Tag Archives: coefficient of friction

A Furry Friction Funny

Q. Two cats are sitting on a roof.  Which one slides off first?

A. The one with the smaller mu!

Of course this joke assumes that the cat in question is totally complacent to slide off the roof, making no effort to maintain his position.  Strange cat.

Anyway, “mu” is pronounced like “mew“, as in the sound made by a cat.  It is a Greek letter, usually represented by the following symbol: µ.  Mu must be the favorite Greek letter of mathematicians and scientists; it pops up in fields as diverse as computer science, number theory, physics, orbital mechanics, chemistry, and pharmacology.  In this joke, µ is meant to represent the coefficient of friction, about which more in a moment.

What is friction?  To greatly oversimplify things, friction is a force that resists relative motion between two surfaces, or between a surface and a fluid.  When you experience resistance while pushing a refrigerator across a tile floor, you’re working against friction.  When you rub your hands together to warm them up, friction is your friend.  Friction is an even greater friend to the skydiver; when she opens her parachute, fluid friction against the atmosphere reduces her speed from a spine-shattering 120 miles per hour to a totally survivable 10 miles per hour.)

Here’s an interesting side note about friction; scientists used to think that the friction was caused by microscopic grooves and bumps that tended to lock surfaces together, requiring extra force to break their grip and get the surfaces sliding past each other.  Now, scientists think that friction is caused by chemical bonds forming between the atoms in the adjacent surfaces.  That’s a strange thought; merely by touching something, you bond with it.  In a way, you become a part of it and it becomes a part of you.  Deep, man.  Deep.

But I digress.  Mathematically, the friction between two surfaces – such as, say, a roof and a cat’s butt – can be expressed using the following formula:

Ff = µ * m * g * cosθ

Ff represents friction, which is measured in units of force called newtons.  The letter m represents the mass of the cat in kilograms, g is the acceleration due to gravity (On Earth, that’s about 9.8 m/s/s) and cosθ is cosine of angle theta, where theta (another Greek letter strongly favored by the academic elite) is the angle that the roof makes with the ground.

Just to have some numbers to play with, let us assume that the cat’s mass is 3 kilograms, giving her an Earthly weight of about 6.6 pounds.  Now let us assume that the roof has a pitch of, say, 30º.  To find the friction between the cat’s derriere and the rooftop, we would substitute and multiply:

Ff = µ * m * g * cosθ

Ff = µ * 3 kg * 9.8 m/s/s * cos(30º)

Ff = µ * 25.5 newtons

I have not yet specified the roof-feline coefficient of friction, because frankly, I don’t know what it is.  My search of the literature has been fruitless.  For the sake of argument, let’s assign a completely arbitrary value of 0.6 to µ, and see what that gets us.

Ff = 0.6 * 25.5 newtons

Ff = 15.3 newtons (about equal to 3.4 pounds of force)

So there you go; there are 15.3 newtons of friction preventing the cat from sliding down the roof.  Whether the cat actually slides or not depends on whether the gravitational component pulling the cat down the roof is greater than the friction holding the cat in place.

But let us assume that the coefficient of friction between the cat and the hot tin roof were smaller, perhaps because the cat had just finished grooming and her fur was unusually even and smooth.  Instead of 0.6, let’s say the coefficient of friction were only 0.3, giving the cat a static friction of only about 7.7 newtons.  Naturally, with a smaller coefficient of friction – a smaller mu – the cat would be less able to hold its position on the roof and more likely to start sliding downward.

So there you have it: the cat with the smaller mu is the one that starts sliding first.  Next time somebody tells you this joke, they’ll be met with less friction, because you’ll understand it purr-fectly.

Okay, I’ll go now.