_{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 dsimanek@lhup.edu.

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 to know.

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 = μ_s N,

where μ_s is called the “static friction coefficient.” If there is sliding, the force due to friction is given by f = μ_k N, where μ_k is the “kinetic friction coefficient.” Friction coefficients are nearly constant for a given interface. For most materials, μ_k is slightly smaller than μ_s. 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?

Make: 169