Friday, November 29, 2013

Snow, snow, snow!

This Thanksgiving break was marked by a lot of snow for those of us who stayed around. Most of the days were marked by tiny white flakes drifting peacefully to earth. This got me to wondering, how long does it take a snowflake to fall to earth?

I found online that the average mass of a snowflake is 3x10-6 kg, its terminal velocity of about 1.5 m/s, and that the density of ice at 0oC is 916.7 kg/m3. Because the snowflake reaches a terminal velocity, this problem has to be broken into two parts: one where the snowflake is constantly accelerating and a second where velocity is constant.
In the first part I am ignoring air resistance and therefore the acceleration is 9.8 m/s2 downwards. Now all we have to do is solve for the time and distance it falls.
 Vf=Vo+at 1.5 m/s=0+(9.8 m/s2)t t=.153 s vf2=vo2+2ax (1.5 m/s)2=0+2(9.8 m/s2)x x=.115 m

I also learned that snow generally falls from nimbostratus clouds, which generally form at about 3000 meters. This gives us all the information we need to find out how long it takes a snowflake to fall.
 t=x/v x=3000m-.115m=2999.885m t=(2999.885 m)/(1.5 m/s) t=1999.9 s Total time=t1+t2=2000 s

This means that it takes a little over half an hour for snowflakes to make it to the ground. So when we look outside and see the first flakes of snow it hasn't just begun snowing, its just finally making it to us.