “kinetic friction coefficient.”
Friction coefficients are nearly constant for a given
interface. For most materials, μk is slightly smaller
than μs. Both are usually less than 1, but for quite
“sticky” surfaces, can exceed 1.
If there’s no sliding of the bodies at their surfaces,
the size and direction of the force acting on a
body due to friction is just equal and opposite to
the tangential component of the vector sum of all
other forces acting on the body. If there is sliding,
the force due to friction is in a direction opposite
to the direction of the sliding (opposing the sliding
motion). In short, the forces due to friction adjust
in size and direction, responding to other forces so
as to prevent sliding. But they have limits. When the
limit is exceeded, sliding occurs, and the force due
to friction acts in a direction opposing the sliding.
The Oscillating Beam Machine
This is an old physics homework problem. A heavy
uniform bar or beam rests on top of two identical
rollers that are continuously turning in opposite
directions, as shown on the following pages. There’s
friction between the rollers and the bar, and the
sliding friction coefficient is constant, independent
of the relative speed of the surfaces. Find the motion
of the bar. What happens if the rotation directions
of both wheels are reversed?