A Better Free Body Diagram!

One of the items I’ve been talking about here are the physics of skiing and focusing on the basic Newtonian Mechanics of skiing. Of late I’ve taken the approach to talk about basic force and have dabbled in energy a bit.

As I have gone over here, I like to ski fast, so putting on my physics hat I’ve taken to analyzing at how fast one can expect to go on a given slope. Again, I wave my hand and in The Wis-Skier’s Ideal World there is no board (whether one or two) – snow friction or resistive forces and wind resistance is similarly dismissed. Also let us assume we are going to ski down the fall line of a perfect slope that is we do not have to worry about rollers or changes in the pitch. Yes, it sound ridiculous but all of those other considerations are nothing but distractions now.

First an improved free body diagram…

Force Breakdown

There are two main forces under consideration, the force of gravity pulling the skier down to the center of the Earth and the force–normal pushing at the skier in a direction perpendicular to the face of the slope (-20° from straight up). However, the force of Gravity is not in line with the force normal and we can break it down into Force a and Force b which when added together form the Force c — the force of gravity.

Accelerating Force

Notice, Force b points straight down the slope and is unopposed! that means Force b will change the motion of the skier. According to Newton’s laws the 34 Kg.s of force will change the skier’s motion according to the formula F=m*a (note, for the particular the italics indicate vector quantities) and the m – the mass is 100 Kg.s and the Force is 34 Newtons, so we have 34 = 100 * a yielding a = .34 meters/second² or .34 meters per second per second.

Go Speed Skier Go!

I will not get into math to prognosticate how fast this accelerating force will make a skier or a snowboarder go, but I am guessing many of you know how to do that. Interestingly enough, this is not enough slope to make me hit the speeds I have reported in the time it took me to get down the slope and we can discuss that in futher posts!