Saturday, 11 April 2015

Skiers Weight

Intuitively you know that something changes as the hill get steeper.  You know that the force of gravity pulling you down the hill is greater but you may not know that your weight is also changing.  The sketch to the left shows with arrows the direction of the various forces of a skier going straight down a 28.5 degree slope.  The vertical arrow is the skier's weight plus equipment on level ground caused by gravity.  This is the weight that is divided up into two other forces, one that pulls you down the hill and the other that holds you on the ground.  You will notice that the one force f1 pulling the skier down hill is in the same direction that the skier is moving and the other f2 is at 90 degrees or perpendicular to the skier's direction. 
On the sketch I have drawn an orange triangle, using arrows superimposed on two of the directional arrows, fw and f2. There is a third arrow using a doted line for f1.  On my original drawing fw is drawn to scale at 2 inches representing me and my skis, boots poles, clothes etc. at 200 pounds.  I am being kind to myself.  The other 2 arrows are drawn both parallel and perpendicular to the hill slope.  F2 starts at the top end of fw and f1 ends at the bottom of f1. Their lengths represent the force pulling me down this hill, f1, and how much I weigh if I could put a scale under my feet.  F2 measured 1.77 inches, the equivalent force of 177 pound, my weight that I will feel on such a slope. The other f1, 0.99 inches or 99 pounds is the force pulling me down the hill.  If you tied a rope around me and tried to hold me still, that's the force you would have to exert to hold me stopped.  Rough estimates.
One rule is that your weight_plus due to gravity, fw is always straight down and the same value. The second rule is that the other two forces change with the slope(always following the rule of parallel and perpendicular to the slope).  The little triangle changes shape due to the change of slope.  The triangle can rotate around the top end of the fw.  As the slope flattens out f1 gets less  and f2 gets longer and approaches your full weight fw  .  And visa versa.
This is a static picture but the dynamics are different when you are moving and change direction or stoping. Acceleration in its many forms kicks in in its many forms and messes up the whole picture.  
Going down a steep hill is a quick way to loose weight for a very short time.
If you are  handy with a scientific calculator, f1=fw x sin(28.5) and f2 = fw cos(28.5).  You can substitute your own weight values and slope angles.  At 45 degrees slope, f1 and f2 are the same, fw x 0.707    .  (I know f1, f2 and fw are vectors.)