me re: my life

Physics, Oh How I've Missed You

I was looking at the snow drifts today, and it reminded me of a ridiculously cool physics proof I learned in high school. So you know how sand in a desert, or snow in a windswept drift, settles into these nice little peaks with smooth angles? Well, it turns out that you can take the angle of that incline (we'll call it theta) and the tangent of that angle is equal to the coefficient of friction of the particles that make up that pile. For all you real world physicists, yes, I realize it's probably much more complicated than this, but bear with me, because I still think its cool. Here's a fun little diagram to help explain!



F = ma

Since once the snow has settled it's not moving, a = 0. So that means that all the forces acting on that one little particle of sand or snow (gravity and friction) have to add up to zero.

mg sin θ = Force of gravity in the direction of the incline.
μ mg cos θ = Force of friction opposing the motion of the particle.

So we already said that mg sin θ must be equal to μ mg cos θ, since our little particle isn't moving. So start cancelling things out and we get: sin θ/cos θ = μ. Well, don't you know that's the same as tan θ = μ. Huh... pretty cool. So I guess that means that if you dribble little piles of sugar on your countertop, it should make the same incline pile every time (assuming your sugar is of even consistency).

posted by Anne @ 11:00 PM